  Classical signal recovery based on $\ell_1$ 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 $\ell_1$ 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.
