Advanced 2-dimensional spectra processing.

Author: Miroslav Morhac

This class contains advanced spectra processing functions.

One-dimensional background estimation functions
Two-dimensional background estimation functions
One-dimensional smoothing functions
Two-dimensional smoothing functions
One-dimensional deconvolution functions
Two-dimensional deconvolution functions
One-dimensional peak search functions
Two-dimensional peak search functions

The algorithms in this class have been published in the following references:

M.Morhac et al.: Background elimination methods for multidimensional coincidence gamma-ray spectra. Nuclear Instruments and Methods in Physics Research A 401 (1997) 113-132.
M.Morhac et al.: Efficient one- and two-dimensional Gold deconvolution and its application to gamma-ray spectra decomposition. Nuclear Instruments and Methods in Physics Research A 401 (1997) 385-408.
M.Morhac et al.: Identification of peaks in multidimensional coincidence gamma-ray spectra. Nuclear Instruments and Methods in Research Physics A 443(2000), 108-125.

These NIM papers are also available as doc or ps files from:

See also the online documentation and tutorials.

All the figures in this page were prepared using the DaqProVis system, Data Acquisition, Processing and Visualization system, developed at the Institute of Physics, Slovak Academy of Sciences, Bratislava, Slovakia.

Definition at line 18 of file TSpectrum2.h.

Public Types
enum	{ kBackIncreasingWindow =0, kBackDecreasingWindow =1, kBackSuccessiveFiltering =0, kBackOneStepFiltering =1 }

Public Types inherited from TObject
enum	{ kIsOnHeap = 0x01000000, kNotDeleted = 0x02000000, kZombie = 0x04000000, kBitMask = 0x00ffffff }

enum	{ kSingleKey = BIT(0), kOverwrite = BIT(1), kWriteDelete = BIT(2) }

enum	EStatusBits { kCanDelete = BIT(0), kMustCleanup = BIT(3), kObjInCanvas = BIT(3), kIsReferenced = BIT(4), kHasUUID = BIT(5), kCannotPick = BIT(6), kNoContextMenu = BIT(8), kInvalidObject = BIT(13) }

Public Member Functions
	TSpectrum2 ()
	Constructor. More...

	TSpectrum2 (Int_t maxpositions, Double_t resolution=1)

virtual	~TSpectrum2 ()
	Destructor. More...

virtual TH1 *	Background (const TH1 hist, Int_t niter=20, Option_t option="")
	This function calculates the background spectrum in the input histogram h. More...

const char *	Background (Double_t **spectrum, Int_t ssizex, Int_t ssizey, Int_t numberIterationsX, Int_t numberIterationsY, Int_t direction, Int_t filterType)
	This function calculates background spectrum from source spectrum. More...

const char *	Deconvolution (Double_t source, Double_t resp, Int_t ssizex, Int_t ssizey, Int_t numberIterations, Int_t numberRepetitions, Double_t boost)
	This function calculates deconvolution from source spectrum according to response spectrum The result is placed in the matrix pointed by source pointer. More...

TH1 *	GetHistogram () const

Int_t	GetNPeaks () const

Double_t *	GetPositionX () const

Double_t *	GetPositionY () const

virtual void	Print (Option_t *option="") const
	Print the array of positions. More...

virtual Int_t	Search (const TH1 hist, Double_t sigma=2, Option_t option="", Double_t threshold=0.05)
	This function searches for peaks in source spectrum in hin The number of found peaks and their positions are written into the members fNpeaks and fPositionX. More...

Int_t	SearchHighRes (Double_t source, Double_t dest, Int_t ssizex, Int_t ssizey, Double_t sigma, Double_t threshold, Bool_t backgroundRemove, Int_t deconIterations, Bool_t markov, Int_t averWindow)
	This function searches for peaks in source spectrum It is based on deconvolution method. More...

void	SetResolution (Double_t resolution=1)
	NOT USED resolution: determines resolution of the neighboring peaks default value is 1 correspond to 3 sigma distance between peaks. More...

const char *	SmoothMarkov (Double_t **source, Int_t ssizex, Int_t ssizey, Int_t averWindow)
	This function calculates smoothed spectrum from source spectrum based on Markov chain method. More...

Public Member Functions inherited from TNamed
	TNamed ()

	TNamed (const char name, const char title)

	TNamed (const TString &name, const TString &title)

	TNamed (const TNamed &named)
	TNamed copy ctor. More...

virtual	~TNamed ()

virtual void	Clear (Option_t *option="")
	Set name and title to empty strings (""). More...

virtual TObject *	Clone (const char *newname="") const
	Make a clone of an object using the Streamer facility. More...

virtual Int_t	Compare (const TObject *obj) const
	Compare two TNamed objects. More...

virtual void	Copy (TObject &named) const
	Copy this to obj. More...

virtual void	FillBuffer (char *&buffer)
	Encode TNamed into output buffer. More...

virtual const char *	GetName () const
	Returns name of object. More...

virtual const char *	GetTitle () const
	Returns title of object. More...

virtual ULong_t	Hash () const
	Return hash value for this object. More...

virtual Bool_t	IsSortable () const

virtual void	ls (Option_t *option="") const
	List TNamed name and title. More...

TNamed &	operator= (const TNamed &rhs)
	TNamed assignment operator. More...

virtual void	SetName (const char *name)
	Set the name of the TNamed. More...

virtual void	SetNameTitle (const char name, const char title)
	Set all the TNamed parameters (name and title). More...

virtual void	SetTitle (const char *title="")
	Set the title of the TNamed. More...

virtual Int_t	Sizeof () const
	Return size of the TNamed part of the TObject. More...

Public Member Functions inherited from TObject
	TObject ()
	TObject constructor. More...

	TObject (const TObject &object)
	TObject copy ctor. More...

virtual	~TObject ()
	TObject destructor. More...

void	AbstractMethod (const char *method) const
	Use this method to implement an "abstract" method that you don't want to leave purely abstract. More...

virtual void	AppendPad (Option_t *option="")
	Append graphics object to current pad. More...

virtual void	Browse (TBrowser *b)
	Browse object. May be overridden for another default action. More...

virtual const char *	ClassName () const
	Returns name of class to which the object belongs. More...

virtual void	Delete (Option_t *option="")
	Delete this object. More...

virtual Int_t	DistancetoPrimitive (Int_t px, Int_t py)
	Computes distance from point (px,py) to the object. More...

virtual void	Draw (Option_t *option="")
	Default Draw method for all objects. More...

virtual void	DrawClass () const
	Draw class inheritance tree of the class to which this object belongs. More...

virtual TObject *	DrawClone (Option_t *option="") const
	Draw a clone of this object in the current selected pad for instance with: `gROOT->SetSelectedPad(gPad)`. More...

virtual void	Dump () const
	Dump contents of object on stdout. More...

virtual void	Error (const char method, const char msgfmt,...) const
	Issue error message. More...

virtual void	Execute (const char method, const char params, Int_t *error=0)
	Execute method on this object with the given parameter string, e.g. More...

virtual void	Execute (TMethod method, TObjArray params, Int_t *error=0)
	Execute method on this object with parameters stored in the TObjArray. More...

virtual void	ExecuteEvent (Int_t event, Int_t px, Int_t py)
	Execute action corresponding to an event at (px,py). More...

