Paper Info
Title
One-Bit Compressive Sensing Of Dictionary-Sparse Signals
Abstract
One-bit compressive sensing has extended the scope of sparse recovery by showing that sparse signals can be accurately reconstructed even when their linear measurements are subject to the extreme quantization scenario of binary samples-only the sign of each linear measurement is maintained. Existing results in one-bit compressive sensing rely on the assumption that the signals of interest are sparse in some fixed orthonormal basis. However, in most practical applications, signals are sparse with respect to an overcomplete dictionary, rather than a basis. There has already been a surge of activity to obtain recovery guarantees under such a generalized sparsity model in the classical compressive sensing setting. Here, we extend the one-bit framework to this important model, providing a unified theory of one-bit compressive sensing under dictionary sparsity. Specifically, we analyze several different algorithms-based on convex programming and on hard thresholding-and show that, under natural assumptions on the sensing matrix (satisfied by Gaussian matrices), these algorithms can efficiently recover analysis-dictionary-sparse signals in the one-bit model.
Year
DOI
Venue
2016
10.1093/imaiai/iax009
INFORMATION AND INFERENCE-A JOURNAL OF THE IMA
Keywords
Field
DocType
compressive sensing, quantization, one-bit compressive sensing, tight frames, convex optimization, thresholding
Mathematical optimization,Pattern recognition,Matrix (mathematics),Gaussian,Orthonormal basis,Artificial intelligence,Unified field theory,Quantization (signal processing),Convex optimization,Compressed sensing,Mathematics,Binary number
Journal
Volume
Issue
ISSN
7
1
2049-8764
Citations 
PageRank 
References 
6
0.46
14
Authors
5
Name
Order
Citations
PageRank
Richard G. Baraniuk15053489.23
Simon Foucart215212.69
Deanna Needell31823121.92
Yaniv Plan4117457.19
Mary Wootters517225.99