### Compressive Sampling and Sparse Reconstruction: ICASSP 2011

In first place I want to make a short comment about the

Today's compressed sensing oral session (SPCOM-L1) was intense:

This paper exploits sparsity in the eigenspace of signal covariance matrices for both compression and denoising. To this end it presents an iterative algorithm which starting from the standard PCA solution converges to a sparse PCA. In this sparse PCA solution some of the principal components are zeroed, hence the compression. The noise reduction comes from the fact that if data are noisy the proposed sparsity-aware eigenspace estimator recovers a subset of the unknown signal subspace basis support, hence reducing the variability of the signal. Nice presentation by Giannakis.

This paper exploits some of the structure of the Basis Pursuit (BP) algorithm in order to derive a distributed algorithm in a sensor network based on the dual of the original optimization problem. The novelty of this work is to use an optimal first-order method to solve an augmented Lagrangian reformulation.

This work proposes an algorithm to estimate multipath channels with Sparse Common Support based on Finite Rate of Innovation sampling. This algorithm presents two main advantages: on the one hand it exploits sparsity in domain of "received paths", and on the other it uses that in practical setups the support of this sparse signal can be considered equal accross multiple antennas. This last points closes the gap to the Cramer-Rao lower bound in the medium SNR regime (the mismatch of the model given the existing distance between the receiver antennas is exhacerbated in the high SNR regime).

In this work the authors propose a semi-blind, iterative, sparse channel estimation method based on minimizing Csiszar’s I-divergence. The proposed semi-blind method accurately estimates the significant tap locations of a sparse channel, and their corresponding magnitudes. The phase ambiguity of each of the channel contributions must be estimated through the use of additional pilots.

The idea behind this work is that the channel support in a practical system changes slowly. Then the domain "differences in the support between one time instant and the next" presents a certain sparsity which can be exploited for channel estimation. To this end the authors employ a modified version of the orthogonal matching pursuit.

This work proposes a deterministic construction of the compression matrix via additive character sequences. While this construction shows good properties in terms of recovery performance, it does not introduce further structure for efficient reconstruction.

This afternoon I gave my talk in the spectrum sensing session, but this will have to wait until I have some time.

**Xampling seminar**by Yonina Eldar and Moshe Mishali. Some colleagues pointed out that the seminar's start was too basic, intended for people not familiar at all with compressed sensing. In my opinion Yonina presented a nice framework (the**subspace union model**) where several problems involving sparsity fit in. In this sense the first part of the presentation was quite general. However, at the end there was not much time left for commenting the main hardware implementation issues before the welcome reception. A pity.Today's compressed sensing oral session (SPCOM-L1) was intense:

**"EIGENSPACE SPARSITY FOR COMPRESSION AND DENOISING"**; Ioannis Schizas, Georgios B. Giannakis, University of Minnesota, USThis paper exploits sparsity in the eigenspace of signal covariance matrices for both compression and denoising. To this end it presents an iterative algorithm which starting from the standard PCA solution converges to a sparse PCA. In this sparse PCA solution some of the principal components are zeroed, hence the compression. The noise reduction comes from the fact that if data are noisy the proposed sparsity-aware eigenspace estimator recovers a subset of the unknown signal subspace basis support, hence reducing the variability of the signal. Nice presentation by Giannakis.

**"BASIS PURSUIT IN SENSOR NETWORKS"**; João Mota, Carnegie Mellon University / Institute of Systems and Robotics, US; João Xavier, Pedro Aguiar, Institute of Systems and Robotics, Portugal; Markus Püschel, ETH Zürich, SwitzerlandThis paper exploits some of the structure of the Basis Pursuit (BP) algorithm in order to derive a distributed algorithm in a sensor network based on the dual of the original optimization problem. The novelty of this work is to use an optimal first-order method to solve an augmented Lagrangian reformulation.

**"ESTIMATING SPARSE MIMO CHANNELS HAVING COMMON SUPPORT"**; Yann Barbotin, Ali Hormati, Ecole Polytechnique Fédérale de Lausanne, Switzerland; Sundeep Rangan, Polytechnic Institute of New York University, United States; Martin Vetterli, Ecole Polytechnique Fédérale de Lausanne, SwitzerlandThis work proposes an algorithm to estimate multipath channels with Sparse Common Support based on Finite Rate of Innovation sampling. This algorithm presents two main advantages: on the one hand it exploits sparsity in domain of "received paths", and on the other it uses that in practical setups the support of this sparse signal can be considered equal accross multiple antennas. This last points closes the gap to the Cramer-Rao lower bound in the medium SNR regime (the mismatch of the model given the existing distance between the receiver antennas is exhacerbated in the high SNR regime).

**"APPLYING CSISZAR'S I-DIVERGENCE TO BLIND SPARSE CHANNEL ESTIMATION"**; Feng Wan, Urbashi Mitra, University of Southern California, USIn this work the authors propose a semi-blind, iterative, sparse channel estimation method based on minimizing Csiszar’s I-divergence. The proposed semi-blind method accurately estimates the significant tap locations of a sparse channel, and their corresponding magnitudes. The phase ambiguity of each of the channel contributions must be estimated through the use of additional pilots.

**"COMPRESSIVE TRACKING OF DOUBLY SELECTIVE CHANNELS IN MULTICARRIER SYSTEMS BASED ON SEQUENTIAL DELAY-DOPPLER SPARSITY"**; Daniel Eiwen, University of Vienna, Austria; Georg Tauböck, Franz Hlawatsch, Vienna University of Technology, Austria; Hans Georg Feichtinger, University of Vienna, AustriaThe idea behind this work is that the channel support in a practical system changes slowly. Then the domain "differences in the support between one time instant and the next" presents a certain sparsity which can be exploited for channel estimation. To this end the authors employ a modified version of the orthogonal matching pursuit.

**"ADDITIVE CHARACTER SEQUENCES WITH SMALL ALPHABETS FOR COMPRESSED SENSING MATRICES"**; Nam Yul Yu, Lakehead University, CanadaThis work proposes a deterministic construction of the compression matrix via additive character sequences. While this construction shows good properties in terms of recovery performance, it does not introduce further structure for efficient reconstruction.

This afternoon I gave my talk in the spectrum sensing session, but this will have to wait until I have some time.

Labels: compressed sensing, icassp 2011

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