Before revision:  We prove theoretically that MISTR correctly recovers most signals distributed as a Gaussian point process  as long as sparsity is at most O \left( N ^{ D(}\right)  1/2 - \delta)}\left( \right) .
After revision:  We prove theoretically that MISTR correctly recovers most signals distributed as a Gaussian point process as long as sparsity is at most O \left( N ^{ D(}\right) 1/2 , where n^d represents pixel size in a fixed image window. In the case that magnitude measurements are corrupted by noise, we provide a thresholding scheme with theoretical guarantees for sparsity at most \mathcal{O}\left( \right) .