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Sparse image reconstruction on the sphere: implications of a new sampling theorem.
Jason D McEwen1, Gilles Puy, Jean-Philippe Thiran
1Department of Physics and Astronomy, University College London, London WC1E 6BT, UK. jason.mcewen@ucl.ac.uk
Summary
A new sampling theorem for spherical data improves sparse image reconstruction fidelity. By reducing required samples, it enhances accuracy in tasks like inpainting, especially for gradient-sparse images.
Area of Science:
- Spherical signal processing
- Computational imaging
- Applied mathematics
Background:
- Sparse image reconstruction aims to recover signals from limited data.
- Band-limited signals on the sphere require specific sampling strategies.
- Efficient sampling is crucial for high-fidelity reconstruction.
Purpose of the Study:
- To investigate the impact of sampling theorems on sparse image reconstruction fidelity on the sphere.
- To demonstrate how reduced sampling requirements enhance reconstruction accuracy.
- To analyze the benefits for gradient-sparse images and inpainting problems.
Main Methods:
- Developed a framework for total variation inpainting on the sphere.
- Incorporated fast computational methods for high-resolution feasibility.
- Utilized a recent sampling theorem reducing sample requirements by half for equiangular schemes.
Main Results:
- Showcased improved fidelity in sparse image reconstruction due to efficient sampling.
- Verified enhanced reconstruction accuracy through numerical simulations.
- Demonstrated the benefits for inpainting problems with gradient-sparse images.
Conclusions:
- Reduced sampling requirements significantly improve sparse image reconstruction fidelity on the sphere.
- The new sampling theorem offers substantial advantages for spherical data processing.
- Efficient sampling is key to accurate and computationally feasible high-resolution image reconstruction.
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