Jobs: Joint-Sparse Optimization From Bootstrap Samples

Classical sparse regression based on l(1) minimization solves the least squares problem with all available measurements via sparsity-promoting regularization. In challenging practical applications with high levels of noise and missing or adversarial samples, solving the problem using all measurements simultaneously may fail. In this paper, we propose a robust global sparse recovery strategy, named JOBS, which uses bootstrap samples of measurements to improve sparse regression in difficult cases. K measurement vectors are generated from the original pool of m measurements via bootstrapping, with each bootstrap sample containing L elements, and then a joint-sparse constraint is enforced to ensure support consistency among multiple predictors. The final estimate is obtained by averaging over K estimators.The performance limits associated with finite bootstrap sampling ratio L/m and number of estimates K is analyzed theoretically. Simulation results validate the theoretical analysis of proper choice of (L, K) and show that the proposed method yields state-of-the-art recovery performance, outperforming l(1) minimization and other existing bootstrap-based techniques, especially when the number of measurements are limited. With a proper choice of bootstrap sampling ratio (0.3 - 0.5) and a reasonably large number of estimates K (>= 30), the SNR improvement over the baseline l(1)-minimization algorithm can reach up to 336%