virtual void	Fatal (const char method, const char msgfmt,...) const
	Issue fatal error message. More...

virtual TObject *	FindObject (const char *name) const
	Must be redefined in derived classes. More...

virtual TObject *	FindObject (const TObject *obj) const
	Must be redefined in derived classes. More...

virtual Option_t *	GetDrawOption () const
	Get option used by the graphics system to draw this object. More...

virtual const char *	GetIconName () const
	Returns mime type name of object. More...

virtual char *	GetObjectInfo (Int_t px, Int_t py) const
	Returns string containing info about the object at position (px,py). More...

virtual Option_t *	GetOption () const

virtual UInt_t	GetUniqueID () const
	Return the unique object id. More...

virtual Bool_t	HandleTimer (TTimer *timer)
	Execute action in response of a timer timing out. More...

virtual void	Info (const char method, const char msgfmt,...) const
	Issue info message. More...

virtual Bool_t	InheritsFrom (const char *classname) const
	Returns kTRUE if object inherits from class "classname". More...

virtual Bool_t	InheritsFrom (const TClass *cl) const
	Returns kTRUE if object inherits from TClass cl. More...

virtual void	Inspect () const
	Dump contents of this object in a graphics canvas. More...

void	InvertBit (UInt_t f)

virtual Bool_t	IsEqual (const TObject *obj) const
	Default equal comparison (objects are equal if they have the same address in memory). More...

virtual Bool_t	IsFolder () const
	Returns kTRUE in case object contains browsable objects (like containers or lists of other objects). More...

Bool_t	IsOnHeap () const

Bool_t	IsZombie () const

void	MayNotUse (const char *method) const
	Use this method to signal that a method (defined in a base class) may not be called in a derived class (in principle against good design since a child class should not provide less functionality than its parent, however, sometimes it is necessary). More...

virtual Bool_t	Notify ()
	This method must be overridden to handle object notification. More...

void	Obsolete (const char method, const char asOfVers, const char *removedFromVers) const
	Use this method to declare a method obsolete. More...

void	operator delete (void *ptr)
	Operator delete. More...

void	operator delete[] (void *ptr)
	Operator delete []. More...

void *	operator new (size_t sz)

void *	operator new (size_t sz, void *vp)

void *	operator new[] (size_t sz)

void *	operator new[] (size_t sz, void *vp)

TObject &	operator= (const TObject &rhs)
	TObject assignment operator. More...

virtual void	Paint (Option_t *option="")
	This method must be overridden if a class wants to paint itself. More...

virtual void	Pop ()
	Pop on object drawn in a pad to the top of the display list. More...

virtual Int_t	Read (const char *name)
	Read contents of object with specified name from the current directory. More...

virtual void	RecursiveRemove (TObject *obj)
	Recursively remove this object from a list. More...

void	ResetBit (UInt_t f)

virtual void	SaveAs (const char filename="", Option_t option="") const
	Save this object in the file specified by filename. More...

virtual void	SavePrimitive (std::ostream &out, Option_t *option="")
	Save a primitive as a C++ statement(s) on output stream "out". More...

void	SetBit (UInt_t f, Bool_t set)
	Set or unset the user status bits as specified in f. More...

void	SetBit (UInt_t f)

virtual void	SetDrawOption (Option_t *option="")
	Set drawing option for object. More...

virtual void	SetUniqueID (UInt_t uid)
	Set the unique object id. More...

virtual void	SysError (const char method, const char msgfmt,...) const
	Issue system error message. More...

Bool_t	TestBit (UInt_t f) const

Int_t	TestBits (UInt_t f) const

virtual void	UseCurrentStyle ()
	Set current style settings in this object This function is called when either TCanvas::UseCurrentStyle or TROOT::ForceStyle have been invoked. More...

virtual void	Warning (const char method, const char msgfmt,...) const
	Issue warning message. More...

virtual Int_t	Write (const char *name=0, Int_t option=0, Int_t bufsize=0)
	Write this object to the current directory. More...

virtual Int_t	Write (const char *name=0, Int_t option=0, Int_t bufsize=0) const
	Write this object to the current directory. More...

Static Public Member Functions
static void	SetAverageWindow (Int_t w=3)
	static function: Set average window of searched peaks see TSpectrum2::SearchHighRes More...

static void	SetDeconIterations (Int_t n=3)
	static function: Set max number of decon iterations in deconvolution operation see TSpectrum2::SearchHighRes More...

static TH1 *	StaticBackground (const TH1 hist, Int_t niter=20, Option_t option="")
	static function (called by TH1), interface to TSpectrum2::Background More...

static Int_t	StaticSearch (const TH1 hist, Double_t sigma=2, Option_t option="goff", Double_t threshold=0.05)
	static function (called by TH1), interface to TSpectrum2::Search More...

Static Public Member Functions inherited from TObject
static Long_t	GetDtorOnly ()
	Return destructor only flag. More...

static Bool_t	GetObjectStat ()
	Get status of object stat flag. More...

static void	SetDtorOnly (void *obj)
	Set destructor only flag. More...

static void	SetObjectStat (Bool_t stat)
	Turn on/off tracking of objects in the TObjectTable. More...

Protected Attributes
TH1 *	fHistogram
	resulting histogram More...

Int_t	fMaxPeaks
	Maximum number of peaks to be found. More...

Int_t	fNPeaks
	number of peaks found More...

Double_t *	fPosition
	[fNPeaks] array of current peak positions More...

Double_t *	fPositionX
	[fNPeaks] X position of peaks More...

Double_t *	fPositionY
	[fNPeaks] Y position of peaks More...

Double_t	fResolution
	NOT USED resolution of the neighboring peaks More...

Protected Attributes inherited from TNamed
TString	fName

TString	fTitle

Static Protected Attributes
static Int_t	fgAverageWindow = 3
	Average window of searched peaks. More...

static Int_t	fgIterations = 3
	Maximum number of decon iterations (default=3) More...

Additional Inherited Members
Protected Member Functions inherited from TObject
virtual void	DoError (int level, const char location, const char fmt, va_list va) const
	Interface to ErrorHandler (protected). More...

void	MakeZombie ()

#include <TSpectrum2.h>

Inheritance diagram for TSpectrum2:

[legend]

Member Enumeration Documentation

◆ anonymous enum

anonymous enum

Enumerator
kBackIncreasingWindow
kBackDecreasingWindow
kBackSuccessiveFiltering
kBackOneStepFiltering

Definition at line 31 of file TSpectrum2.h.

Constructor & Destructor Documentation

◆ TSpectrum2() [1/2]

TSpectrum2::TSpectrum2 ( )

Constructor.

Definition at line 57 of file TSpectrum2.cxx.

◆ TSpectrum2() [2/2]

TSpectrum2::TSpectrum2	(	Int_t	maxpositions,
		Double_t	resolution = `1`
	)

maxpositions: maximum number of peaks
resolution: NOT USED determines resolution of the neighbouring peaks default value is 1 correspond to 3 sigma distance between peaks. Higher values allow higher resolution (smaller distance between peaks. May be set later through SetResolution.

Definition at line 77 of file TSpectrum2.cxx.

◆ ~TSpectrum2()

TSpectrum2::~TSpectrum2 ( )

virtual

Destructor.

Definition at line 92 of file TSpectrum2.cxx.

