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Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform
Published on: February 12, 2014
Convergence of the Schulz-Snyder phase retrieval algorithm to local minima
Kerkil Choi1, Aaron D Lanterman, Raviv Raich
1School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA. kerkil@untu.edu
Summary
The Schulz-Snyder algorithm for phase retrieval can get stuck in local minima. This study provides conditions and tests to identify these local minima in image reconstruction.
Area of Science:
- Image processing
- Computational imaging
- Applied mathematics
Background:
- Phase retrieval algorithms aim to reconstruct images from limited measurements.
- The Schulz-Snyder algorithm is an iterative method for phase retrieval using autocorrelation.
- Minimizing I-divergence is a common objective in this algorithm.
Purpose of the Study:
- To investigate the convergence properties of the Schulz-Snyder algorithm.
- To identify conditions under which the algorithm may converge to a local minimum.
- To provide methods for verifying local minimality of retrieved estimates.
Main Methods:
- Analysis of the I-divergence surface using gradient and Hessian matrix properties.
- Development of sufficient conditions for local minima.
- Implementation of numerical tests to assess estimate minimality.
Main Results:
- Demonstration that the Schulz-Snyder algorithm can be trapped in local minima.
- Sufficient conditions for identifying local minima are derived.
- Numerical tests confirm the local minimality of certain estimates.
Conclusions:
- The Schulz-Snyder algorithm's susceptibility to local minima is confirmed.
- The derived conditions offer a means to detect and potentially avoid suboptimal solutions.
- Further examination of numerical issues and phenomena in phase retrieval is warranted.
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