Deep Plug-and-Play HIO Approach for Phase Retrieval

This nonlinear inverse problem arises in a variety of applications such as microscopy [3, 4], crystallography [5], optical imaging [6, 7], and astronomy [8]. In its most commonly encountered form known as Fourier phase retrieval, the available measurements are Fourier intensities. Due to its nonlinear and ill-posed nature, solving the phase retrieval problem, particularly Fourier phase retrieval, is challenging even though a unique solution can be almost always guaranteed in various practical scenarios of interest [9]. Although several solution approaches exist for the phase retrieval problems, each of them has its own drawbacks. Classical approaches are alternating projection-based methods such as the popular Gerchberg-Saxton (GS), error-reduction and hybrid input-output (HIO) algorithms, and their variants [10, 11]. Such projection-based methods are widely used due to their computational e!ciency, simple implementation and flexibility to be used for di"erent phase retrieval problems. These methods jointly utilize available intensity measurements and information known a priori, and alternate between space and measurement domains to impose these constraints through projections [10-13].