Member Function Documentation

◆ Background() [1/2]

TH1 * TSpectrum2::Background	(	const TH1 *	h,
		Int_t	number_of_iterations = `20`,
		Option_t *	option = `""`
	)

virtual

This function calculates the background spectrum in the input histogram h.

The background is returned as a histogram.

Function parameters:

h: input 2-d histogram
numberIterations, (default value = 20) Increasing numberIterations make the result smoother and lower.
option: may contain one of the following options
- to set the direction parameter "BackIncreasingWindow". By default the direction is BackDecreasingWindow
- filterOrder-order of clipping filter. Possible values:
  - "BackOrder2" (default)
  - "BackOrder4"
  - "BackOrder6"
  - "BackOrder8"
- "nosmoothing"- if selected, the background is not smoothed By default the background is smoothed.
- smoothWindow-width of smoothing window. Possible values:
  - "BackSmoothing3" (default)
  - "BackSmoothing5"
  - "BackSmoothing7"
  - "BackSmoothing9"
  - "BackSmoothing11"
  - "BackSmoothing13"
  - "BackSmoothing15"
- "Compton" if selected the estimation of Compton edge will be included.
- "same" : if this option is specified, the resulting background histogram is superimposed on the picture in the current pad.

NOTE that the background is only evaluated in the current range of h. ie, if h has a bin range (set via h->GetXaxis()->SetRange(binmin,binmax), the returned histogram will be created with the same number of bins as the input histogram h, but only bins from binmin to binmax will be filled with the estimated background.

Definition at line 155 of file TSpectrum2.cxx.

◆ Background() [2/2]

const char * TSpectrum2::Background	(	Double_t **	spectrum,
		Int_t	ssizex,
		Int_t	ssizey,
		Int_t	numberIterationsX,
		Int_t	numberIterationsY,
		Int_t	direction,
		Int_t	filterType
	)

This function calculates background spectrum from source spectrum.

The result is placed to the array pointed by spectrum pointer.

Function parameters:

spectrum-pointer to the array of source spectrum
ssizex-x length of spectrum
ssizey-y length of spectrum
numberIterationsX-maximal x width of clipping window
numberIterationsY-maximal y width of clipping window for details we refer to manual
direction- direction of change of clipping window
- possible values=kBackIncreasingWindow kBackDecreasingWindow
filterType-determines the algorithm of the filtering
- possible values=kBackSuccessiveFiltering kBackOneStepFiltering

Background estimation

Goal: Separation of useful information (peaks) from useless information (background)

method is based on Sensitive Nonlinear Iterative Peak (SNIP) clipping algorithm [1]
there exist two algorithms for the estimation of new value in the channel \( i_1,i_2\)

Algorithm based on Successive Comparisons:

It is an extension of one-dimensional SNIP algorithm to another dimension. For details we refer to [2].

Algorithm based on One Step Filtering:

New value in the estimated channel is calculated as:

\[ a = \nu_{p-1}(i_1,i_2)\]

\[ b = \frac{\nu_{p-1}(i_1-p,i_2-p) - 2\nu_{p-1}(i_1-p,i_2) + \nu_{p-1}(i_1-p,i_2+p) - 2\nu_{p-1}(i_1,i_2-p)}{4} + \]

\[ \frac{-2\nu_{p-1}(i_1,i_2+p) + \nu_{p-1}(i_1+p,i_2-p) - 2\nu_{p-1}(i_1+p,i_2) + \nu_{p-1}(i_1+p,i_2+p)}{4} \]

\[ \nu_{p-1}(i_1,i_2) = min(a,b)\]

where p = 1, 2, ..., number_of_iterations.

References:

[1] C. G Ryan et al.: SNIP, a statistics-sensitive background treatment for the quantitative analysis of PIXE spectra in geoscience applications. NIM, B34 (1988), 396-402.

[2] M. Morhac;, J. Kliman, V. Matouoek, M. Veselsky, I. Turzo.: Background elimination methods for multidimensional gamma-ray spectra. NIM, A401 (1997) 113-132.

Example 1 - script Back_gamma64.c

Fig. 1 Original two-dimensional gamma-gamma-ray spectrum

Fig. 2 Background estimated from data from Fig. 1 using decreasing clipping window with widths 4, 4 and algorithm based on successive comparisons. The estimate includes not only continuously changing background but also one-dimensional ridges.

Fig. 3 Resulting peaks after subtraction of the estimated background (Fig. 2) from original two-dimensional gamma-gamma-ray spectrum (Fig. 1).

Script:

Example to illustrate the background estimator (class TSpectrum). To execute this example, do:

root > .x Back_gamma64.C

#include <TSpectrum>
void Back_gamma64() {
   Int_t i, j;
   Double_t nbinsx = 64;
   Double_t nbinsy = 64;
   Double_t xmin = 0;
   Double_t xmax = (Double_t)nbinsx;
   Double_t ymin = 0;
   Double_t ymax = (Double_t)nbinsy;
   Double_t ** source = new Double_t*[nbinsx];
   for (i=0;i<nbinsx;i++)
      source[i]=new Double_t[nbinsy];
   TH2F *back = new TH2F("back","Background estimation",nbinsx,xmin,xmax,nbinsy,ymin,ymax);
   TFile *f = new TFile("spectra2/TSpectrum2.root");
   back=(TH2F*) f->Get("back1;1");
   TCanvas *Background = new TCanvas("Background","Estimation of background with increasing window",10,10,1000,700);
   TSpectrum *s = new TSpectrum();
   for (i = 0; i < nbinsx; i++){
      for (j = 0; j < nbinsy; j++){
         source[i][j] = back->GetBinContent(i + 1,j + 1);
      }
   }
   s->Background(source,nbinsx,nbinsy,4,4,kBackDecreasingWindow,kBackSuccessiveFiltering);
   for (i = 0; i < nbinsx; i++){
      for (j = 0; j < nbinsy; j++)
         back->SetBinContent(i + 1,j + 1, source[i][j]);
   }
   back->Draw("SURF");
}

Example 2- script Back_gamma256.c

Fig. 4 Original two-dimensional gamma-gamma-ray spectrum 256x256 channels

Fig. 5 Peaks after subtraction of the estimated background (increasing clipping window with widths 8, 8 and algorithm based on successive comparisons) from original two-dimensional gamma-gamma-ray spectrum (Fig. 4).

Script:

To execute this example, do

root > .x Back_gamma256.C

#include <TSpectrum>
void Back_gamma256() {
   Int_t i, j;
   Double_t nbinsx = 64;
   Double_t nbinsy = 64;
   Double_t xmin = 0;
   Double_t xmax = (Double_t)nbinsx;
   Double_t ymin = 0;
   Double_t ymax = (Double_t)nbinsy;
   Double_t** source = new Double_t*[nbinsx];
   for (i=0;i<nbinsx;i++)
      source[i]=new Double_t[nbinsy];
   TH2F *back = new TH2F("back","Background estimation",nbinsx,xmin,xmax,nbinsy,ymin,ymax);
   TFile *f = new TFile("spectra2/TSpectrum2.root");
   back=(TH2F*) f->Get("back2;1");
   TCanvas *Background = new TCanvas("Background","Estimation of background with increasing window",10,10,1000,700);
   TSpectrum *s = new TSpectrum();
   for (i = 0; i < nbinsx; i++){
      for (j = 0; j < nbinsy; j++){
         source[i][j] = back->GetBinContent(i + 1,j + 1);
      }
   }
   s->Background(source,nbinsx,nbinsy,8,8,kBackIncreasingWindow,kBackSuccessiveFiltering);
   for (i = 0; i < nbinsx; i++){
      for (j = 0; j < nbinsy; j++)
         back->SetBinContent(i + 1,j + 1, source[i][j]);
   }
   back->Draw("SURF");
}

Example 3- script Back_synt256.c

Fig. 6 Original two-dimensional synthetic spectrum 256x256 channels

Fig. 7 Peaks after subtraction of the estimated background (increasing clipping window with widths 8, 8 and algorithm based on successive comparisons) from original two-dimensional gamma-gamma-ray spectrum (Fig. 6). One can observe artefacts (ridges) around the peaks due to the employed algorithm.

