A Graduated Non-Convexity Technique for Dealing Large Point Spread Functions

This paper focuses on reducing the computational cost of a GNC Algorithm for deblurring images when dealing with full symmetric Toeplitz block matrices composed of Toeplitz blocks. Such a case is widespread in real cases when the PSF has a vast range. The analysis in this paper centers around the cl...

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Bibliographic Details
Published in:Applied sciences 2023-05, Vol.13 (10), p.5861
Main Authors: Boccuto, Antonio, Gerace, Ivan, Giorgetti, Valentina
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Energy
GNC technique
image deblurring
image denoising
Image processing
Image quality
Methods
Operators (mathematics)
Optimization
Partial differential equations
Point spread functions
Signal processing
Space telescopes
Toeplitz matrix approximation
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Summary:This paper focuses on reducing the computational cost of a GNC Algorithm for deblurring images when dealing with full symmetric Toeplitz block matrices composed of Toeplitz blocks. Such a case is widespread in real cases when the PSF has a vast range. The analysis in this paper centers around the class of gamma matrices, which can perform vector multiplications quickly. The paper presents a theoretical and experimental analysis of how γ-matrices can accurately approximate symmetric Toeplitz matrices. The proposed approach involves adding a minimization step for a new approximation of the energy function to the GNC technique. Specifically, we replace the Toeplitz matrices found in the blocks of the blur operator with γ-matrices in this approximation. The experimental results demonstrate that the new GNC algorithm proposed in this paper reduces computation time by over 20% compared with its previous version. The image reconstruction quality, however, remains unchanged.
ISSN:2076-3417
2076-3417
DOI:10.3390/app13105861