Monday, August 10, 2009

CS: A Short Note on Compressed Sensing, Non-Iterative Reweighted-Norm Least-Squares Local l_0 Minimization, CVPR09 and a talk

Today, we have two papers, some conference papers and a presentation, here we go:

In this short note, we propose another demonstration of the recovery of sparse signals in Compressed Sensing when their support is partially known. In particular, without very surprising conclusion, this paper extends the results presented recently in [VL09] to the cases of compressible signals and noisy measurements by slightly adapting the proof developed in [Can08].

Laurent also mentions on his page that if somebody finds an error he would be happy to get your feedback.

We present a non-iterative algorithm for computing sparse solutions to underdetermined M×N linear systems of equations. The algorithm computes a solution which is a local minimum of the l_0 norm (number of nonzero values) obtained from the l_1 norm (sum of absolute values) minimum. At each step, it uses reweighted-norm least-squares minimization to compute the l_pp norm for values of p decreasing from 2 to 0. The result is similar to the l_1 solution, but uses less computation (solution of ten M×M systems of equations), and there are no convergence issues.
Andy makes the difference between iteration and recursion. I think his approach is different compared to the current reweighted l_p strategies. I look forward to someone implementing this algorithm.

The CVPR '09 paper that are on the web are listed here.

Frank Curtis will make a presentation at Lehigh University, Bethlehem, PA on 19-21 August 2009 with the title: A Sequential Quadratic Programming Method for Nonsmooth Optimization
The desscription of the talk:

Algorithms for the solution of smooth, constrained optimization problems have enjoyed great successes in recent years. In particular, the framework known as sequential quadratic programming (SQP) has been studied and applied to a variety of interesting applications. Similarly, there has been a great deal of recent work on the solution of nonsmooth, unconstrained optimization applications. One approach that has been successful in this context is gradient sampling (GS) — a method that, unlike the many variations of bundle methods, only requires the computation of gradients during the solution process. In this talk, we combine elements of SQP and GS to create an algorithm for nonsmooth, constrained optimization and illustrate the potential for such an approach on illustrative test problems in eigenvalue optimization and compressed sensing.

Credit: NASA/JPL/Space Science Institute, Punching through the F Ring, Released: August 7, 2009 (PIA 11662). Something is going through Saturn's F ring as it turns out Saturn's Equinox comes up every fifteen years and this inclination allows one to see in greater details things that are going through the rings. Via Bad Astronomy Blog. This is interesting, as we recently saw comets hitting Jupiter in a fifteen year interval. I know this sound stupid but has anyone evalute if the angle of inclination of this "thing" is the same as that of the other "thing" that Jupiter two weeks ago ?

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