Fig. 8 Peaks after subtraction of the estimated background (increasing clipping window with widths 8, 8 and algorithm based on one step filtering) from original two-dimensional gamma-gamma-ray spectrum (Fig. 6). The artefacts from the above given Fig. 7 disappeared.

Script:

Example to illustrate the background estimator (class TSpectrum). To execute this example, do

root > .x Back_synt256.C

#include <TSpectrum>
void Back_synt256() {
   Int_t i, j;
   Double_t nbinsx = 64;
   Double_t nbinsy = 64;
   Double_t xmin = 0;
   Double_t xmax = (Double_t)nbinsx;
   Double_t ymin = 0;
   Double_t ymax = (Double_t)nbinsy;
   Double_t** source = new Double_t*[nbinsx];
   for (i=0;i<nbinsx;i++)
      source[i]=new Double_t[nbinsy];
   TH2F *back = new TH2F("back","Background estimation",nbinsx,xmin,xmax,nbinsy,ymin,ymax);
   TFile *f = new TFile("spectra2/TSpectrum2.root");
   back=(TH2F*) f->Get("back3;1");
   TCanvas *Background = new TCanvas("Background","Estimation of background with increasing window",10,10,1000,700);
   TSpectrum *s = new TSpectrum();
   for (i = 0; i < nbinsx; i++){
      for (j = 0; j < nbinsy; j++){
         source[i][j] = back->GetBinContent(i + 1,j + 1);
      }
   }
   s->Background(source,nbinsx,nbinsy,8,8,
                 kBackIncreasingWindow,kBackSuccessiveFiltering);//kBackOneStepFiltering
   for (i = 0; i < nbinsx; i++){
      for (j = 0; j < nbinsy; j++)
         back->SetBinContent(i + 1,j + 1, source[i][j]);
   }
   back->Draw("SURF");
}

Definition at line 483 of file TSpectrum2.cxx.

◆ Deconvolution()

const char * TSpectrum2::Deconvolution	(	Double_t **	source,
		Double_t **	resp,
		Int_t	ssizex,
		Int_t	ssizey,
		Int_t	numberIterations,
		Int_t	numberRepetitions,
		Double_t	boost
	)

This function calculates deconvolution from source spectrum according to response spectrum The result is placed in the matrix pointed by source pointer.

Function parameters:

source-pointer to the matrix of source spectrum
resp-pointer to the matrix of response spectrum
ssizex-x length of source and response spectra
ssizey-y length of source and response spectra
numberIterations, for details we refer to manual
numberRepetitions, for details we refer to manual
boost, boosting factor, for details we refer to manual

Deconvolution

Goal: Improvement of the resolution in spectra, decomposition of multiplets

Mathematical formulation of the 2-dimensional convolution system is

\[ y(i_1,i_2) = \sum_{k_1=0}^{N_1-1} \sum_{k_2=0}^{N_2-1} h(i_1-k_1,i_2-k_2)x(k_1,k_2) \]

\[ i_1 = 0,1,2, ... ,N_1-1, i_2 = 0,1,2, ... ,N_2-1 \]

where h(i,j) is the impulse response function, x, y are input and output matrices, respectively, \( N_1, N_2\) are the lengths of x and h matrices

let us assume that we know the response and the output matrices (spectra) of the above given system.
the deconvolution represents solution of the overdetermined system of linear equations, i.e., the calculation of the matrix x.
from numerical stability point of view the operation of deconvolution is extremely critical (ill-posed problem) as well as time consuming operation.
the Gold deconvolution algorithm proves to work very well even for 2-dimensional systems. Generalisation of the algorithm for 2-dimensional systems was presented in [1], [2].
for Gold deconvolution algorithm as well as for boosted deconvolution algorithm we refer also to TSpectrum

References:

[1] M. Morhac;, J. Kliman, V. Matouoek, M. Veselsky, I. Turzo.: Efficient one- and two-dimensional Gold deconvolution and its application to gamma-ray spectra decomposition. NIM, A401 (1997) 385-408.

[2] Morhac; M., Matouoek V., Kliman J., Efficient algorithm of multidimensional deconvolution and its application to nuclear data processing, Digital Signal Processing 13 (2003) 144.

Example 5 - script Decon.c

response function (usually peak) should be shifted to the beginning of the coordinate system (see Fig. 13)

Fig. 13 2-dimensional response spectrum

Fig. 14 2-dimensional gamma-gamma-ray input spectrum (before deconvolution)

Fig. 15 Spectrum from Fig. 14 after deconvolution (1000 iterations)

Script:

Example to illustrate the Gold deconvolution (class TSpectrum2). To execute this example, do

root > .x Decon.C

#include <TSpectrum2>
void Decon() {
   Int_t i, j;
   Double_t nbinsx = 256;
   Double_t nbinsy = 256;
   Double_t xmin = 0;
   Double_t xmax = (Double_t)nbinsx;
   Double_t ymin = 0;
   Double_t ymax = (Double_t)nbinsy;
   Double_t** source = new Double_t*[nbinsx];
   for (i=0;i<nbinsx;i++)
      source[i]=new Double_t[nbinsy];
   TH2F *decon = new TH2F("decon","Gold deconvolution",nbinsx,xmin,xmax,nbinsy,ymin,ymax);
   TFile *f = new TFile("spectra2/TSpectrum2.root");
   decon=(TH2F*) f->Get("decon1;1");
   Double_t** response = new Double_t*[nbinsx];
   for (i=0;i<nbinsx;i++)
      response[i]=new Double_t[nbinsy];
   TH2F *resp = new TH2F("resp","Response matrix",nbinsx,xmin,xmax,nbinsy,ymin,ymax);
   resp=(TH2F*) f->Get("resp1;1");
   TCanvas *Deconvol = new TCanvas("Deconvolution","Gold deconvolution",10,10,1000,700);
   TSpectrum *s = new TSpectrum();
   for (i = 0; i < nbinsx; i++){
      for (j = 0; j < nbinsy; j++){
         source[i][j] = decon->GetBinContent(i + 1,j + 1);
      }
   }
   for (i = 0; i < nbinsx; i++){
      for (j = 0; j < nbinsy; j++){
         response[i][j] = resp->GetBinContent(i + 1,j + 1);
      }
   }
   s->Deconvolution(source,response,nbinsx,nbinsy,1000,1,1);
   for (i = 0; i < nbinsx; i++){
      for (j = 0; j < nbinsy; j++)
         decon->SetBinContent(i + 1,j + 1, source[i][j]);
   }
   decon->Draw("SURF");
}

Example 6 - script Decon2.c

Fig. 16 Response spectrum

Fig. 17 Original synthetic input spectrum (before deconvolution). It is composed of 17 peaks. 5 peaks are overlapping in the outlined multiplet and two peaks in doublet.

