BM3D-PRGAMP: Compressive phase retrieval based on BM3D denoising

The explosion of computational imaging has seen the frontier of image processing move past linear problems, like denoising and deblurring, and towards non-linear problems such as phase retrieval. There has a been a corresponding research thrust into non-linear image recovery algorithms, but in many ways this research is stuck where linear problem research was twenty years ago: Models, if used at all, are simple designs like sparsity or smoothness. In this paper we use denoisers to impose elaborate and accurate models in order to perform inference on generalized linear systems. More specifically, we use the state-of-the-art BM3D denoiser within the Generalized Approximate Message Passing (GAMP) framework to solve compressive phase retrieval in a variety of different contexts. Our method demonstrates recovery performance equivalent to existing techniques using fewer than half as many measurements. This dramatic improvement in compressive phase retrieval performance opens the door for a whole new class of imaging systems.