Ptychography promises diffraction limited resolution without the need for high resolution lenses. To achieve high resolution one has to solve the phase problem for many partially overlapping frames. Here we review some of the existing methods for solving ptychographic phase retrieval problem from a numerical analysis point of view, and propose alternative methods based on numerical optimization.

## Type of Work

Article (101) Book (0) Theses (0) Multimedia (0)

## Peer Review

Peer-reviewed only (92)

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## Campus

UC Berkeley (25) UC Davis (10) UC Irvine (8) UCLA (5) UC Merced (1) UC Riverside (4) UC San Diego (6) UCSF (4) UC Santa Barbara (0) UC Santa Cruz (0) UC Office of the President (0) Lawrence Berkeley National Laboratory (75) UC Agriculture & Natural Resources (0)

## Department

Computing Sciences (65) Energy Sciences (17) School of Medicine (5) Donald Bren School of Information and Computer Sciences (4) Department of Computer Science (4)

Samueli School of Engineering (4) Electrical Engineering and Computer Science (4)

## Journal

Dermatology Online Journal (1)

## Discipline

Engineering (2) Physical Sciences and Mathematics (1)

## Reuse License

BY - Attribution required (12) BY-NC - Attribution; NonCommercial use only (1) BY-NC-ND - Attribution; NonCommercial use; No derivatives (1)

## Scholarly Works (101 results)

We present a practical approach to calculate the complex band structure of an electrode for quantum transport calculations. This method is designed for plane wave based Hamiltonian with nonlocal pseudopotentials and the auxiliary periodic boundary condition transport calculation approach. Currently there is no direct method to calculate all the evanescent states for a given energy for systems with nonlocal pseudopotentials. On the other hand, in the auxiliary periodic boundary condition transport calculation, there is no need for all the evanescent states at a given energy. The current method fills this niche. The method has been used to study copper and gold nanowires and bulk electrodes.

Large-scale eigenvalue problems arise in a number of DOE applications. This paper provides an overview of the recent development of eigenvalue computation in the context of two SciDAC applications. We emphasize the importance of Krylov subspace methods, and point out its limitations. We discuss the value of alternative approaches that are more amenable to the use of preconditioners, and report the progresson using the multi-level algebraic sub-structuring techniques to speed up eigenvalue calculation. In addition to methods for linear eigenvalue problems, we also examine new approaches to solving two types of non-linear eigenvalue problems arising from SciDAC applications.

The three-dimensional reconstruction of macromolecules from two-dimensional single-particle electron images requires determination and correction of the contrast transfer function (CTF) and envelope function. A computational algorithm based on constrained non-linear optimization is developed to estimate the essential parameters in the CTF and envelope function model simultaneously and automatically. The application of this estimation method is demonstrated with focal series images of amorphous carbon film as well as images of ice-embedded icosahedral virus particles suspended across holes.