Fig. 18 Spectrum from Fig. 17 after deconvolution (1000 iterations). Resolution is improved but the peaks in multiplet remained unresolved.

Script:

Example to illustrate the Gold deconvolution (class TSpectrum2). To execute this example, do

root > .x Decon2.C

#include <TSpectrum2>
void Decon2() {
   Int_t i, j;
   Double_t nbinsx = 64;
   Double_t nbinsy = 64;
   Double_t xmin = 0;
   Double_t xmax = (Double_t)nbinsx;
   Double_t ymin = 0;
   Double_t ymax = (Double_t)nbinsy;
   Double_t** source = new Double_t*[nbinsx];
   for (i=0;i<nbinsx;i++)
      source[i]=new Double_t[nbinsy];
   TH2F *decon = new TH2F("decon","Gold deconvolution",nbinsx,xmin,xmax,nbinsy,ymin,ymax);
   TFile *f = new TFile("spectra2/TSpectrum2.root");
   decon=(TH2F*) f->Get("decon2;1");
   Double_t** response = new Double_t*[nbinsx];
   for (i=0;i<nbinsx;i++)
      response[i]=new Double_t[nbinsy];
   TH2F *resp = new TH2F("resp","Response matrix",nbinsx,xmin,xmax,nbinsy,ymin,ymax);
   resp=(TH2F*) f->Get("resp2;1");
   TCanvas *Deconvol = new TCanvas("Deconvolution","Gold deconvolution",10,10,1000,700);
   TSpectrum *s = new TSpectrum();
   for (i = 0; i < nbinsx; i++){
      for (j = 0; j < nbinsy; j++){
         source[i][j] = decon->GetBinContent(i + 1,j + 1);
      }
   }
   for (i = 0; i < nbinsx; i++){
      for (j = 0; j < nbinsy; j++){
         response[i][j] = resp->GetBinContent(i + 1,j + 1);
      }
   }
   s->Deconvolution(source,response,nbinsx,nbinsy,1000,1,1);
   for (i = 0; i < nbinsx; i++){
      for (j = 0; j < nbinsy; j++)
         decon->SetBinContent(i + 1,j + 1, source[i][j]);
   }
   decon->Draw("SURF");
}

Example 7 - script Decon2HR.c

Fig. 19 Spectrum from Fig. 17 after boosted deconvolution (50 iterations repeated 20 times, boosting coefficient was 1.2). All the peaks in multiplet as well as in doublet are completely decomposed.

Script:

Example to illustrate boosted Gold deconvolution (class TSpectrum2). To execute this example, do

root > .x Decon2HR.C

#include <TSpectrum2>
void Decon2HR() {
   Int_t i, j;
   Double_t nbinsx = 64;
   Double_t nbinsy = 64;
   Double_t xmin = 0;
   Double_t xmax = (Double_t)nbinsx;
   Double_t ymin = 0;
   Double_t ymax = (Double_t)nbinsy;
   Double_t** source = new Double_t*[nbinsx];
   for (i=0;i<nbinsx;i++)
      source[i]=new Double_t[nbinsy];
   TH2F *decon = new TH2F("decon","Boosted Gold deconvolution",nbinsx,xmin,xmax,nbinsy,ymin,ymax);
   TFile *f = new TFile("spectra2/TSpectrum2.root");
   decon=(TH2F*) f->Get("decon2;1");
   Double_t** response = new Double_t*[nbinsx];
   for (i=0;i<nbinsx;i++)
      response[i]=new Double_t[nbinsy];
   TH2F *resp = new TH2F("resp","Response matrix",nbinsx,xmin,xmax,nbinsy,ymin,ymax);
   resp=(TH2F*) f->Get("resp2;1");
   TCanvas *Deconvol = new TCanvas("Deconvolution","Gold deconvolution",10,10,1000,700);
   TSpectrum *s = new TSpectrum();
   for (i = 0; i < nbinsx; i++){
      for (j = 0; j < nbinsy; j++){
         source[i][j] = decon->GetBinContent(i + 1,j + 1);
      }
   }
   for (i = 0; i < nbinsx; i++){
      for (j = 0; j < nbinsy; j++){
         response[i][j] = resp->GetBinContent(i + 1,j + 1);
      }
   }
   s->Deconvolution(source,response,nbinsx,nbinsy,1000,1,1);
   for (i = 0; i < nbinsx; i++){
      for (j = 0; j < nbinsy; j++)
         dec   on->SetBinContent(i + 1,j + 1, source[i][j]);
   }
   decon->Draw("SURF");
}

Definition at line 1134 of file TSpectrum2.cxx.

◆ GetHistogram()

TH1* TSpectrum2::GetHistogram ( ) const

inline

Definition at line 42 of file TSpectrum2.h.

◆ GetNPeaks()

Int_t TSpectrum2::GetNPeaks ( ) const

inline

Definition at line 43 of file TSpectrum2.h.

◆ GetPositionX()

Double_t* TSpectrum2::GetPositionX ( ) const

inline

Definition at line 44 of file TSpectrum2.h.

◆ GetPositionY()

Double_t* TSpectrum2::GetPositionY ( ) const

inline

Definition at line 45 of file TSpectrum2.h.

◆ Print()

void TSpectrum2::Print ( Option_t * option = "" ) const

virtual

Print the array of positions.

Reimplemented from TNamed.

Definition at line 166 of file TSpectrum2.cxx.

◆ Search()

Int_t TSpectrum2::Search	(	const TH1 *	hin,
		Double_t	sigma = `2`,
		Option_t *	option = `""`,
		Double_t	threshold = `0.05`
	)

virtual

This function searches for peaks in source spectrum in hin The number of found peaks and their positions are written into the members fNpeaks and fPositionX.

The search is performed in the current histogram range.

Function parameters:

hin: pointer to the histogram of source spectrum
sigma: sigma of searched peaks, for details we refer to manual
threshold: (default=0.05) peaks with amplitude less than threshold*highest_peak are discarded. 0<threshold<1

By default, the background is removed before deconvolution. Specify the option "nobackground" to not remove the background.

By default the "Markov" chain algorithm is used. Specify the option "noMarkov" to disable this algorithm Note that by default the source spectrum is replaced by a new spectrum

By default a polymarker object is created and added to the list of functions of the histogram. The histogram is drawn with the specified option and the polymarker object drawn on top of the histogram. The polymarker coordinates correspond to the npeaks peaks found in the histogram. A pointer to the polymarker object can be retrieved later via:
TList *functions = hin->GetListOfFunctions();
TPolyMarker *pm = (TPolyMarker*)functions->FindObject("TPolyMarker")
Specify the option "goff" to disable the storage and drawing of the polymarker.

Definition at line 206 of file TSpectrum2.cxx.

◆ SearchHighRes()

Int_t TSpectrum2::SearchHighRes	(	Double_t **	source,
		Double_t **	dest,
		Int_t	ssizex,
		Int_t	ssizey,
		Double_t	sigma,
		Double_t	threshold,
		Bool_t	backgroundRemove,
		Int_t	deconIterations,
		Bool_t	markov,
		Int_t	averWindow
	)

This function searches for peaks in source spectrum It is based on deconvolution method.

