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Published on: January 28, 2019
Optimal reconstruction of images from localized phase
1Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel.
Summary
Localized phase is crucial for signal representation and image reconstruction. Geometric images reconstruct best from spectral phase using the projection onto convex sets (POCS) algorithm, unlike symmetric images.
Area of Science:
- Signal processing
- Image reconstruction
- Computational imaging
Background:
- Localized phase is a key component in signal representation.
- Spectral phase information is vital for reconstructing images.
- The projection onto convex sets (POCS) algorithm is commonly used for image reconstruction.
Purpose of the Study:
- To investigate the significance of localized phase in signal representation.
- To analyze the convergence rate of the POCS algorithm for phase-only image reconstruction.
- To characterize images that are optimally reconstructed from phase-only information.
Main Methods:
- Analysis of the convergence rate of the POCS algorithm.
- Characterization of image properties related to phase-only reconstruction.
- Investigation of localized versus global phase representation approaches.
Main Results:
- The POCS algorithm's convergence rate for spectral phase-based image reconstruction is defined and analyzed.
- Images with geometric forms are most efficiently reconstructed from spectral phase.
- Images with symmetric forms exhibit the poorest convergence characteristics.
- A continuous transition is observed between geometric and symmetric image reconstruction behaviors.
Conclusions:
- Localized phase representation offers advantages over global approaches for specific image types.
- Geometric images are best reconstructed using spectral phase information.
- Symmetric images present challenges for phase-only reconstruction.
- The findings suggest potential for novel image compression schemes based on phase information.
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