JOBS: Joint-Sparse Optimization from Bootstrap Samples
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Classical signal recovery based on ℓ_1 minimization solves the least squares problem with all available measurements via sparsity-promoting regularization. In practice, it is often the case that not all measurements are available or required for recovery. Measurements might be corrupted/missing or they arrive sequentially in streaming fashion. In this paper, we propose a global sparse recovery strategy based on subsets of measurements, named JOBS, in which multiple measurements vectors are generated from the original pool of measurements via bootstrapping, and then a joint-sparse constraint is enforced to ensure support consistency among multiple predictors. The final estimate is obtained by averaging over the K predictors. The performance limits associated with different choices of number of bootstrap samples L and number of estimates K is analyzed theoretically. Simulation results validate some of the theoretical analysis, and show that the proposed method yields state-of-the-art recovery performance, outperforming ℓ_1 minimization and a few other existing bootstrap-based techniques in the challenging case of low levels of measurements and is preferable over other bagging-based methods in the streaming setting since it performs better with small K and L for data-sets with large sizes.
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