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Reconstruction of complex signals using minimum Rényi information
Applied Optics
|November 6, 2010
Summary
Rényi
Area of Science:
- Image reconstruction
- Information theory
- Signal processing
Background:
- Information divergence quantifies distance between probability distributions.
- Amari's α-divergences offer desirable properties like convexity.
- Rényi's information Dα is a convex α-divergence.
Purpose of the Study:
- To apply Rényi's information Dα for image reconstruction.
- To leverage convexity for efficient minimization.
- To reconstruct complex images, such as in inverse synthetic-aperture radar imaging.
Main Methods:
- Minimizing Dα to achieve minimum distance between images.
- Replacing probabilities with complex amplitudes in the Rényi form.
- Constructing a bias image from a smoothed linear Fourier reconstruction.
Main Results:
- The Rényi reconstruction approach enables superresolution in low-noise scenarios.
- Higher fidelity is achieved compared to linear reconstructions in noisy cases.
- Simulated data demonstrated the effectiveness of the method.
Conclusions:
- Rényi's information Dα provides an effective method for image reconstruction.
- The approach offers advantages in both low-noise (superresolution) and high-noise (fidelity) conditions.
- This technique is valuable for complex image reconstruction tasks.
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