Abstract

Simplicity and few finely tuned parameters are the main advantages of alternating projection (AP) methods, a fundamental class of phase retrieval (PR) methods in the optical imaging field. However, AP methods often suffer from low-quality imaging when few diffraction patterns are recorded. Regularized PR methods avoid this deficiency by using some proper regularization models, but many finely tuned parameters are needed. In this work, we propose a novel unified framework called constrained PR (ConPR), which brings the AP method and the regularization approach together. The proposed ConPR framework not only can recover high-quality images from few diffraction patterns, but also does not need fine-tuning of the parameters. Our proposed generalized constrained PR optimization model consists of a relation function term, a regularization term, and a measurement constraint. The measurement constraint ensures that the recovered image matches with the measurement, and the regularization term can impose some desirable properties on the recovered image. The relation function promotes the approximation of the two underlying variables. The sparsity under the block-matching and 3D filtering frame is incorporated into the proposed ConPR framework. The problem formulation consists of an image updating sub-problem and a constrained optimization sub-problem. The epigraph set of the data fidelity function is defined, and the constrained optimization sub-problem is solved via the epigraph concept. Diffraction imaging from one noisy coded diffraction pattern demonstrates the effectiveness of the proposed algorithm.

© 2018 Optical Society of America

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