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.

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.

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.

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.

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

Many communications and Radar receivers must process data over a very wide band, which requires either high-rate analog-to-digital converters (ADCs) or multichannel receivers. The information content of that wideband data, however, is often sparse in some basis. Analog-to-Information (A2I) receivers exploit this sparseness in both the digital and analog domains by non-adaptively spreading the signal energy (analog) and using digital signal processing to recover the signal from an ADC sampling at a sub-Nyquist rate. A subsampled ADC implies the use of fewer receiver channels or less expensive, lower- rate devices. This report documents the signal processing techniques for such receivers developed by the MIT Lincoln Laboratory/GMR Research and Technology team in the study phase of the A2I program. We have developed two new A2I signal processing methods, both significantly outperforming compressed sensing (CS) techniques currently in the literature, which typically fail when signals occupy more than 15-20% of the downsampled band. One of our methods, Nonlinear Affine processing (NoLaff), uses a nonlinear front-end to spread signal energy before the sub-Nyquist ADC, and uses hypothesis testing to reconstruct the signal. In simulations, this technique has shown that it can reconstruct wideband signals occupying up to 72% of the downsampled basis, It is also much less sensitive to the difficulties CS has detecting signals with large magnitude variation in the compressible basis. Our other method, called Variable Projection and Unfolding (VPU), spreads the signal energy using random linear projections similar to those used in compressed sensing, but is able to reconstruct signals occupying nearly 100% of the downsampled basis. VPU achieves this using a technique similar to matching pursuit; the key difference being that VPU searches over blocks of consecutive columns rather than one column at a time.

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.

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 |

SS-1.1: COMPRESSIVE SENSING ON A CMOS SEPARABLE TRANSFORM IMAGE SENSOR |

; |

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 |

SS-1.2: COMPUTING PERFORMANCE GUARANTEES FOR COMPRESSED SENSING |

Kiryung Lee; University of Illinois at Urbana-Champaign |

Yoram Bresler; University of Illinois at Urbana-Champaign |

SS-1.3: FINDING NEEDLES IN NOISY HAYSTACKS |

Rui Castro; University of Wisconsin - Madison |

Jarvis Haupt; University of Wisconsin - Madison |

Robert Nowak; University of Wisconsin - Madison |

Gil Raz; University of Wisconsin - Madison |

SS-1.4: WAVELET-DOMAIN COMPRESSIVE SIGNAL RECONSTRUCTION USING A HIDDEN MARKOV TREE MODEL |

Marco Duarte; Rice University |

Michael Wakin; University of Michigan |

Richard Baraniuk; Rice University |

SS-1.5: DISTRIBUTED COMPRESSED SENSING: SPARSITY MODELS AND RECONSTRUCTION ALGORITHMS USING ANNIHILATING FILTER |

Ali Hormati; Ecole Polytechnique Federale de Lausanne |

Martin Vetterli; Ecole Polytechnique Federale de Lausanne |

SS-1.6: ON THE UNIQUENESS OF NON-NEGATIVE SPARSE AND REDUNDANT REPRESENTATIONS |

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 |

SPTM-L5.1: COMPRESSED SENSING WITH SEQUENTIAL OBSERVATIONS |

Dmitry Malioutov; MIT |

Sujay Sanghavi; MIT |

Alan Willsky; MIT |

SPTM-L5.2: RECONSTRUCTING SPARSE SIGNALS FROM THEIR ZERO CROSSINGS |

Petros Boufounos; Rice |

Richard Baraniuk; Rice |

SPTM-L5.3: SPECTRUM-BLIND RECONSTRUCTION OF MULTI-BAND SIGNALS |

Moshe Mishali; Technion |

Yonina Eldar; Technion |

SPTM-L5.4: FAST COMPRESSIVE SAMPLING WITH STRUCTURALLY RANDOM MATRICES |

Thong Do; The Johns Hopkins University |

Trac Tran; The Johns Hopkins University |

Gan Lu; University of Liverpool |

SPTM-L5.5: SPARSE RECONSTRUCTION BY SEPARABLE APPROXIMATION |

Stephen Wright; University of Wisconsin |

Robert Nowak; University of Wisconsin |

Mário Figueiredo; Instituto Superior Técnico |

SPTM-L5.6: COMPRESSED SENSING - PROBABILISTIC ANALYSIS OF A NULL-SPACE CHARACTERIZATION |

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 |

SPTM-P11.1: FUNDAMENTAL PERFORMANCE BOUNDS FOR A COMPRESSIVE SAMPLING SYSTEM |

Anna Gilbert; University of Michigan |

Martin Strauss; University of Michigan |

SPTM-P11.2: COMPRESSED SIGNAL RECONSTRUCTION USING THE CORRENTROPY INDUCED METRIC |

Sohan Seth; University of Florida |

Jose C. Principe; University of Florida |

SPTM-P11.3: APPROXIMATE LOWER BOUNDS FOR RATE-DISTORTION IN COMPRESSIVE SENSING SYSTEMS |

Bernard Mulgrew; The University of Edinburgh |

Michael Davies; The University of Edinburgh |

SPTM-P11.4: EXPLICIT MEASUREMENTS WITH ALMOST OPTIMAL THRESHOLDS FOR COMPRESSED SENSING |

Farzad Parvaresh; California Institute of Technology |

Babak Hassibi; California Institute of Technology |

SPTM-P11.5: COMPRESSED SENSING – A LOOK BEYOND LINEAR PROGRAMMING |

Christian R. Berger; University of Connecticut |

Javier Areta; University of Connecticut |

Krishna Pattipati; University of Connecticut |

Peter Willett; University of Connecticut |

SPTM-P11.6: MIXED-SIGNAL PARALLEL COMPRESSED SENSING AND RECEPTION FOR COGNITIVE RADIO |

Zhuizhuan Yu; Texas A&M University |

Sebastian Hoyos; Texas A&M University |

Brian M. Sadler; Army Research Laboratory |

SPTM-P11.7: COMPRESSIVE SENSING AND WAVEFORM DESIGN FOR THE IDENTIFICATION OF LINEAR TIME-VARYING SYSTEMS |

Jun Zhang; Arizona State University |

Antonia Papandreou-Suppappola; Arizona State University |

SPTM-P11.8: ITERATIVELY REWEIGHTED ALGORITHMS FOR COMPRESSIVE SENSING |

Rick Chartrand; Los Alamos National Laboratory |

Wotao Yin; Rice University |

SPTM-P11.9: SUBSPACE COMPRESSIVE DETECTION FOR SPARSE SIGNALS |

Zhongmin Wang; Uinversity of Delaware |

Gonzalo R. Arce; Uinversity of Delaware |

Brian M. Sadler; Army Research Laboratory |

SPTM-P11.10: AVERAGE CASE ANALYSIS OF SPARSE RECOVERY WITH THRESHOLDING: NEW BOUNDS BASED ON AVERAGE DICTIONARY COHERENCE |

Mohammad Golbabaee; Ecole Polytechnique Federale de Lausanne |

Pierre Vandergheynst; Ecole Polytechnique Federale de Lausanne |

SPTM-P11.11: COMPLEX-VALUED SPARSE REPRESENTATION BASED ON SMOOTHED L0 NORM |

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) |

SPTM-P11.12: STABLE SPARSE APPROXIMATIONS VIA NONCONVEX OPTIMIZATION |

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

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