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Nonlinear approaches for the single-distance phase retrieval problem involving regularizations with sparsity
Valentina Davidoiu1, Bruno Sixou, Max Langer
1Université de Lyon, CREATIS, CNRS UMR5220, Inserm U1044, INSA-Lyon, Université Lyon 1, Lyon, France. valentina.davidoiu@creatis.insa-lyon.fr
Applied Optics
|June 14, 2013
Summary
This study compares nonlinear phase retrieval methods using sparsity constraints. The first method, combining Fréchet derivative and iterative thresholding, significantly reduces reconstruction errors compared to linear approaches.
Area of Science:
- X-ray imaging
- Computational imaging
- Applied mathematics
Background:
- Phase retrieval is a nonlinear, ill-posed problem crucial for imaging.
- Hard X-ray synchrotron diffraction patterns offer phase contrast information.
- Sparsity constraints enhance phase retrieval accuracy.
Purpose of the Study:
- To compare the convergence of nonlinear phase retrieval algorithms.
- To evaluate methods incorporating sparsity constraints in wavelet bases.
- To identify superior nonlinear approaches for phase retrieval.
Main Methods:
- Developed and tested two nonlinear phase retrieval algorithms with sparsity constraints.
- Algorithm 1: Alternating Fréchet derivative and iterative thresholding in wavelet coordinates.
- Algorithm 2: Ramlau-Teschke generalization of classical thresholding.
- Evaluated on a 3D Shepp-Logan phantom with Gaussian noise.
Main Results:
- The first method demonstrated superior convergence and accuracy across various noise levels.
- Significantly reduced reconstruction errors compared to classical linear methods.
- Effective phase retrieval achieved even with noisy data.
Conclusions:
- Nonlinear phase retrieval with sparsity constraints offers substantial improvements.
- The proposed Fréchet derivative and iterative thresholding method is highly effective.
- This approach advances hard X-ray imaging and phase contrast techniques.
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