I am trying to minimize a nonlinear objective:
||y- f(x_bar)||^2 + mu_s ||D_s x_bar||^2
Obviously, first term is data fitting term and second is regularization term involving spatial regularization. (more details about objective later).
The calculation of objective function is very time consuming which makes optimization also very time consuming. Also, I have to do it for 1/2 millon voxels (3d equivalent of pixels).
Fortunately I can precalculate my objective partwise and use it for each voxel. It seems that I can not use “lsqnonlin” as I can not input fixed step-size. I have the understanding that genetic algorithm can do this. I can easily map my objective to integer minimization.
Could someone please help me formulate this problem for genetic algorithm? Or some guidance would be highly appreciated.
Details about the objective:
In the objective, x_bar is a column vector consisting of αk (k = 1,..., N) and N is the number of voxel. I plan to choose αk from linearly spaced points as candidates (i.e. 0:005:0.35)
Of course, rather than solving entire ½ million at one go, I can solve 20 x 20 x 20 voxel (3D) at a time.