Sparse linear regression with compressed and low-precision data via concave quadratic programming
This work addresses sparse signal recovery in compressed sensing with low-precision data, offering an incremental improvement over existing methods for applications like signal processing.
The paper tackles the problem of recovering a sparse vector from compressed, quantized measurements by proposing a non-convex quadratic programming method that uses prior magnitude information to improve support recovery, with numerical simulations demonstrating its feasibility.
We consider the problem of the recovery of a k-sparse vector from compressed linear measurements when data are corrupted by a quantization noise. When the number of measurements is not sufficiently large, different $k$-sparse solutions may be present in the feasible set, and the classical l1 approach may be unsuccessful. For this motivation, we propose a non-convex quadratic programming method, which exploits prior information on the magnitude of the non-zero parameters. This results in a more efficient support recovery. We provide sufficient conditions for successful recovery and numerical simulations to illustrate the practical feasibility of the proposed method.