On the Global Minimizers of Real Robust Phase Retrieval With Sparse Noise

We study a class of real robust phase retrieval problems under Gaussian assumption on the coding matrix when received signal is sparsely corrupted by noise. The goal to establish conditions sparsity which input vector can be exactly recovered. recovery problem formulated as residual minimization in ℓ 1 -norm. main contribution counterpart seminal paper Candes and Tao compressed sensing (ℓ regression) [Decoding linear programming. IEEE Transactions Information Theory, 51(12):4203-4215, 2005]. analysis depends key new property called Absolute Range Property (ARP) analogue Null Space (NSP) sensing. When residuals are computed using squared magnitudes, we show that ARP follows from standard Restricted Isometry (RIP). However, absolute different kind RIP or growth required. conclude showing objectives sharp with respect their minimizers high probability.