Compressive phase retrieval via complex constrained total variation regularization

The imaging quality of inline digital holography is challenged by the twin-image artefact because the phase retrieval problem is severely ill-conditioned. Sparsity-promoting regularizers such as the total variation (TV) seminorms have been explored to tackle the ill-posedness and proved effective in modeling real-world objects. However, previous works are mainly based on the TV seminorms for real-valued images, which limit their application in digital holography where we are often dealing with complex-valued signals. In this work, we introduce the complex constrained TV regularizers and propose an efficient proximal gradient algorithm for solving the phase retrieval problem. The proposed complex TV model and the corresponding algorithm are verified by numerical and experimental results. We believe that the proposed algorithmic framework can cast new light on solving a large class of optimization problems based on complex constrained TV regularization.