Fit a sum of basis functions to an array

Can someone give me an idea how do I fit a sum of basis functions to an array? The context is image analysis and I am trying to find a convolution kernel from one image to the other. I am able to form the basis set, but unable to move forward from there on. P.S. I am very new to MATLAB.

Answer 1

[Kim Winter]

Hi, I have included an example below that might be pretty different than yours, but you can put your own values in. Below, I first create a function handle, with an array of my functions(in this case, sin(x) and cos(x)^2). I then create a series of inputs, x, using linspace. This creates 1000 equally spaced points between 1 and 1000. I then run my inputs through. Finally, I add my answers together.

%define basis functions using function handles
basis_funcs=@(x)sin(x);
basis_funcs2= @(x)(cos(x).^2);

%evenly spaced input array
inputs=linspace(1,1000,1000);

%input arrays into functions
output=basis_funcs(inputs);
output2=basis_funcs2(inputs);

%add outputs
outputfin=output+output2;

Hopefully this is what you're looking for!

[Anshuman Borgohain]

Dear Kim,

Thank you for your reply. I understand that you are showing how to create the basis set and then add them. But my goal is to fit a sum of the basis functions to some data and get the coefficients of fit. Its like:

mydata = a*basis_funcs + b*basis_funcs2 + ..........

and I need a and b using some minimisation.

Best,

Anshuman