Fast convergent splitting algorithms for blind phase retrieval with/without sparse prior

       In this talk, we discuss how to design convergent splitting algorithm and improve the quality of reconstructed images driven by the sparse prior. We first consider the bind ptychography problem. We address a general least squares model by maximum likelihood estimation and adopt fast alternating direction method of multipliers to solve it. Under mild conditions, we establish the global convergence to stationary points. Numerically, the proposed algorithm outperforms the state-of-the-art algorithms in both speed and image quality. Then we consider a noisy phase retrieval problem with measured intensities corrupted by strong Gaussian or Poisson noises. Sparse regularization methods, e.g. Total Variation, Dictionary Learning and BM3D filters, are utilized to denoise phaseless measurements, and as a result, the quality of recovery images is greatly increased from noisy (or incomplete) data. This is a joint work with Stefano Marchesini in LBNL, Yifei Lou in UT Dallas, Yuping Duan in Tianjin U., Michael K. Ng and Tieyong Zeng in HKBU.