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Mathematical extrapolation of image spectrum for constraint-set design and set-theoretic superresolution
Supratik Bhattacharjee1, Malur K Sundareshan
1Department of Electrical and Computer Engineering, University of Arizona, Tucson, Arizona 85721-0104, USA.
Summary
This study introduces a novel method for image super-resolution and restoration. It enhances image spectrum extrapolation, enabling super-resolution by expanding the image bandwidth beyond sensor limits.
Area of Science:
- Image processing
- Computational imaging
- Optical engineering
Background:
- Iterative algorithms are used for image restoration and super-resolution.
- Current methods treat spectrum extrapolation as a byproduct, requiring post-processing verification.
- This limits the direct control and assessment of resolution enhancement.
Purpose of the Study:
- To develop a new approach for image super-resolution and restoration.
- To directly incorporate mathematical image spectrum extrapolation into algorithm design.
- To improve the control and verification of super-resolution performance.
Main Methods:
- Mathematically extrapolating the image spectrum.
- Designing constraint sets for set-theoretic estimation procedures.
- Evaluating a projection-onto-convex-sets algorithm with the new approach.
Main Results:
- The presented method allows for direct spectrum extrapolation for super-resolution.
- It enables the design of constraint sets for improved image restoration.
- Performance evaluation demonstrates the effectiveness for degraded images.
Conclusions:
- The novel approach integrates spectrum extrapolation directly into the super-resolution process.
- This method offers enhanced control over image bandwidth expansion.
- It provides a more direct pathway to achieving super-resolution beyond sensor limitations.