Deep prior-based sparse representation model for diffraction imaging: A plug-and-play method

Diffraction imaging problem, i.e. recovery of a high-resolution or high-quality image from the intensity diffraction pattern, arises in many science and engineering fields. Recent efforts to solve this problem are exploiting sparse representation techniques. However, existing sparse representation models cannot explore inherent priors of the images to be reconstructed sufficiently. Imaging algorithms employed such traditional sparse representation models often suffer from low-quality reconstructions in the case of the noise or low-resolution observation. To address this issue, we propose a deep prior-based sparse representation (DPSR) regularization model that can impose the sparsity and the deep prior on the unknown image. The DPSR model is a plug-and-play model, namely that one can plug any effective deep denoiser into this model. We apply this model to coded diffraction imaging. To perform high-resolution imaging, a sub-pixel resolution coded diffraction pattern observation model is proposed. Based on this observation model, a diffraction imaging optimization problem is formulated. The formulated optimization problem is tackled by using the alternating optimization strategy and the epigraph concept. Compared to the benchmark diffraction imaging algorithms, the proposed algorithm has a notable peak signal-to-noise ratio (PSNR) gain of about 2 dB. Meanwhile, the proposed algorithm can perform high-resolution diffraction imaging with the pixel super-resolution factor of 4 under the single observation case. A demo code of the proposed algorithm is available at https://github.com/shibaoshun/DPSR.