Sparsity-assisted solution to the twin image problem in phase retrieval.

The problem of iterative phase retrieval from Fourier transform magnitude data for complex-valued objects is known to suffer from the twin image problem. In particular, when the object support is centrosymmetric, the iterative solution often stagnates such that the resultant complex image contains the features of both the desired solution and its inverted and complex-conjugated replica. In this work we make an important observation that the ideal solution without the twin image is typically more sparse in some suitable transform domain as compared to the stagnated solution. We further show that introducing a sparsity-enhancing step in the iterative algorithm can address the twin image problem without the need to change the object support throughout the iterative process even when the object support is centrosymmetric. In a simulation study, we use binary and gray-scale pure phase objects and illustrate the effectiveness of the sparsity-assisted phase recovery in the context of the twin image problem.