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## Thursday, January 24, 2008

### Compressed Sensing: SSP 2007, Some papers and posters and the ICASSP 2008 Abstracts

I found the following papers and posters on the Compressed Sensing subject at the 2007 IEEE Statistical Signal Processing Workshop. I know it is a little late but I have not seen some of them on the Rice Repository yet. It took place at the end of August 2007.

Sparse MRI Reconstruction via Multiscale L0-Continuation by Joshua Trzasko, Armando Manduca, Eric Borisch. The abstract reads:
Compressed Sensing” and related L1-minimization methods for reconstructing sparse magnetic resonance images (MRI) acquired at sub-Nyquist rates have shown great potential for dramatically reducing exam duration. Nonetheless, the nontriviality of numerical implementation and computational intensity of these reconstruction algorithms has thus far precluded their widespread use in clinical practice. In this work, we propose a novel MRI reconstruction framework based on homotopy continuation of the L0 semi-norm using redescending M-estimator functions. Following analysis of the continuation scheme, the sparsity measure is extended to multiscale form and a simple numerical solver that can achieve accurate reconstructions in a matter of seconds on a standard desktop computer is presented.
Differences between Observation and Sampling Error in Sparse Signal Reconstruction by Galen Reeves, Michael Gastpar. The abstract reads:
The field of Compressed Sensing has shown that a relatively small number of random projections provide sufficient information to accurately reconstruct sparse signals. Inspired by applications in sensor networks in which each sensor is likely to observe a noisy version of a sparse signal and subsequently add sampling error through computation and communication, we investigate how the distortion differs depending on whether noise is introduced before sampling (observation error) or after sampling (sampling error). We analyze the optimal linear estimator (for known support) and an $\ell_1$ constrained linear inverse (for unknown support). In both cases, observation noise is shown to be less detrimental than sampling noise and low sampling rates. We also provide sampling bounds for a non-stochastic $\ell_\infty$ bounded noise model.
Previously it was mentioned that EEG signals were interesting for CS because of their sparsity. Selin Aviyente made a similar finding (Sparse Representation for Signal Classification Ke Huang and Selin Aviyente) and continued her investigation by looking at an implementation of Compressed Sensing for EEG signals in
Compressed Sensing Framework for EEG Compression by Selin Aviyente. The abstract reads:
Many applications in signal processing require the efficient representation and processing of data. The traditional approach to efficient signal representation is compression. In recent years, there has been a new approach to compression at the sensing level. Compressed sensing (CS) is an emerging field which is based on the revelation that a small collection of linear projections of a sparse signal contains enough information for reconstruction. In this paper, we propose an application of compressed sensing in the field of biomedical signal processing, particularly electro-encophelogram (EEG) collection and storage. A compressed sensing framework is introduced for efficient representation of multichannel, multiple trial EEG data. The proposed framework is based on the revelation that EEG signals are sparse in a Gabor frame. The sparsity of EEG signals in a Gabor frame is utilized for compressed sensing of these signals. A simultaneous orthogonal matching pursuit algorithm is shown to be effective in the joint recovery of the original multiple trail EEG signals from a small number of projections.

Mona Sheikh, Shriram Sarvotham, Olgica Milenkovic, Richard Baraniuk. The abstract reads:
We propose a signal recovery method using Belief Propagation (BP) for nonlinear Compressed Sensing (CS) and demonstrate its utility in DNA array decoding. In a CS DNA microarray, the array spots identify DNA sequences that are shared between multiple organisms, thereby reducing the number of spots required in a traditional DNA array. The sparsity in DNA sequence commonality between different organisms translates to conditions that render Belief Propagation (BP) ideal for signal decoding. However a high concentration of target molecules has a nonlinear effect on the measurements - it causes saturation in the spot intensities. We propose a tailored BP technique to estimate the target signal in spite of the nonlinearity and show that the original signal coefficients can be recovered from saturated values of their linear combinations.
Related report/papers from the Rice repository are: Compressed Sensing DNA Microarrays and DNA array decoding from nonlinear measurements by belief propagation

Rate-Distortion Bounds for Sparse Approximation by Alyson Fletcher, Sundeep Rangan, Vivek Goyal. The abstract reads:
Sparse signal models arise commonly in audio and image processing. Recent work in the area of compressed sensing has provided estimates of the performance of certain widely-used sparse signal processing techniques such as basis pursuit and matching pursuit. However, the optimal achievable performance with sparse signal approximation remains unknown. This paper provides bounds on the ability to estimate a sparse signal in noise. Specifically, we show that there is a critical minimum signal-to-noise ratio (SNR) that is required for reliable detection of the sparsity pattern of the signal. We furthermore relate this critical SNR to the asymptotic mean squared error of the maximum likelihood estimate of a sparse signal in additive Gaussian noise. The critical SNR is a simple function of the problem dimensions.

