Inh.: Dr. Renate Gorre
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Series in Communication Theory
Edited by Helmut Bölcskei
Structured Sparce Signal Recovery in General Hilbert Spaces
1st edition 2014. XXII, 196 pages; € 64,00. ISBN 3-86628-514-0
Data analysis is fundamental to many parts of modern society. This work examines how we can use sparsity to extract meaning and structure from complex data sets.
We begin by establishing a general framework for imposing a model on the sparse representation of a signal. This not only encompasses many of the existing theoretical results, but allows us to use more complex notions of sparsity in our models. We present both deterministic recovery thresholds and probabilistic results stating when we can recover sparse signals and what we gain by using these more complex notions of sparsity.
Furthermore, we develop a new notion of sparsity which we use to identify peptides in biological samples. We show how we use our new framework to model these particular signals and then, due to the overwhelming problem size, we develop specific algorithms to solve this problem in an efficient manner.
About the author
Graeme Pope was born in Canberra, Australia, in 1984.
He received a BSc with First Class Honours and University Medal in Pure Mathematics in 2006 and a BEng with First Class Honours and University Medal in Electrical Engineering in 2007 from the University of Sydney, Australia.
In 2009 he received a MSc in Computer Science from ETH Zurich, Switzerland, after which he joined the Communication Technology Laboratory at ETH Zurich, where he graduated with the Dr. sc. degree in Electrical Engineering in 2013.
Keywords: Uncertainty relations, Sparse signal recovery, Sparse noise, Deterministic recovery guarantees, Probabilistic recovery guarantees,l1 minimization, Coherence, Basis Pursuit, Compressed sensing, Nuclear Norm Minimization, Block Sparsity
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