library: libHist #include "TSpectrum2.h" |
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public:
TSpectrum2() TSpectrum2(Int_t maxpositions, Float_t resolution = 1) TSpectrum2(const TSpectrum2&) virtual ~TSpectrum2() virtual const char* Background(const TH1* hist, int niter, Option_t* option = "goff") const char* Background(float** spectrum, Int_t ssizex, Int_t ssizey, Int_t numberIterationsX, Int_t numberIterationsY, Int_t direction, Int_t filterType) static TClass* Class() const char* Deconvolution(float** source, float** resp, Int_t ssizex, Int_t ssizey, Int_t numberIterations, Int_t numberRepetitions, Double_t boost) TH1* GetHistogram() const Int_t GetNPeaks() const Float_t* GetPositionX() const Float_t* GetPositionY() const virtual TClass* IsA() const TSpectrum2& operator=(const TSpectrum2&) virtual void Print(Option_t* option = "") const virtual Int_t Search(const TH1* hist, Double_t sigma = 2, Option_t* option = "goff", Double_t threshold = 0.05) Int_t SearchHighRes(float** source, float** 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) void SetResolution(Float_t resolution = 1) virtual void ShowMembers(TMemberInspector& insp, char* parent) const char* SmoothMarkov(float** source, Int_t ssizex, Int_t ssizey, Int_t averWindow) virtual void Streamer(TBuffer& b) void StreamerNVirtual(TBuffer& b)
protected:
Int_t fMaxPeaks Maximum number of peaks to be found Int_t fNPeaks number of peaks found Float_t* fPosition [fNPeaks] array of current peak positions Float_t* fPositionX [fNPeaks] X position of peaks Float_t* fPositionY [fNPeaks] Y position of peaks Float_t fResolution resolution of the neighboring peaks TH1* fHistogram resulting histogram public:
static const enum TSpectrum2:: kBackIncreasingWindow static const enum TSpectrum2:: kBackDecreasingWindow static const enum TSpectrum2:: kBackSuccessiveFiltering static const enum TSpectrum2:: kBackOneStepFiltering
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 These functions were written by: Miroslav Morhac Institute of Physics Slovak Academy of Sciences Dubravska cesta 9, 842 28 BRATISLAVA SLOVAKIA email:fyzimiro@savba.sk, fax:+421 7 54772479 The original code in C has been repackaged as a C++ class by R.Brun The algorithms in this class have been published in the following references: [1] 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. [2] 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. [3] 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 Postscript files from: ftp://root.cern.ch/root/SpectrumDec.ps.gz ftp://root.cern.ch/root/SpectrumSrc.ps.gz ftp://root.cern.ch/root/SpectrumBck.ps.gz
maxpositions: maximum number of peaks 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.
ONE-DIMENSIONAL BACKGROUND ESTIMATION FUNCTION This function calculates background spectrum from source in h. The result is placed in the vector pointed by spectrum pointer. Function parameters: spectrum: pointer to the vector of source spectrum size: length of spectrum and working space vectors number_of_iterations, for details we refer to manual
ONE-DIMENSIONAL PEAK SEARCH FUNCTION 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. Function parameters: hin: pointer to the histogram of source spectrum sigma: sigma of searched peaks, for details we refer to manual Note that sigma is in number of bins threshold: (default=0.05) peaks with amplitude less than threshold*highest_peak are discarded. if option is not equal to "goff" (goff is the default), then 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")
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.
TWO-DIMENSIONAL BACKGROUND ESTIMATION FUNCTION - RECTANGULAR RIDGES 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 “”
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
.
where p = 1, 2, …, number_of_iterations.
Function:
const char* TSpectrum2::Background (float **spectrum, int ssizex, int ssizey, int numberIterationsX, int numberIterationsY, int direction, int filterType)
This function calculates background spectrum from the source spectrum. The result is placed in the matrix pointed by spectrum pointer. One can also switch the direction of the change of the clipping window and to select one of the two above given algorithms. On successful completion it returns 0. On error it returns pointer to the string describing error.
