Proximal Heterogeneous Block Input-Output Method and application to Blind Ptychographic Diffraction Imaging
Provides a theoretically grounded and provably convergent algorithm for blind ptychographic imaging, a problem in computational imaging.
The paper proposes a general alternating minimization algorithm for nonconvex optimization with separable structure and nonconvex coupling, applied to blind ptychographic imaging. The algorithm is provably convergent under verifiable assumptions and outperforms state-of-the-art methods on simulated and experimental data.
We propose a general alternating minimization algorithm for nonconvex optimization problems with separable structure and nonconvex coupling between blocks of variables. To fix our ideas, we apply the methodology to the problem of blind ptychographic imaging. Compared to other schemes in the literature, our approach differs in two ways: (i) it is posed within a clear mathematical framework with practically verifiable assumptions, and (ii) under the given assumptions, it is provably convergent to critical points. A numerical comparison of our proposed algorithm with the current state-of-the-art on simulated and experimental data validates our approach and points toward directions for further improvement.