A difficult multi-curve fitting problem

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Karl 2011-9-16

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https://ww2.mathworks.cn/matlabcentral/answers/16010-a-difficult-multi-curve-fitting-problem

Hi, I have a question. Say I had a matrix (of, lets say nxm size, where n and m are ~= 1000). In this matrix there is the information of k (around 10-20) functions. The way the functions appear on the matrix is by being radially symmetric and super imposed about some centre (where all different functions have a different centre). That is to say that say all the functions were simply 1 then the matrix would appear as a superposition of k circles of value 1 centred at different values. The actual values are not, of course, 1 though and vary quite a lot over the range. So my first question would be is there a way that I could use a matlab curve fitting toolbox or function to extract these k functions using least squares?

The second question (if the first is possible) is there some way to "relax" the circularly symmetric condition, i.e., say that it is only circularly symmetric for 90 degrees of the circle (thereby increasing the number of functions to k*4 since each quadrant of the original function is now its own function independent of the other 3 quadrants). Thank you very much for any help! Please ask if I need to be more specific but I think the problem is difficult to explain.

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bym 2011-9-16

sounds like you might have to do some image processing before applying a curve fit

Andrew Newell 2011-9-17

This is not really a MATLAB question until you are able to define the statistical question more clearly. Perhaps it would help if you explained why you are trying to do this. Also, when you say "if all the functions were 1", do you mean the coefficients?

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