Compressive Sampling Rate Optimization for Multiple Measurement Vector Problems

Abstract

Joint sparse recovery is a recently proposed signal processing approach which has become conventional due to its capability of solving a wide range of optimization problems. However, despite the appropriate performance of existing joint sparse recovery algorithms, all of them suffer from the same drawback: They collect pre-defined number of compressed measurements, which may be too small to precisely reconstruct the row support, or may be unnecessarily large which leads to the wastage of sampling resources. To address this issue and unlike the previous studies, this paper proposes a novel compressed sensing-based method to adaptively adjust the optimal sampling rate of joint sparse recovery problem. A data-driven approach based on Monte Carlo simulation is introduced to obtain the minimum number of samples which is required for precise row support estimation using several well-known joint sparse recovery techniques. Then, a sequential joint sparse recovery framework is developed where the first step predicts the optimal number of measurements and the second step reconstructs signal vectors applying the determined sampling rate. Numerical simulations investigate the effectiveness of suggested method to reduce both the required number of measurements and average algorithm runtime, without losing the recovery performance.