I don't remember it so clearly described but the updated page on Gradient Projection for SparseReconstruction: Application to Compressed Sensing and Other Inverse Problems by Mario Figueiredo, Robert Nowak, Stephen Wright features the new updated paper on the technique and how it compares with other techniques. Besides explaining the algorithm, the authors must be thanked for making clear the connection between compressed sensing and other techniques such as LASSO that are using the L1 norm and for what purpose. I touched upon the reason for using L1 before but it was not framed in this exceptionally clear "background" discussion. Thank you guys.
L1 reconstruction is assumed to obtain exact recovery for sparse signals as shown in Candes paper (Compressive Sampling)but the expression for minimum number of measurements for a given sparsity does not show any dependence of sparsity on the compression rate(decay of coefficients) of the sparse signal?Does any expression exists including the compression rate?
ReplyDeleteNot that I am aware of, but then again I should not be considered a specialist. One more thing, the compression rate is generally associated with "compressible signals" not sparse ones. Most results in compressed sensing are for sparse signals, the use of compressible signals in compressed sensing is generally an extension of the sparse case and I have not seen (but I can be wrong) much connection between the exponent of the decay rate and the recovery by L1 methods.
ReplyDeleteIgor.
Thanks Igor,
ReplyDeleteFor practical signals which are not exactly sparse(themselves or in transform domain),is L1 reconstruction a better option than sliding window?
Yes I think this is the point of going that route. The drawback is the fact that l1 reconstruction is expected to be slow but accurate as opposed to an l2 method that is fast but potentially very much inaccurate.
ReplyDeleteIgor.