Physical Sciences and Mathematics Commons^™

One-Bit Compressive Sensing Of Dictionary-Sparse Signals, Richard Baraniuk, Simon Foucart, Deanna Needell, Yaniv Plan, Mary Wootters

CMC Faculty Publications and Research

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 …