Applications of algorithmic differentiation to phase retrieval algorithms.
@article{Jurling2014ApplicationsOA,
title={Applications of algorithmic differentiation to phase retrieval algorithms.},
author={Alden S. Jurling and James R. Fienup},
journal={Journal of the Optical Society of America. A, Optics, image science, and vision},
year={2014},
volume={31 7},
pages={
1348-59
}
}In this paper, we generalize the techniques of reverse-mode algorithmic differentiation to include elementary operations on multidimensional arrays of complex numbers. We explore the application of the algorithmic differentiation to phase retrieval error metrics and show that reverse-mode algorithmic differentiation provides a framework for straightforward calculation of gradients of complicated error metrics without resorting to finite differences or laborious symbolic differentiation.
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References
SHOWING 1-10 OF 20 REFERENCES
Evaluating derivatives - principles and techniques of algorithmic differentiation, Second Edition
- BiologyFrontiers in applied mathematics
- 2000
This second edition has been updated and expanded to cover recent developments in applications and theory, including an elegant NP completeness argument by Uwe Naumann and a brief introduction to scarcity, a generalization of sparsity.
Algorithm 755: ADOL-C: a package for the automatic differentiation of algorithms written in C/C++
- Computer ScienceTOMS
- 1996
The C++ package ADOL-C described here facilitates the evaluation of first and higher derivatives of vector functions that are defined by computer programs written in C or C++. The resulting…
Phase retrieval algorithms: a comparison.
- Computer ScienceApplied optics
- 1982
Iterative algorithms for phase retrieval from intensity data are compared to gradient search methods and it is shown that both the error-reduction algorithm for the problem of a single intensity measurement and the Gerchberg-Saxton algorithm forThe problem of two intensity measurements converge.
Phase-retrieval algorithms for a complicated optical system.
- MathematicsApplied optics
- 1993
Improved algorithms permit a more accurate characterization of complicated optical systems from their point spread functions, independent of the number of coefficients or phase points.
The Tapenade automatic differentiation tool: Principles, model, and specification
- Computer ScienceTOMS
- 2013
The principles of Tapenade are described, a subset of the general principles of AD, and the extensions of the tool that are planned in a foreseeable future are presented, deriving from the ongoing research on AD.
Graph-Based Software Design for Managing Complexity and Enabling Concurrency in Multiphysics PDE Software
- Computer ScienceTOMS
- 2012
This work presents a design strategy that shifts focus away from high-level algorithmic concerns to low-level data dependencies, and makes problems with complex dependencies entirely tractable, and removes virtually all logic from the algorithm itself.
Phase retrieval for undersampled broadband images
- Physics
- 1999
Generalizations of phase-retrieval algorithms, which accommodate broadband light, allow for undersampled images, permit fitting of multiple images simultaneously, and have a flexible description of the aberrations, are described in this study.
Quasi-Newton Methods
- Mathematics
- 1978
The problem to be solved is formulated precisely and the introduction of quasi-Newton methods is motivated by considering the classical Newton and secant methods and their properties. Three highly…
Joint estimation of object and aberrations by using phase diversity
- Physics
- 1992
The joint estimation of an object and the aberrations of an incoherent imaging system from multiple images incorporating phase diversity is investigated and an expectation-maximization algorithm that enforces a nonnegativity constraint in a natural fashion is constructed for use in the Poisson noise case.