Differences between Observation and Sampling Error in Sparse Signal Reconstruction by G. Reeves and M. Gastpar. The abstract reads:
The field of Compressed Sensing has shown that a relatively small number of random projections provide sufficient information to accurately reconstruct sparse signals. Inspired by applications in sensor networks in which each sensor is likely to observe a noisy version of a sparse signal and subsequently add sampling error through computation and communication, we investigate how the distortion differs depending on whether noise is introduced before sampling (observation error) or after sampling (sampling error). We analyze the optimal linear estimator (for known support) and an $\ell_1$ constrained linear inverse (for unknown support). In both cases, observation noise is shown to be less detrimental than sampling noise and low sampling rates. We also provide sampling bounds for a non-stochastic $\ell_\infty$ bounded noise model.

Variable Projection and Unfolding in Compressed Sensing by Joel Goodman, Benjamin Miller, Gil Raz, Andrew Bolstad. The abstract reads:
The performance of linear programming techniques that are applied in the signal identification and reconstruction process in compressed sensing (CS) is governed by both the number of measurements taken and the number of non-zero coefficients in the discrete orthormal basis used to represent the signal. To enhance the capabilities of CS, we have developed a technique called Variable Projection and Unfolding (VPU) to extend the identification and reconstruction capability of linear programming techniques to signals with a much greater number of non-zero coefficients in the orthonormal basis in which the signals are best compressible.
Some details of this study can be found in this report entitled Analog-to-Information Study Phase
with the following abstract:
So in short the VPU is a greedy algorithm.

Colored Random Projections for Compressed Sensing by Zhongmin Wang; Arce, G.R.; Paredes, J.L. The abstract reads:
The emerging theory of compressed sensing (CS) has led to the remarkable result that signals having a sparse representation in some known basis can be represented (with high probability) by a small sample set, taken from random projections of the signal. Notably, this sample set can be smaller than that required by the ubiquitous Nyquist sampling theorem. Much like the generalized Nyquist sampling theorem dictates that the sampling rate can be further reduced for the representation of bandlimited signals, this paper points to similar results for the sampling density in CS. In particular, it is shown that if additional spectral information of the underlying sparse signals is known, colored random projections can be used in CS in order to further reduce the number of measurements needed. Such a priori information is often available in signal processing applications and communications. Algorithms to design colored random projection vectors are developed. Further, an adaptive CS sampling method is developed for applications where non-uniform spectral characteristics of the signal are expected but are not known a priori.

Compressed Sensing for Wideband Cognitive Radios by Zhi Tian and Giannakis, G.B. The Abstract reads:
In the emerging paradigm of open spectrum access, cognitive radios dynamically sense the radio-spectrum environment and must rapidly tune their transmitter parameters to efficiently utilize the available spectrum. The unprecedented radio agility envisioned, calls for fast and accurate spectrum sensing over a wide bandwidth, which challenges traditional spectral estimation methods typically operating at or above Nyquist rates. Capitalizing on the sparseness of the signal spectrum in open-access networks, this paper develops compressed sensing techniques tailored for the coarse sensing task of spectrum hole identification. Sub-Nyquist rate samples are utilized to detect and classify frequency bands via a wavelet-based edge detector. Because spectrum location estimation takes priority over fine-scale signal reconstruction, the proposed novel sensing algorithms are robust to noise and can afford reduced sampling rates.

Laurent Duval mentioned to me that ICASSP 2008 will take place in Las Vegas and will feature three sessions on Compressed Sensing. Hopefully what will happen in Vegas will not stay in Vegas :-). I note the first Show and Tell Presentation session that is supposed to draw a large crowd. The deadline for proposing one of these show and tell presentation is February 1st, I am sure that a good presentation on dramatic improvement related to Compressed Sensing would go a long way toward making people think how it could be used in their own field. An enterprising student might even make a name for her/himself doing that. Here is the list of abstracts from the three sessions.

