Phase retrieval with sparsity priors and application to microscopy video reconstruction

The theory of compressed sensing (CS) predicts that structured images can be sampled in a compressive manner with very few nonadaptive linear measurements, made in a proper adjacent domain. However, is such a recovery still possible with non-linear measurements, such as optical-based Fourier modulus? In this paper, we study the problem of Fourier phase retrieval required for optical Fourier CS imaging. We propose an algorithm to solve this problem, exploiting a specific TV-based regularization constraint. We demonstrate the performance of the proposed method on synthetic and real test sequences, in the context of microscopy video reconstructions.