Robust Dequantized Compressive Sensing
This work addresses robust signal reconstruction for applications with limited-bit observations, but it is incremental as it builds on existing compressed sensing methods with enhanced error handling.
The paper tackles the problem of reconstructing signals from compressed sensing observations with quantization and saturation errors by proposing a weighted ℓ2-ℓ1 objective with explicit constraints, solved via an augmented Lagrangian method, and proves stronger asymptotic consistency results without oversampling while showing computational improvements over prior formulations.
We consider the reconstruction problem in compressed sensing in which the observations are recorded in a finite number of bits. They may thus contain quantization errors (from being rounded to the nearest representable value) and saturation errors (from being outside the range of representable values). Our formulation has an objective of weighted $\ell_2$-$\ell_1$ type, along with constraints that account explicitly for quantization and saturation errors, and is solved with an augmented Lagrangian method. We prove a consistency result for the recovered solution, stronger than those that have appeared to date in the literature, showing in particular that asymptotic consistency can be obtained without oversampling. We present extensive computational comparisons with formulations proposed previously, and variants thereof.