TV-based phase retrieval for speckle coded diffraction imaging

Speckle coded diffraction imaging (SCDI) has emerged as a new and developing lensless imaging method, which provides an effective imaging method for dense and connected objects. The conventional alternating-projection-based phase retrieval algorithm for SCDI relies on phase constraints between multiple diffraction images, and its disadvantage is that it often necessitates a large number of measurements to ensure high-quality reconstruction. In order to reduce the measurements, we propose to regularize the non-convex phase retrieval with total variation (TV)–based prior, and thus construct the TV-based cost function for SCDI. The alternating direction method is used to solve the nonlinear cost function, and recover the object and unknown speckle illumination. As both simulations and experiments demonstrate, the proposed TV-based reconstruction algorithm can recover the complex object and the unknown speckle pattern with high fidelity using 16 measurements, compared with hundreds of measurements used for AP-based algorithm.