2012/07/03 by Ji Liu, Stephen J. Wright, Liu, Ji +1
Computer Science · Engineering · Mathematics · Medicine · #Advanced MRI Techniques and Applications #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Microwave Imaging and Scattering Analysis #Sparse and Compressive Sensing Techniques #cs.LG #stat.ML
paper · pdf · doi:10.48550/arxiv.1207.0577
openalex publication_date 2012/07/03 · arxiv created 2013/10/10 · arxiv updated 2013/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ℓ2-ℓ1 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.