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Full-Text Articles in Physical Sciences and Mathematics
Exponential Decay Of Reconstruction Error From Binary Measurements Of Sparse Signals, Richard Baraniuk, Simon Foucart, Deanna Needell, Yaniv Plan, Mary Wootters
Exponential Decay Of Reconstruction Error From Binary Measurements Of Sparse Signals, Richard Baraniuk, Simon Foucart, Deanna Needell, Yaniv Plan, Mary Wootters
CMC Faculty Publications and Research
Binary measurements arise naturally in a variety of statistical and engineering applications. They may be inherent to the problem—e.g., in determining the relationship between genetics and the presence or absence of a disease—or they may be a result of extreme quantization. A recent influx of literature has suggested that using prior signal information can greatly improve the ability to reconstruct a signal from binary measurements. This is exemplified by onebit compressed sensing, which takes the compressed sensing model but assumes that only the sign of each measurement is retained. It has recently been shown that the number of one-bit measurements …
Two-Part Reconstruction With Noisy-Sudocodes, Yanting Ma, Dror Baron, Deanna Needell
Two-Part Reconstruction With Noisy-Sudocodes, Yanting Ma, Dror Baron, Deanna Needell
CMC Faculty Publications and Research
We develop a two-part reconstruction framework for signal recovery in compressed sensing (CS), where a fast algorithm is applied to provide partial recovery in Part 1, and a CS algorithm is applied to complete the residual problem in Part 2. Partitioning the reconstruction process into two complementary parts provides a natural trade-off between runtime and reconstruction quality. To exploit the advantages of the two-part framework, we propose a Noisy-Sudocodes algorithm that performs two-part reconstruction of sparse signals in the presence of measurement noise. Specifically, we design a fast algorithm for Part 1 of Noisy-Sudocodes that identifies the zero coefficients of …