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One-Bit Compressive Sensing Of Dictionary-Sparse Signals, Richard Baraniuk, Simon Foucart, Deanna Needell, Yaniv Plan, Mary Wootters
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 …
Constrained Adaptive Sensing, Mark A. Davenport, Andrew K. Massimino, Deanna Needell, Tina Woolf
Constrained Adaptive Sensing, Mark A. Davenport, Andrew K. Massimino, Deanna Needell, Tina Woolf
CMC Faculty Publications and Research
Suppose that we wish to estimate a vector x∈Cn from a small number of noisy linear measurements of the form y=Ax+z, where z represents measurement noise. When the vector x is sparse, meaning that it has only s nonzeros with s≪n, one can obtain a significantly more accurate estimate of x by adaptively selecting the rows of A based on the previous measurements provided that the signal-to-noise ratio (SNR) is sufficiently large. In this paper we consider the case where we wish to realize the potential of adaptivity but where the rows of A are subject to physical constraints. In …