Parameters:
spectrum-pointer to the matrix of source spectrum
ssizex, ssizey-lengths of the spectrum matrix
numberIterationsX, numberIterationsYmaximal widths of clipping
window,
direction- direction of change of clipping window
- possible values=kBackIncreasingWindow
kBackDecreasingWindow
filterType-type of the clipping algorithm,
-possible values=kBack SuccessiveFiltering
kBackOneStepFiltering
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. Morháč, J. Kliman, V. Matoušek, M. Veselský, I. Turzo.: Background elimination methods for multidimensional gamma-ray spectra. NIM, A401 (1997) 113-132.
TWO-DIMENSIONAL MARKOV SPECTRUM SMOOTHING FUNCTION 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
being defined from the normalization condition
n is the length of the smoothed spectrum and
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is the probability of the change of
the peak position from channel i to the channel i+1. is the normalization constant so
that
and m is a width of smoothing window. We have extended this
algortihm to two dimensions.
Function:
const char* TSpectrum2::SmoothMarkov(float **fSpectrum, int ssizex, int ssizey, int averWindow)
This function calculates smoothed spectrum from the source spectrum based on Markov chain method. The result is placed in the vector pointed by source pointer. On successful completion it returns 0. On error it returns pointer to the string describing error.
Parameters:
fSpectrum-pointer to the matrix of source spectrum
ssizex, ssizey -lengths of the spectrum matrix
averWindow-width of averaging smoothing window
Reference:
[1] Z.K. Silagadze, A new algorithm for automatic photopeak searches. NIM A 376 (1996), 451.
TWO-DIMENSIONAL DECONVOLUTION FUNCTION 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
![]() |
where h(i,j) is the impulse
response function, x, y are input and output matrices, respectively, 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. Generalization 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
Function:
const char* TSpectrum2::Deconvolution(float **source, const float **resp, int ssizex, int ssizey, int numberIterations, int numberRepetitions, double boost)
This function calculates deconvolution from source spectrum according to response spectrum using Gold deconvolution algorithm. The result is placed in the matrix pointed by source pointer. On successful completion it returns 0. On error it returns pointer to the string describing error. If desired after every numberIterations one can apply boosting operation (exponential function with exponent given by boost coefficient) and repeat it numberRepetitions times.
Parameters:
source-pointer to the matrix of source spectrum
resp-pointer to the matrix of response spectrum
ssizex, ssizey-lengths of the spectrum matrix
numberIterations-number of iterations
numberRepetitions-number of repetitions for boosted deconvolution. It must be
greater or equal to one.
boost-boosting coefficient, applies only if numberRepetitions is greater than one.
Recommended range <1,2>.
References:
[1] M. Morháč, J. Kliman, V. Matoušek, M. Veselský, I. Turzo.: Efficient one- and two-dimensional Gold deconvolution and its application to gamma-ray spectra decomposition. NIM, A401 (1997) 385-408.
[2] Morháč M., Matoušek V., Kliman J., Efficient algorithm of multidimensional deconvolution and its application to nuclear data processing, Digital Signal Processing 13 (2003) 144.
TWO-DIMENSIONAL HIGH-RESOLUTION PEAK SEARCH FUNCTION 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-averanging 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
Function:
Int_t TSpectrum2::SearchHighRes (float **source,float **dest, int ssizex, int ssizey, float sigma, double threshold, bool backgroundRemove,int deconIterations, bool markov, int averWindow)
This function searches for peaks in source spectrum. It is based on deconvolution method. First the background is removed (if desired), then Markov smoothed spectrum is calculated (if desired), then the response function is generated according to given sigma and deconvolution is carried out. The order of peaks is arranged according to their heights in the spectrum after background elimination. The highest peak is the first in the list. On success it returns number of found peaks.
Parameters:
source-pointer to the matrix of source spectrum
dest-resulting spectrum after deconvolution
ssizex, ssizey-lengths of the source and destination spectra
sigma-sigma of searched peaks
threshold- threshold value in % for selected peaks, peaks with amplitude less than threshold*highest_peak/100 are ignored
backgroundRemove- background_remove-logical variable, true 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-width of averaging smoothing window
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. Morháč, J. Kliman, V. Matoušek, M. Veselský, 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.