Sparse disjointed recovery from noninflating measurements

We investigate the minimal number of linear measurements needed to recover sparse disjointed vectors robustly in the presence of measurement error. First, we analyze an iterative hard thresholding algorithm relying on a dynamic program computing sparse disjointed projections to upper-bound the order of the minimal number of measurements. Next, we show that this order cannot be reduced by any robust algorithm handling noninflating measurements. As a consequence, we conclude that there is no benefit in knowing the simultaneity of sparsity and disjointedness over knowing only one of these structures.