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Mar 19, 2010

Compressed sensing's day at the ICASSP

Texas skyline As I commented in the previous post on game theory at the ICASSP, today was the compressed sensing day at the ICASSP. Although I tried to be selective in the lectures/posters I attended I finished with a bunch of interesting papers, from a wide range of topics on compressive sensing. Let's go sequentially.


The fact that each author can cover up to 4 papers was used by Mihailo Stojnic to present four single author papers at the conference. Since all of them where scheduled into the same poster session (SPTM-P5: Compressive Sensing) the author had a difficult time from one spot to another. These papers were mostly related to generalizations of the Donoho-Tanner border under different models (for more information on the Donoho-Tanner border check Nuit-Blanche on precise undersampling theorems).

Yonina Eldar was also there explaining a different application of her Modulated Wideband Converter: in this case pulse delay recovery. Paper's title reads TIME DELAY ESTIMATION: COMPRESSED SENSING OVER AN INFINITE UNION OF SUBSPACES by Kfir Gedalyahu et al. Later Y. Eldar left the poster session to give the talk presenting SUB-NYQUIST PROCESSING WITH THE MODULATED WIDEBAND CONVERTER by M. Mishali et al. in a simultaneous lecture session.

Some more interesting work presented in the poster session was on compressive sensing with not perferct knowledge of the compression matrix (SENSITIVITY TO BASIS MISMATCH IN COMPRESSED SENSING by Yuejie Chi et al.) and on sparse reconstruction with partially known support (MODIFIED BASIS PURSUIT DENOISING(MODIFIED-BPDN) FOR NOISY COMPRESSIVE SENSING WITH PARTIALLY KNOWN SUPPORT by Wei Lu et al.)


The afternoon's session SPTM-L6: Compressive Sensing: Theory and Methods was chaired by Yonina Eldar (what for a ubiquitous person). From there I want to cite the work ALTERNATING MINIMIZATION TECHNIQUES FOR THE EFFICIENT RECOVERY OF A SPARSELY CORRUPTED LOW-RANK MATRIX by Silvia Gandy et al., which uses sparsity in two ways. First it assumes that the meassurement matrix presents low rank so that nuclear norm can be used for reconstruction, but on the other hand it assumes that the corrupting noise is also sparse in the coefficients domain, that is, that most of the matrix entries are unaffected by the noise. I have to take a closer look to the algorithms CoSaMP and ADMIRA, since they are used in an alternating way to solve the proposed problem.

In a poster session Zvika Ben-Haim was presenting the work ON UNBIASED ESTIMATION OF SPARSE VECTORS CORRUPTED BY GAUSSIAN NOISE by A. Jung et al. I found it quite impressive since they analyze the fundamental limits on the estimation performance of sparse vectors (since of course in practical scenarios the reconstruction cannot be perfect). They had found previously that the Cramer-Rao lower bound becomes not tight in the low SNR regime and that other bounds must be used to analyze estimator performance in this regime. Since the tighter Barankin bound (BB) has no closed expression in general, they analyze an upper and a lower bound on the BB showing a soft transition from low SNR to high SNR in the sparse estimation performance. I have to say that I really liked both the result and its presentation.

To finish this post I will cite two alternatives to the commonly used norm 1 based reconstruction. The first one (AN L0 NORM BASED METHOD FOR FREQUENCY ESTIMATION FROM IRREGULARLY SAMPLED DATA by Md Mashud Hyder et al.) proposes to substitute the norm 0 term (that penalizes the least squares error to guarantee sparsity in the solution) by an exponential transformation instead of using the norm 1. The second approach is completely different and it is presented in the paper RECONSTRUCTION OF SPARSE SIGNALS FROM L1 DIMENSIONALITY-REDUCED CAUCHY RANDOM-PROJECTIONS by Gonzalo Arce et al. This reconstruction algorithm proposes to use Cauchy random matrices, instead of the commonly used Gaussian, as compression matrices. These matrices have the property of conserving the norm 1 of the meassurement (instead of the norm 2 by the Gaussian) what allows the use of a novel reconstruction algorithm.

And that's all for now. I posted here the papers I found interesting or related to my research. If someone is interested in other works on compressed sensing presented at the ICASSP you can check ESPACE VIDE's post on CORNUCOPIA OF COMPRESSED SENSING.

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