Robust approaches to multichannel sparse recovery
Esa Ollila (Aalto University, Finland)
February 03, 2015 — 10:30 — Location: None
We consider multichannel sparse recovery problem where the objective is to find good recovery of jointly sparse unknown signal vectors from the given multiple measurement vectors which are different linear combinations of the same known elementary vectors (atoms). The model is thus an extension of single measurement vector setting used in compressed sensing (CS). Many popular greedy or convex algorithms proposed for multichannel sparse recovery problem perform poorly under non-Gaussian heavy-tailed noise conditions or in the face of outliers (gross errors), i.e., are not robust. In this talk, we consider different types of mixed robust norms on data fidelity (residual matrix) term and conventional L0-norm constraint on the signal matrix to promote row-sparsity. We devise algorithms based normalized iterative hard thresholding (blumesath and davies, 2010) which is a simple, computationally efficient and scalable approach for solving the simultaneous sparse approximation problem. Performance assessment conducted on simulated data highlights the effectiveness of the proposed approaches to cope with different noise environments (i.i.d., row i.i.d, etc) and outliers. Usefulness of the methods are illustrated in image denoising problem and source localization application with sensor arrays. Finally (if time permits) a (non- robust) Bayesian perspective to multichannel recovery problem is discussed as well.
Esa Ollila received the M.Sc. degree in mathematics from the University of Oulu, in 1998, Ph.D. degree in statistics with honors from the University of yvaskyla, in 2002, and the D.Sc.(Tech) degree with honors in signal processing from Aalto University, in 2010. From 2004 to 2007 he was a post-doctoral fellow of the Academy of Finland. He has also been a Senior Researcher and a Senior Lecturer at Aalto University and University of Oulu, respectively. Currently, from August 2010, he is appointed as an Academy Research Fellow of the Academy of Finland at the Department of Signal Processing and Acoustics, Aalto University, Finland. He is also adjunct Professor (statistics) of University of Oulu. During the Fall-term 2001 he was a Visiting Researcher with the Department of Statistics, Pennsylvania State University, State College, PA while the academic year 2010-2011 he spent as a Visiting Research Associate with the Department of Electrical Engineering, Princeton University, Princeton, NJ. His research interests focus on theory and methods of statistical signal processing, blind source separation, complex-valued signal processing, array and radar signal processing and robust and non-parametric statistical methods.