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Hi,

I'm currently working with sequences of images and I'm interested in the temporal dynamics of individual pixels. Typically I have a series of approx. 50 images with 250 000 pixels of interest and I want to fit them to 5-10 time-activity curves of reference. I need to do a non-negative fitting because negative coefficients are physically nonsensical in my problem.

At the moment, I'm basically doing this

nPixels = 250 000;

nRefTACs = 5;

nImages = 50;

% imTS := image time series data [nImages x nPixels]

% refTACs := reference time-activity curves [nImages x nRefTACs]

% nnCoeff := fitting coefficients [nRefTACs x nPixels]

nnCoeff = zeros(nRefTACs, nPixels);

for k = 1:nPixels

nnCoeff(:,k) = lsqnonneg(refTACs, imTS(:,k));

end

I'm wondering if there would be a way to speed this up by vectorization or by using another optimization function. I've been browsing the optimization toolbox documentation for some time, but I'm not very familiar with optimization in general.

Any help would be appreciated.

Matthias Klemm
on 9 Dec 2011

Silas Leavesley
on 1 Dec 2012

Hi David,

Would you mind posting your modified lsqnonneg, or at least the modified portion of it? I am currently using lsqnonneg for spectral image analysis and would like to see if this would speed things up. Thanks.

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Sean de Wolski
on 23 Nov 2011

preallocate nnCoeff so that it doesn't change size on each iteration.

nnCoeff = zeros(nRedTACs,nPixels);

for k ...

nnCoeff(:,k) = lsqnonneg(refTACs, imTS);

end

Steve Grikschat
on 13 Dec 2011

Can you expand this into one large problem? That may or may not make things slower, but it could be worth a try. Additionally, if you have Parallel Computing Toolbox, you could solve these problems in parallel easily.

The reason that (\) is faster than lsqnonneg is that lsqnonneg has to solve a series of linear systems using (\) in order to satisfy the non-negativity constraint.

FYI: I assume that you are actually changing the RHS (imTS) in the loop as well. Your code snippet doesn't show that.

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