First the background is removed (if desired), then Markov spectrum is calculated (if desired), then the response function is generated according to given sigma and deconvolution is carried out.

Function parameters:

source-pointer to the matrix of source spectrum
dest-pointer to the matrix of resulting deconvolved spectrum
ssizex-x length of source spectrum
ssizey-y length of source spectrum
sigma-sigma of searched peaks, for details we refer to manual
threshold-threshold value in % for selected peaks, peaks with amplitude less than threshold*highest_peak/100 are ignored, see manual
backgroundRemove-logical variable, set if the removal of background before deconvolution is desired
deconIterations-number of iterations in deconvolution operation
markov-logical variable, if it is true, first the source spectrum is replaced by new spectrum calculated using Markov chains method.
averWindow-averaging window of searched peaks, for details we refer to manual (applies only for Markov method)

Peaks searching

Goal: to identify automatically the peaks in spectrum with the presence of the continuous background, one-fold coincidences (ridges) and statistical fluctuations - noise.

The common problems connected with correct peak identification in two-dimensional coincidence spectra are

non-sensitivity to noise, i.e., only statistically relevant peaks should be identified
non-sensitivity of the algorithm to continuous background
non-sensitivity to one-fold coincidences (coincidences peak - background in both dimensions) and their crossings
ability to identify peaks close to the edges of the spectrum region. Usually peak finders fail to detect them
resolution, decomposition of doublets and multiplets. The algorithm should be able to recognise close positioned peaks.
ability to identify peaks with different sigma

References:

[1] M.A. Mariscotti: A method for identification of peaks in the presence of background and its application to spectrum analysis. NIM 50 (1967), 309-320.

[2] M. Morhac;, J. Kliman, V. Matouoek, M. Veselsky, I. Turzo.:Identification of peaks in multidimensional coincidence gamma-ray spectra. NIM, A443 (2000) 108-125.

[3] Z.K. Silagadze, A new algorithm for automatic photopeak searches. NIM A 376 (1996), 451.

Examples of peak searching method

SearchHighRes function provides users with the possibility to vary the input parameters and with the access to the output deconvolved data in the destination spectrum. Based on the output data one can tune the parameters.

Example 8 - script Src.c

Fig. 20 Two-dimensional spectrum with found peaks denoted by markers (sigma=2, threshold=5%, 3 iterations steps in the deconvolution)

Fig. 21 Spectrum from Fig. 20 after background elimination and deconvolution

Script:

Example to illustrate high resolution peak searching function (class TSpectrum). To execute this example, do

`root > .x Src.C

 #include <TSpectrum2>
 void Src() {
    Int_t i, j, nfound;
    Double_t nbinsx = 64;
    Double_t nbinsy = 64;
    Double_t xmin = 0;
    Double_t xmax = (Double_t)nbinsx;
    Double_t ymin = 0;
    Double_t ymax = (Double_t)nbinsy;
    Double_t** source = new Double_t*[nbinsx];
    for (i=0;i<nbinsx;i++)
       source[i]=new Double_t[nbinsy];
    Double_t** dest = new Double_t*[nbinsx];
    for (i=0;i<nbinsx;i++)
       dest[i]=new Double_t[nbinsy];
    TH2F *search = new TH2F("search","High resolution peak searching",nbinsx,xmin,xmax,nbinsy,ymin,ymax);/
    TFile *f = new TFile("spectra2/TSpectrum2.root");
    search=(TH2F*) f->Get("search4;1");
    TCanvas *Searching = new TCanvas("Searching","High resolution peak searching",10,10,1000,700);
    TSpectrum2 *s = new TSpectrum2();
    for (i = 0; i < nbinsx; i++){
       for (j = 0; j < nbinsy; j++){
          source[i][j] = search->GetBinContent(i + 1,j + 1);
       }
    }
    nfound = s->SearchHighRes(source, dest, nbinsx, nbinsy, 2, 5, kTRUE, 3, kFALSE, 3);
    printf("Found %d candidate peaks\n",nfound);
    for(i=0;i<nfound;i++)
       printf("posx= %d, posy= %d, value=%d\n",(Int_t)(fPositionX[i]+0.5), (Int_t)(fPositionY[i]+0.5),
       (Int_t)source[(Int_t)(fPositionX[i]+0.5)][(Int_t)(fPositionY[i]+0.5)]);
}

Example 9 - script Src2.c

Fig. 22 Two-dimensional noisy spectrum with found peaks denoted by markers (sigma=2, threshold=10%, 10 iterations steps in the deconvolution). One can observe that the algorithm is insensitive to the crossings of one-dimensional ridges. It identifies only two-coincidence peaks.

Fig. 23 Spectrum from Fig. 22 after background elimination and deconvolution

Script:

Example to illustrate high resolution peak searching function (class TSpectrum). To execute this example, do

root > .x Src2.C

#include <TSpectrum2>
void Src2() {
   Int_t i, j, nfound;
   Double_t nbinsx = 256;
   Double_t nbinsy = 256;
   Double_t xmin = 0;
   Double_t xmax = (Double_t)nbinsx;
   Double_t ymin = 0;
   Double_t ymax = (Double_t)nbinsy;
   Double_t** source = new Double_t*[nbinsx];
   for (i=0;i<nbinsx;i++)
      source[i]=new Double_t[nbinsy];
   Double_t** dest = new Double_t*[nbinsx];
   for (i=0;i<nbinsx;i++)
      dest[i]=new Double_t[nbinsy];
   TH2F *search = new TH2F("search","High resolution peak searching",nbinsx,xmin,xmax,nbinsy,ymin,ymax);
   TFile *f = new TFile("spectra2/TSpectrum2.root");
   search=(TH2F*) f->Get("back3;1");
   TCanvas *Searching = new TCanvas("Searching","High resolution peak searching",10,10,1000,700);
   TSpectrum2 *s = new TSpectrum2();
   for (i = 0; i < nbinsx; i++){
      for (j = 0; j < nbinsy; j++){
         source[i][j] = search->GetBinContent(i + 1,j + 1);
      }
   }
   nfound = s->SearchHighRes(source, dest, nbinsx, nbinsy, 2, 10, kTRUE, 10, kFALSE, 3);
   printf("Found %d candidate peaks\n",nfound);
   for(i=0;i<nfound;i++)
      printf("posx= %d, posy= %d, value=%d\n",(Int_t)(fPositionX[i]+0.5), (Int_t)(fPositionY[i]+0.5),
      (Int_t)source[(Int_t)(fPositionX[i]+0.5)][(Int_t)(fPositionY[i]+0.5)]);
}

Example 10 - script Src3.c

Fig. 24 Two-dimensional spectrum with 15 found peaks denoted by markers. Some peaks are positioned close to each other. It is necessary to increase number of iterations in the deconvolution. In next 3 Figs. we shall study the influence of this parameter.

Fig. 25 Spectrum from Fig. 24 after deconvolution (# of iterations = 3). Number of identified peaks = 13.

Fig. 26 Spectrum from Fig. 24 after deconvolution (# of iterations = 10). Number of identified peaks = 13.

