Improved Error Reduction and Hybrid Input Output Algorithms for Phase Retrieval by including a Sparse Dictionary Learning-Based Inpainting Method

Abstract EN

The phase retrieval (PR), reconstructing an object from its Fourier magnitudes, is equivalent to a nonlinear inverse problem.

In this paper, we proposed a two-step algorithm that traditional ER/HIO iteration plays as the coarse feature reconstruction, whereas the KSVD-based inpainting technique deals with the fine feature set accordingly.

Since the KSVD allows the content of oversampled dictionary with sparse representation to adaptively fit a given set of object examples, as long as the ER/HIO algorithms provide decent object estimation at early stage, the pixels violating the object constraint can be restored with superior image quality.

The numerical analyses demonstrated the effectiveness of ER + KSVD and HIO + KSVD through multiple independent initial Fourier phases.

With its versatility and simplicity, the proposed method can be generalized to be implemented with more PR state-of-the-arts.