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Tuesday, March 20, 2012

Around the blogs in 80 hours

On the Advanced Matrix Factroization Group, a question just came up:

I've factored my problem currently to something like: p=Ax
A is a transform matrix relating them and I wish to find an x that results in a P matrix that has a somewhat sparse diagonal form. (elements primarily around diagonal in symmetric form)
The objective function has the same x variables but is say: b-Ax l2 norm.
I'm primarily interested in suggestions to constrain/get force the form of the solution.
In the Compressive Sensing Group, there were several questions:Does anybody knows if there is some International Conference/Workshop focused in CS topics and another on:Compressed Sensing/Sparse Reconstruction with Custom Dictionaries/Penalty Functions

On the blogs we have:

1 comment:

Anonymous said...

Hi igor,
This comment is related to the question above.
I remenber reading on your blog, about analysis sparsity. I hope this problem can be solved in a similar manner.
Objective function is to minimize b-Px l2 norm and the sparsity constraint is to be imposed on Ax. If the matrix Ax is having a sparse structure (can minimize nuclear norm), then you might solve the optimization problem:
minimize ||Ax||_nuclear subject to ||y-Px||_2<eps

or If the matrix Ax happens to be close to diagonal and has a sparse diagonal, then you cam minimize ||diag(Ax)||_1 in the place of nuclear norm also.