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information-theoretically_optimal_compressed_sensing_via_spatial_coupling_and_approximate_message_passing [2016/09/01 19:15] (current)
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 +Abstract: We study the compressed sensing reconstruction problem for a broad class of
 +random, band-diagonal sensing matrices. This construction is inspired by the idea of spatial
 +coupling in coding theory. We use an approximate message passing (AMP) algorithm and
 +show that it e ectively solves the reconstruction problem at information-theoretically optimal
 +rates. More speci cally,​ we show that the approach is successful as soon as the undersampling
 +rate exceeds the (upper) Renyi information dimension of the signal.
 +For sparse signals, i.e., sequences of dimension n and k(n) non-zero entries, this implies
 +reconstruction from k(n)+o(n) measurements. For `discrete'​ signals, i.e., signals whose coor-
 +dinates take a xed nite set of values, this implies reconstruction from o(n) measurements.
 +The result is robust with respect to noise, does not apply uniquely to random signals, but
 +requires the knowledge of the empirical distribution of the signal pX.
 +In the second part of the talk, I will discuss how the idea of spatial coupling can be
 +implemented through Gabor transform in sampling theory.
 +This is based on joint work with David L. Donoho and Andrea Montanari.
 +Bio: Adel Javanmard is currently nishing the Ph.D. degree in the Department of Electri-
 +cal Engineering at Stanford University, advised by Andrea Montanari. He received Master'​s
 +degree in Electrical Engineering from Stanford University (2011), a Bachelor'​s degree in Elec-
 +trical Engineering and a Bachelor'​s degree in Pure Mathematics both from Sharif University,
 +Tehran (2009). During summers 2011 and 2012, he interned with Microsoft Research (MSR).
 +His research interests include machine learning, high-dimensional statistics, graphical models,
 +and convex optimization. He was awarded Stanford Electrical Engineering Fellowship (2009),
 +and Stanford Graduate Fellowship (2010-2012).
information-theoretically_optimal_compressed_sensing_via_spatial_coupling_and_approximate_message_passing.txt ยท Last modified: 2016/09/01 19:15 (external edit)