Fig. 27 Spectrum from Fig. 24 after deconvolution (# of iterations = 100). Number of identified peaks = 15. Now the algorithm is able to decompose two doublets in the spectrum.

Script:

Example to illustrate high resolution peak searching function (class TSpectrum). To execute this example, do

root > .x Src3.C

 #include <TSpectrum2>
 void Src3() {
    Int_t i, j, nfound;
    Double_t nbinsx = 64;
    Double_t nbinsy = 64;
    Double_t xmin = 0;
    Double_t xmax = (Double_t)nbinsx;
    Double_t ymin = 0;
    Double_t ymax = (Double_t)nbinsy;
    Double_t** source = new Double_t*[nbinsx];
    for (i=0;i<nbinsx;i++)
       source[i]=new Double_t[nbinsy];
    Double_t** dest = new Double_t*[nbinsx];
    for (i=0;i<nbinsx;i++)
       dest[i]=new Double_t[nbinsy];
    TH2F *search = new TH2F("search","High resolution peak searching",nbinsx,xmin,xmax,nbinsy,ymin,ymax);
    TFile *f = new TFile("spectra2/TSpectrum2.root");
    search=(TH2F*) f->Get("search1;1");
    TCanvas *Searching = new TCanvas("Searching","High resolution peak searching",10,10,1000,700);
    TSpectrum2 *s = new TSpectrum2();
    for (i = 0; i < nbinsx; i++){
       for (j = 0; j < nbinsy; j++){
          source[i][j] = search->GetBinContent(i + 1,j + 1);
       }
    }
    nfound = s->SearchHighRes(source, dest, nbinsx, nbinsy, 2, 2, kFALSE, 3, kFALSE, 1);//3, 10, 100
    printf("Found %d candidate peaks\n",nfound);
    for(i=0;i<nfound;i++)
       printf("posx= %d, posy= %d, value=%d\n",(Int_t)(fPositionX[i]+0.5), (Int_t)(fPositionY[i]+0.5),
       (Int_t)source[(Int_t)(fPositionX[i]+0.5)][(Int_t)(fPositionY[i]+0.5)]);
}

Example 11 - script Src4.c

Fig. 28 Two-dimensional spectrum with peaks with different sigma denoted by markers (sigma=3, threshold=5%, 10 iterations steps in the deconvolution, Markov smoothing with window=3)

Fig. 29 Spectrum from Fig. 28 after smoothing and deconvolution.

Script:

Example to illustrate high resolution peak searching function (class TSpectrum). To execute this example, do

root > .x Src4.C

 #include <TSpectrum2>
 void Src4() {
 Int_t i, j, nfound;
    Double_t nbinsx = 64;
    Double_t nbinsy = 64;
    Double_t xmin = 0;
    Double_t xmax = (Double_t)nbinsx;
    Double_t ymin = 0;
    Double_t ymax = (Double_t)nbinsy;
    Double_t** source = new Double_t*[nbinsx];
    for (i=0;i<nbinsx;i++)
       source[i]=new Double_t[nbinsy];
    Double_t** dest = new Double_t*[nbinsx];
    for (i=0;i<nbinsx;i++)
       dest[i]=new Double_t[nbinsy];
    TH2F *search = new TH2F("search","High resolution peak searching",nbinsx,xmin,xmax,nbinsy,ymin,ymax);
    TFile *f = new TFile("spectra2/TSpectrum2.root");
    search=(TH2F*) f->Get("search2;1");
    TCanvas *Searching = new TCanvas("Searching","High resolution peak searching",10,10,1000,700);
    TSpectrum2 *s = new TSpectrum2();
    for (i = 0; i < nbinsx; i++){
       for (j = 0; j < nbinsy; j++){
          source[i][j] = search->GetBinContent(i + 1,j + 1);
       }
     }
    nfound = s->SearchHighRes(source, dest, nbinsx, nbinsy, 3, 5, kFALSE, 10, kTRUE, 3);
    printf("Found %d candidate peaks\n",nfound);
    for(i=0;i<nfound;i++)
       printf("posx= %d, posy= %d, value=%d\n",(Int_t)(fPositionX[i]+0.5), (Int_t)(fPositionY[i]+0.5),
       (Int_t)source[(Int_t)(fPositionX[i]+0.5)][(Int_t)(fPositionY[i]+0.5)]);
}

Example 12 - script Src5.c`

Fig. 30 Two-dimensional spectrum with peaks positioned close to the edges denoted by markers (sigma=2, threshold=5%, 10 iterations steps in the deconvolution)

Fig. 31 Spectrum from Fig. 30 after deconvolution.

Script:

Example to illustrate high resolution peak searching function (class TSpectrum). To execute this example, do

root > .x Src5.C

 #include <TSpectrum2>
 void Src5() {
    Int_t i, j, nfound;
    Double_t nbinsx = 64;
    Double_t nbinsy = 64;
    Double_t xmin = 0;
    Double_t xmax = (Double_t)nbinsx;
    Double_t ymin = 0;
    Double_t ymax = (Double_t)nbinsy;
    Double_t** source = new Double_t*[nbinsx];
    for (i=0;i<nbinsx;i++)
       source[i]=new Double_t[nbinsy];
    Double_t** dest = new Double_t*[nbinsx];
    for (i=0;i<nbinsx;i++)
       dest[i]=new Double_t[nbinsy];
    TH2F *search = new TH2F("search","High resolution peak searching",nbinsx,xmin,xmax,nbinsy,ymin,ymax);
    TFile *f = new TFile("spectra2/TSpectrum2.root");
    search=(TH2F*) f->Get("search3;1");
    TCanvas *Searching = new TCanvas("Searching","High resolution peak searching",10,10,1000,700);
    TSpectrum2 *s = new TSpectrum2();
    for (i = 0; i < nbinsx; i++){
       for (j = 0; j < nbinsy; j++){
          source[i][j] = search->GetBinContent(i + 1,j + 1);
       }
    }
    nfound = s->SearchHighRes(source, dest, nbinsx, nbinsy, 2, 5, kFALSE, 10, kFALSE, 1);
    printf("Found %d candidate peaks\n",nfound);
    for(i=0;i<nfound;i++)
       printf("posx= %d, posy= %d, value=%d\n",(Int_t)(fPositionX[i]+0.5), (Int_t)(fPositionY[i]+0.5),
       (Int_t)source[(Int_t)(fPositionX[i]+0.5)][(Int_t)(fPositionY[i]+0.5)]);
}

Definition at line 1589 of file TSpectrum2.cxx.

◆ SetAverageWindow()

void TSpectrum2::SetAverageWindow ( Int_t w = 3 )

static

static function: Set average window of searched peaks see TSpectrum2::SearchHighRes

Definition at line 104 of file TSpectrum2.cxx.

◆ SetDeconIterations()

void TSpectrum2::SetDeconIterations ( Int_t n = 3 )

static

static function: Set max number of decon iterations in deconvolution operation see TSpectrum2::SearchHighRes

Definition at line 113 of file TSpectrum2.cxx.

◆ SetResolution()

void TSpectrum2::SetResolution ( Double_t resolution = 1 )

NOT USED resolution: determines resolution of the neighboring peaks default value is 1 correspond to 3 sigma distance between peaks.

Higher values allow higher resolution (smaller distance between peaks. May be set later through SetResolution.

Definition at line 287 of file TSpectrum2.cxx.

