CS: Bayesian Compressive Sensing using Laplace Priors, Distilled Sensing

I do not know if it is a clue of things to come but over the course of two days, two graduate students ( Derin Babacan and Jarvis Haupt ) have set up pages for their projects and wanted to make an announcement on Nuit Blanche. I am gladly obliging with the added word that I am very impressed to see students taking these initiatives. It used to be only Assistant Professors who would go for some self promotion but I am glad students are doing it as it shows their interest in providing the full strength of their ideas to the community.

First, Derin Babacan let me know that his research team has made available two papers and attendant source code on their Bayesian approach to compressive sensing. The two papers are:
Bayesian Compressive Sensing using Laplace Priors by S. Derin Babacan, Rafael Molina, and Aggelos Katsaggelos. The abstract reads:

In this paper we model the components of the compressive sensing (CS) problem, i.e., the signal acquisition process, the unknown signal coefficients and the model parameters for the signal and noise using the Bayesian framework. We utilize a hierarchical form of the Laplace prior to model sparsity of the unknown signal. We describe the relationship among a number of sparsity priors proposed in the literature, and show the advantages of the proposed model including its high degree of sparsity. Moreover, we show that some of the existing models are special cases of the proposed model. We present two algorithms resulting from our model; one global optimization algorithm and one constructive (greedy) algorithm designed for fast reconstruction useful in practical settings. Unlike most existing CS reconstruction methods, both algorithms are fully-automated, i.e., the unknown signal coefficients and all necessary parameters are estimated solely from the observation and therefore no user-intervention is needed. Additionally, the proposed algorithms provide estimates of the uncertainty of the reconstructions. We provide experimental results with synthetic 1D signals and images, and compare with the state-of-the-art CS reconstruction algorithms demonstrating the superior performance of the proposed approach.

and Fast Bayesian Compressive Sensing using Laplace Priors. by S. Derin Babacan, Rafael Molina, and Aggelos Katsaggelos. The abstract reads:

In this paper we model the components of the compressive sensing (CS) problem using the Bayesian framework by utilizing a hierarchical form of the Laplace prior to model sparsity of the unknown signal. This signal prior includes some of the existing models as special cases and achieves a high degree of sparsity. We develop a constructive (greedy) algorithm resulting from this formulation where necessary parameters are estimated solely from the observation and therefore no user-intervention is needed. We provide experimental results with synthetic 1D signals and images, and compare with the state-of-the-art CS reconstruction algorithms demonstrating the superior performance of the proposed approach.

The source code can be found on the project webpage.



The algorithm is compared with BCS, BP, OMP, StOMP with CFAR thresholding (denoted by FAR) and GPSR.


Jarvis Haupt put together a page describing (at a relatively high-level) what Distilled Sensing is and how it works:

http://homepages.cae.wisc.edu/~jhaupt/ds.html

Jarvis also let me know that the latest DS paper is Distilled Sensing: Selective Sampling for Sparse Signal Recovery by Jarvis Haupt, Rui Castro and Robert Nowak. The abstract readss;

A selective sampling procedure called distilled sensing (DS) is proposed, and shown to be an effective method for recovering sparse signals in noise. Based on the notion that it is often easier to rule out locations that do not contain signal than it is to directly identify non-zero signal components, DS is a sequential method that systematically focuses sensing resources towards the signal subspace. This adaptivity in sensing results in rather surprising gains in sparse signal recovery dramatically weaker sparse signals can be recovered using DS compared with conventional non-adaptive sensing procedures.

Jarvis also told me that some toy model illustrating the DS algorithm will be available soon.

Thank you Jarvis and Derin.