Sparse Affine Sampling: Ambiguity-Free and Efficient Sparse Phase Retrieval

Conventional sparse phase retrieval schemes can recover signals from the magnitude of linear measurements only up to a global ambiguity. This work proposes novel approach that instead utilizes affine achieve ambiguity-free signal reconstruction. The proposed method relies on two-stage consists support identification followed by exact recovery nonzero entries. In noise-free case, perfect using simple counting rule is guaranteed subject mild condition sparsity, and subsequent entries be obtained in closed-form. then extended two noisy scenarios, namely, noise (or outliers) non-sparse bounded noise. For both cases, still ensured under conditions model, size for outliers power Under identification, achieved majority scenario, reconstruction error least-squares (LS) estimation scenario. analytic performance guarantee latter case also sheds light construction sensing matrix bias vector. fact, we show near optimal with high probability random generation vector according uniform distribution over circle. Computer simulations synthetic real-world data sets are provided demonstrate effectiveness scheme.