CS: L1 Homotopy, Capturing Functions in Infinite Dimensions, ABCS: Approximate Bayesian Compressed Sensing

Muhammad Salman Asif and Justin Romberg just released the code implementing their recent preprint previously mentioned here:

L1 Homotopy: A MATLAB toolbox for homotopy algorithms in L1 norm minimization problems
The page reads:

Introduction:

In this package we have implemented some homotopy algorithms to recover sparse signals from linear measurements.

The convex optimization problems we solve are:

· Basis pursuit denoising (BPDN) \ LASSO
· Dantzig selector
· L1 decoding
· Robust L1 decoding

In addition to solving these problems from scratch, we provide dynamic algorithms to update the solution as

· New measurements are sequentially added to the system
· Signal varies over time

The preprint is: Dynamic updating for L1 minimization by Muhammad Salman Asif and Justin Romberg. I'll add the code shortly to the reconstruction section of the Compressive Sensing Big Picture page.

Albert Cohen just released the 4th course notes of Ron DeVore's 4th lecture in Paris entitled Capturing Functions in Infinite Dimensions ( the third lecture is here, and the first and second are here), The abstract reads:

The following are notes on stochastic and parametric PDEs of the short course in Paris. Lecture 4: Capturing Functions in Infinite Dimensions
Finally, we want to give an example where the problem is to recover a function of infinitely many variables. We will first show how such problems occur in the context of stochastic partial differential equations.

Following last entry on CSBP, here is yet another Bayesian approach:

ABCS: Approximate Bayesian Compressed Sensing by Avishy Carmi, Pini Gurfil, Dimitri Kanevsky, Bhuvana Ramabhadran.The abstract reads:

In this work we present a new approximate Bayesian compressed sensing scheme. The new method is based on a unique type of sparseness-promoting prior, termed here semi-Gaussian owing to its Gaussian-like formulation. The semi-Gaussian prior facilitates the derivation of a closed-formrecursion for solving the noisy compressed sensing problem. As part of this, the discrepancy between the exact and the approximate posterior pdf is shown to be of the order of a quantity that is computed online by the new scheme. In the second part of this work, a random field-based classifier utilizing the approximate Bayesian CS scheme is shown to attain a zero error rate when applied to fMRI classification.

At some point we probably need to have a way to compare all these Bayesian approaches.