Ptychographic Algorithm Using Dual-Tree Complex Wavelet Transform

Abstract

Reconstructing the interesting complex image from multiple diffraction patterns is the goal of the ptychography. Previous ptychographic algorithms often suffer from low reconstruction quality under the low overlap ratios. To address this issue, we proposed a novel ptychographic phase retrieval (PR) algorithm of exploiting the sparsity of the image in dual-tree complex wavelet domain. The Fourier magnitude measurements are utilized to construct a data fidelity term, and the sparse representation model of the image over the dual-tree complex wavelet transform is utilized for the sparse induced regularization term. The data fidelity term and the proposed regularization term are combined to formulate a ptychographic PR optimization problem. Alternating direction method of multipliers (ADMM) and gradient descent algorithm are utilized for solving the corresponding optimization problem. Compared with previous algorithms, the experimental results indicate that the proposed algorithm can obtain reconstructed images with high quality even at low overlap ratios.