DeepAI

# On one-stage recovery for ΣΔ-quantized compressed sensing

Compressed sensing (CS) is a signal acquisition paradigm to simultaneously acquire and reduce dimension of signals that admit sparse representations. When such a signal is acquired according to the principles of CS, the measurements still take on values in the continuum. In today's "digital" world, a subsequent quantization step, where these measurements are replaced with elements from a finite set is crucial. We focus on one of the approaches that yield efficient quantizers for CS: ΣΔ quantization, followed by a one-stage tractable reconstruction method, which was developed by Saab et al. with theoretical error guarantees in the case of sub-Gaussian matrices. We propose two alternative approaches that extend this result to a wider class of measurement matrices including (certain unitary transforms of) partial bounded orthonormal systems and deterministic constructions based on chirp sensing matrices.

• 3 publications
• 17 publications
11/18/2019

### Deterministic partial binary circulant compressed sensing matrices

Compressed sensing (CS) is a signal acquisition paradigm to simultaneous...
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### Analyzing Cross Validation In Compressed Sensing With Mixed Gaussian And Impulse Measurement Noise With L1 Errors

Compressed sensing (CS) involves sampling signals at rates less than the...
11/18/2019

### RIP constants for deterministic compressed sensing matrices-beyond Gershgorin

Compressed sensing (CS) is a signal acquisition paradigm to simultaneous...
02/02/2023

### QCM-SGM+: Improved Quantized Compressed Sensing With Score-Based Generative Models for General Sensing Matrices

In realistic compressed sensing (CS) scenarios, the obtained measurement...
01/26/2018

### Fast binary embeddings, and quantized compressed sensing with structured matrices

This paper deals with two related problems, namely distance-preserving b...
01/30/2011

### Statistical Compressed Sensing of Gaussian Mixture Models

A novel framework of compressed sensing, namely statistical compressed s...
04/19/2012

### Estimating Unknown Sparsity in Compressed Sensing

In the theory of compressed sensing (CS), the sparsity ||x||_0 of the un...