◆ SmoothMarkov()

const char * TSpectrum2::SmoothMarkov	(	Double_t **	source,
		Int_t	ssizex,
		Int_t	ssizey,
		Int_t	averWindow
	)

This function calculates smoothed spectrum from source spectrum based on Markov chain method.

The result is placed in the array pointed by source pointer.

Function parameters:

source-pointer to the array of source spectrum
ssizex-x length of source
ssizey-y length of source
averWindow-width of averaging smoothing window

Smoothing

Goal: Suppression of statistical fluctuations the algorithm is based on discrete Markov chain, which has very simple invariant distribution

\[ U_2 = \frac{p_{1.2}}{p_{2,1}}U_1, U_3 = \frac{p_{2,3}}{p_{3,2}}U_2 U_1, ... , U_n = \frac{p_{n-1,n}}{p_{n,n-1}}U_{n-1} ... U_2 U_1 \]

\(U_1\) being defined from the normalization condition \( \sum_{i=1}^{n} U_i = 1\) n is the length of the smoothed spectrum and

\[ p_{i,i\pm1} = A_i \sum_{k=1}^{m} exp\left[\frac{y(i\pm k)-y(i)}{y(i\pm k)+y(i)}\right] \]

is the probability of the change of the peak position from channel i to the channel i+1. \(A_i\) is the normalization constant so that \( p_{i,i-1}+p_{i,i+1}=1\) and m is a width of smoothing window. We have extended this algorithm to two dimensions.

Reference:

[1] Z.K. Silagadze, A new algorithm for automatic photopeak searches. NIM A 376 (1996), 451.

Example 4 - script Smooth.c

Fig. 9 Original noisy spectrum.

Fig. 10 Smoothed spectrum m=3 Peaks can hardly be observed. Peaks become apparent.

Fig. 11 Smoothed spectrum m=5

Fig.12 Smoothed spectrum m=7

Script:

Example to illustrate the Markov smoothing (class TSpectrum). To execute this example, do

root > .x Smooth.C

#include <TSpectrum>
void Smooth() {
   Int_t i, j;
   Double_t nbinsx = 256;
   Double_t nbinsy = 256;
   Double_t xmin = 0;
   Double_t xmax = (Double_t)nbinsx;
   Double_t ymin = 0;
   Double_t ymax = (Double_t)nbinsy;
   Double_t** source = new Double_t*[nbinsx];
   for (i=0;i<nbinsx;i++)
      source[i] = new Double_t[nbinsy];
   TH2F *smooth = new TH2F("smooth","Background estimation",nbinsx,xmin,xmax,nbinsy,ymin,ymax);
   TFile *f = new TFile("spectra2/TSpectrum2.root");
   smooth=(TH2F*) f->Get("smooth1;1");
   TCanvas *Smoothing = new TCanvas("Smoothing","Markov smoothing",10,10,1000,700);
   TSpectrum *s = new TSpectrum();
   for (i = 0; i < nbinsx; i++){
      for (j = 0; j < nbinsy; j++){
         source[i][j] = smooth->GetBinContent(i + 1,j + 1);
      }
   }
   s->SmoothMarkov(source,nbinsx,nbinsx,3); //5,7
   for (i = 0; i < nbinsx; i++){
      for (j = 0; j < nbinsy; j++)
         smooth->SetBinContent(i + 1,j + 1, source[i][j]);
   }
   smooth->Draw("SURF");
}

Definition at line 736 of file TSpectrum2.cxx.

◆ StaticBackground()

TH1 * TSpectrum2::StaticBackground	(	const TH1 *	hist,
		Int_t	niter = `20`,
		Option_t *	option = `""`
	)

static

static function (called by TH1), interface to TSpectrum2::Background

Definition at line 2216 of file TSpectrum2.cxx.

◆ StaticSearch()

Int_t TSpectrum2::StaticSearch	(	const TH1 *	hist,
		Double_t	sigma = `2`,
		Option_t *	option = `"goff"`,
		Double_t	threshold = `0.05`
	)

static

static function (called by TH1), interface to TSpectrum2::Search

Definition at line 2207 of file TSpectrum2.cxx.

Member Data Documentation

◆ fgAverageWindow

Int_t TSpectrum2::fgAverageWindow = 3

staticprotected

Average window of searched peaks.

Definition at line 27 of file TSpectrum2.h.

◆ fgIterations

Int_t TSpectrum2::fgIterations = 3

staticprotected

Maximum number of decon iterations (default=3)

Definition at line 28 of file TSpectrum2.h.

◆ fHistogram

TH1* TSpectrum2::fHistogram

protected

resulting histogram

Definition at line 26 of file TSpectrum2.h.

◆ fMaxPeaks

Int_t TSpectrum2::fMaxPeaks

protected

Maximum number of peaks to be found.

Definition at line 20 of file TSpectrum2.h.

◆ fNPeaks

Int_t TSpectrum2::fNPeaks

protected

number of peaks found

Definition at line 21 of file TSpectrum2.h.

◆ fPosition

Double_t* TSpectrum2::fPosition

protected

[fNPeaks] array of current peak positions

Definition at line 22 of file TSpectrum2.h.

◆ fPositionX

Double_t* TSpectrum2::fPositionX

protected

[fNPeaks] X position of peaks

Definition at line 23 of file TSpectrum2.h.

◆ fPositionY

Double_t* TSpectrum2::fPositionY

protected

[fNPeaks] Y position of peaks

Definition at line 24 of file TSpectrum2.h.

◆ fResolution

Double_t TSpectrum2::fResolution

protected

NOT USED resolution of the neighboring peaks

Definition at line 25 of file TSpectrum2.h.

The documentation for this class was generated from the following files:

hist/spectrum/inc/TSpectrum2.h
hist/spectrum/src/TSpectrum2.cxx

Public Types

Public Member Functions

Static Public Member Functions

Protected Attributes

Static Protected Attributes

Additional Inherited Members

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ TSpectrum2() [1/2]

◆ TSpectrum2() [2/2]

◆ ~TSpectrum2()

Member Function Documentation

◆ Background() [1/2]

◆ Background() [2/2]

Background estimation

References:

Example 1 - script Back_gamma64.c

Script:

Example 2- script Back_gamma256.c

Script:

Script:

◆ Deconvolution()

Deconvolution

References:

Example 5 - script Decon.c

Script:

Example 6 - script Decon2.c

Script:

Example 7 - script Decon2HR.c

Script:

◆ GetHistogram()

◆ GetNPeaks()

◆ GetPositionX()

◆ GetPositionY()

◆ Print()

◆ Search()

◆ SearchHighRes()

Peaks searching

References:

Examples of peak searching method

Example 8 - script Src.c

Script:

Example 9 - script Src2.c

Script:

Example 10 - script Src3.c

Script:

Example 11 - script Src4.c

Script:

Example 12 - script Src5.c`

Script:

◆ SetAverageWindow()

◆ SetDeconIterations()

◆ SetResolution()

◆ SmoothMarkov()

Smoothing

Reference:

Example 4 - script Smooth.c

Script:

◆ StaticBackground()

◆ StaticSearch()

Member Data Documentation

◆ fgAverageWindow

◆ fgIterations

◆ fHistogram

◆ fMaxPeaks

◆ fNPeaks

◆ fPosition

◆ fPositionX

◆ fPositionY

◆ fResolution