How to interpret result of deconvolution?

[Vladislav]

Hello!

I am novice in deconvolution theme.
I have several questions.
May be you can help me.

Root version is 5.34/36.
My system: Scientific Linux release 7.2 (Nitrogen).
My gcc: gcc (GCC) 4.8.5 20150623 (Red Hat 4.8.5-4).

My problem:
My signal (channels vs time) is sum of overlapped individual signals (around 300 individual signals).
I want to find true start time and amplitude(if there is double or triple signal) of individual signals .
I know pulse shape for individual signal.
I know two solutions for this problem (if you know another, please, let me know):

1. fitting by sum of individual signals
2. deconvolution

For my previous task I used 1st method, because I had only 2 or 3 overlapped individual signals and data were noisy.

Now I decided to use 2nd method, because I have too many overlapped signals and data are not so noisy.

I wrote simple code to simulate different cases:

void unfold_vlad()
{
    TSpectrum *s = new TSpectrum();

    const double time_scale = 0.1;
    const int numberIterations = 10000;
    const int numberRepetitions = 1;
    const int boost = 1;
    const double response_rangle_from = -15;
    const Int_t ssize = 700;


    float source[ssize];
    float response[ssize];
    float xv_response[ssize];

    cout << "ssize = " << ssize << endl;
    for (int i = 0; i < ssize; ++i)
    {
        double time =  i*time_scale + response_rangle_from;
        xv_response[i] = time;
        response[i] = TMath::Gaus(time, 0);
        source[i] = (TMath::Gaus(time, 30) + TMath::Gaus(time, 40));
    }

    TCanvas* canv = new TCanvas("c", "c", 0, 0, 1900, 1500);
    canv->Divide(2, 2);

    TGraph *graph = new TGraph(ssize, &xv_response[0], &response[0]);
    graph->SetTitle("response");
    graph->SetMarkerStyle(20);
    graph->SetMarkerSize(0.7);
    canv->cd(1);
    graph->Draw("AP");


    TGraph *graph_source = new TGraph(ssize, &xv_response[0], &source[0]);
    graph_source->SetTitle("original signal");
    graph_source->SetMarkerStyle(20);
    graph_source->SetMarkerSize(0.7);
    canv->cd(2);
    graph_source->Draw("AP");


    s->Deconvolution(source,response,ssize,numberIterations,numberRepetitions,boost);

    TGraph *graph_unfold = new TGraph(ssize, &xv_response[0], &source[0]);
    graph_unfold->SetTitle("unfold signal");
    graph_unfold->SetMarkerStyle(20);
    graph_unfold->SetMarkerSize(0.9);
    canv->cd(4);
    graph_unfold->Draw("AP");

}

This code gives expected result:

But I confused, because for shift response I have the same unfold signal:

response[i] = TMath::Gaus(time, 5);
source[i] = (TMath::Gaus(time, 30) + TMath::Gaus(time, 40));

Result (I expected delta-functions at 25 and 35):

The negative value gives the same result(I expected delta-functions at 35 and 45):

response[i] = TMath::Gaus(time, -5);
source[i] = (TMath::Gaus(time, 30) + TMath::Gaus(time, 40));

For negative amplitudes I see strange results too.

For

response[i] = -TMath::Gaus(time, 0);
source[i] = -(TMath::Gaus(time, 30) + TMath::Gaus(time, 40));

Result:

For

response[i] = -TMath::Gaus(time, 5);
source[i] = -(TMath::Gaus(time, 30) + TMath::Gaus(time, 40));

Result:

For

response[i] = -TMath::Gaus(time, -5);
source[i] = -(TMath::Gaus(time, 30) + TMath::Gaus(time, 40));

Thank you in advance.
Best regards, Vladislav.

[Vladislav]

Also two interesting cases:

const double response_rangle_from = 0;
...
response[i] = TMath::Gaus(time, 10);
source[i] = (TMath::Gaus(time, 30) + TMath::Gaus(time, 40));

Result:

And for

const double response_rangle_from = 0;
...
response[i] = -TMath::Gaus(time, 10);
source[i] = -(TMath::Gaus(time, 30) + TMath::Gaus(time, 40));

Result:

Only the second case is correct.

[moneta]

Hi,

I would recommend to look carefully at the TSpectrum documentation

root.cern.ch/doc/master/classTSpectrum.html

in particular for the deconvolution method, which is well documented.
Also look at the cited papers.
Unfortunately the author of the Spectrum package cannot be contacted anymore, but maybe you can try contacting some of the co-authors of the papers who should have experience in these methods.

Best Regards

Lorenzo

[Sabaism]

Hi Vladislav,

I am not used to the TSpectrum class, but if you are interested in deconvolution in general
feel free to contact me by writing me a private message, maybe I can give you a little help on this.

Cheers
Johannes