## SS-1: Compressed Sensing I

 Session Type: Special Lecture Time: Tuesday, April 1, 10:30 - 12:30 Location: Lecture Room 1 ; Ryan Robucci; Georgia Institue of Technology Leung Kin Chiu; Georgia Institue of Technology Jordan Gray; Georgia Institue of Technology Justin Romberg; Georgia Institue of Technology Paul Hasler; Georgia Institue of Technology David Anderson; Georgia Institue of Technology Kiryung Lee; University of Illinois at Urbana-Champaign Yoram Bresler; University of Illinois at Urbana-Champaign Rui Castro; University of Wisconsin - Madison Jarvis Haupt; University of Wisconsin - Madison Robert Nowak; University of Wisconsin - Madison Gil Raz; University of Wisconsin - Madison Marco Duarte; Rice University Michael Wakin; University of Michigan Richard Baraniuk; Rice University Ali Hormati; Ecole Polytechnique Federale de Lausanne Martin Vetterli; Ecole Polytechnique Federale de Lausanne Alfred M. Bruckstein; The Computer-Science Department Michael Elad; The Computer-Science Department Michael Zibulevsky; The Computer-Science Department

## SPTM-L5: Compressed Sensing II

Session Type: Lecture
Time: Friday, April 4, 09:30 - 11:30
Location: Lecture Room 4

Dmitry Malioutov; MIT
Sujay Sanghavi; MIT
Alan Willsky; MIT

Petros Boufounos; Rice
Richard Baraniuk; Rice

Moshe Mishali; Technion
Yonina Eldar; Technion

Thong Do; The Johns Hopkins University
Trac Tran; The Johns Hopkins University
Gan Lu; University of Liverpool

Stephen Wright; University of Wisconsin
Robert Nowak; University of Wisconsin
Mário Figueiredo; Instituto Superior Técnico

Mihailo Stojnic; California Institute of Technology
Weiyu Xu; California Institute of Technology
Babak Hassibi; California Institute of Technology

## SPTM-P11: Compressed Sensing III

Session Type: Poster
Time: Friday, April 4, 13:00 - 15:00
Location: Poster Area 5

Anna Gilbert; University of Michigan
Martin Strauss; University of Michigan

Sohan Seth; University of Florida
Jose C. Principe; University of Florida

Bernard Mulgrew; The University of Edinburgh
Michael Davies; The University of Edinburgh

Farzad Parvaresh; California Institute of Technology
Babak Hassibi; California Institute of Technology

Christian R. Berger; University of Connecticut
Javier Areta; University of Connecticut
Krishna Pattipati; University of Connecticut
Peter Willett; University of Connecticut

Zhuizhuan Yu; Texas A&M University
Sebastian Hoyos; Texas A&M University
Brian M. Sadler; Army Research Laboratory

Jun Zhang; Arizona State University
Antonia Papandreou-Suppappola; Arizona State University

Rick Chartrand; Los Alamos National Laboratory
Wotao Yin; Rice University

Zhongmin Wang; Uinversity of Delaware
Gonzalo R. Arce; Uinversity of Delaware
Brian M. Sadler; Army Research Laboratory

Mohammad Golbabaee; Ecole Polytechnique Federale de Lausanne
Pierre Vandergheynst; Ecole Polytechnique Federale de Lausanne

G. Hosein Mohimani; Electrical Engineering Department, Sharif University of Technology
Massoud Babaie-Zadeh; Electrical Engineering Department, Sharif University of Technology
Christian Jutten; Labratoire des Images et de Signaux (LIS), Institut National Polytechnique de Grenoble (INPG)

Rayan Saab; The University of British Columbia
Rick Chartrand; Los Alamos National Laboratory
Ozgur Yilmaz; The University of British Columbia

Finally there is another talk but not in the Compressed Sensing
Session: SPCOM-P2: Channel Modeling and Estimation
Location: Poster Area 2
Time: Tuesday, April 1, 10:30 - 12:30
Presentation: Poster
Topic: Signal Processing for Communications and Networking: Signal Transmission and Reception
Title: A COMPRESSED SENSING TECHNIQUE FOR OFDM CHANNEL ESTIMATION IN MOBILE ENVIRONMENTS: EXPLOITING CHANNEL SPARSITY FOR REDUCING PILOTS

Authors: Georg Tauboeck, Franz Hlawatsch
Abstract: We consider the estimation of doubly selective wireless channels within pulse-shaping multicarrier systems (which include OFDM systems as a special case). A new channel estimation technique using the recent methodology of compressed sensing (CS) is proposed. CS-based channel estimation exploits a channel’s delay-Doppler sparsity to reduce the number of pilots and, hence, increase spectral efficiency. Simulation results demonstrate a significant reduction of the number of pilots relative to least-squares channel estimation.

and two panels might be of relevance:
Tuesday, April 1

PANEL-1: Compressed Sensing, Sparse Signal Processing, Rate of Innovation, Real Field Coding, and Irregular Sampling
Organized by Farokh Marvasti

and

Wednesday, April 2

PANEL-2: Convex Optimization Theory and Practice in Signal Processing
Organized by Yonina Eldar