Phase retrieval (PR) consists of recovering complex-valued objects from their oversampled Fourier magnitudes and takes a central place in scientific imaging. A critical issue around PR is the typical nonconvexity in natural formulations and the associated bad local minimizers. The issue is exacerbated when the support of the object is not precisely known and hence must be overspecified in practice. Practical methods for PR hence involve convolved algorithms, e.g., multiple cycles of hybrid input-output (HIO) + error reduction (ER), to avoid the bad local minimizers and attain reasonable speed, and heuristics to refine the support of the object, e.g., the famous shrinkwrap trick. Overall, the convolved algorithms and the support-refinement heuristics induce multiple algorithm hyperparameters, to which the recovery quality is often sensitive. In this work, we propose a novel PR method by parameterizing the object as the output of a learnable neural network, i.e., deep image prior (DIP). For complex-valued objects in PR, we can flexibly parametrize the magnitude and phase, or the real and imaginary parts separately by two DIPs. We show that this simple idea, free from multi-hyperparameter tuning and support-refinement heuristics, can obtain superior performance than gold-standard PR methods. For the session: Computational Imaging using Fourier Ptychography and Phase Retrieval.
In most optic systems images are captured using a CCD/CMOS sensor, where the phases of the converted photons are inevitably lost. Fourier Ptychographic Microscopy (FPM) circumvents this issue by capturing normal microscopy images, and Fourier transforming them computationally (hence the name). Reconstructing the complex object not only yields amplitude but also phase information, enhanced up to super-resolution. Yet one disadvantage remains unsolved: FPM is a very ill-posed problem, the algorithm is not guaranteed to converge to the correct solution, if it converges at all. In practice this means that there is reasonable doubt if the recovered image actually represents the object under the microscope. This work inquires the quality of FPM reconstruction under variation of important system parameters in simulation and experiment. It shows that the alignment of the illumination source is quite critical: even 0.2 degrees off renders reconstruction useless. This paper thus furthers the costbenefit analysis of which amount of computation time should be spent on digital post-correction.