scholarly journals The Restoration of Textured Images Using Fractional-Order Regularization

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Ying Fu ◽  
Xiaohua Li ◽  
Lei Liang ◽  
Yi Zhang ◽  
Jiliu Zhou
Keyword(s):  
Image Restoration ◽  
Fractional Order ◽  
Noise Removal ◽  
Energy Functional ◽  
Edge Preservation ◽  
Gradient Domain ◽  
Nonconvex Energy ◽  
Ill Posed ◽  
Sparse Prior ◽  
Restoration Algorithms

Image restoration problem is ill-posed, so most image restoration algorithms exploit sparse prior in gradient domain to regularize it to yield high-quality results, reconstructing an image with piecewise smooth characteristics. While sparse gradient prior has good performance in noise removal and edge preservation, it also tends to remove midfrequency component such as texture. In this paper, we introduce the sparse prior in fractional-order gradient domain as texture-preserving strategy to restore textured images degraded by blur and/or noise. And we solve the unknown variables in the proposed model using method based on half-quadratic splitting by minimizing the nonconvex energy functional. Numerical experiments show our algorithm's robust outperformance.

Image Denoising Based on Reaction-Diffusion Equation and Curvelet Transform

2010 ◽  
Vol 40-41 ◽  
pp. 554-559
Author(s):  
Yi Mei Song ◽  
Xiao Qing Shang
Keyword(s):  
Image Denoising ◽  
Curvelet Transform ◽  
Reaction Diffusion ◽  
Speckle Noise ◽  
Noise Removal ◽  
Energy Functional ◽  
Reaction Diffusion Equation ◽  
Ill Posed ◽  
Diffusion Function ◽  
Improved Model

To reduce the pseudo-Gibbs effects and the “curvelet like” aliased curves resulted from using curvelet transform for image denoising, we proposed a noise removal method which combines computational harmonic analysis and variation. Firstly, we presented a nonlinear reaction-diffusion digital filter based on Nordström energy functional. For effectively overcoming speckle noise due to the reaction-diffusion process of digital filtering and the ill-posed of diffusion coefficient, we gave an improved model by introducing curvelet smoothing operator and the new diffusion function. Numerical results show that the model is not only for images with Gaussian noise, Salt&pepper noise or Speckle noise, but also suitable for mixed noise, the denoised image has higher PSNR and good visual effect.

scholarly journals A Novel Fractional-Order Variational Approach for Image Restoration Based on Fuzzy Membership Degrees

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Mushtaq Ahmad Khan ◽  
Asmat Ullah ◽  
Sahib Khan ◽  
Murtaza Ali ◽  
Sheraz Khan ◽  
...  
Keyword(s):  
Image Restoration ◽  
Fractional Order ◽  
Variational Approach ◽  
Fuzzy Membership

Fast Adaptive Iterative Image Restoration Algorithms

1988 ◽  
Author(s):  
Serafim N. Efstratiadis ◽  
Aggelos K. Katsaggelos
Keyword(s):  
Image Restoration ◽  
Restoration Algorithms

Nonconvex-TV Based Image Restoration with Impulse Noise Removal

2017 ◽  
Vol 10 (3) ◽  
pp. 1627-1667 ◽  
Author(s):  
Xiongjun Zhang ◽  
Minru Bai ◽  
Michael K. Ng
Keyword(s):  
Image Restoration ◽  
Impulse Noise ◽  
Noise Removal ◽  
Impulse Noise Removal

scholarly journals HST Image Restoration: Current Capabilities and Future Prospects

1994 ◽  
Vol 158 ◽  
pp. 61-69 ◽  
Author(s):  
Robert J. Hanisch ◽  
Richard L. White
Keyword(s):  
Image Restoration ◽  
Dynamic Range ◽  
Hubble Space Telescope ◽  
Spherical Aberration ◽  
Wide Field ◽  
Secondary Mirror ◽  
Faint Object ◽  
Spread Function ◽  
Restoration Algorithms ◽  
Space Variant

The spherical aberration in the primary mirror of the Hubble Space Telescope causes more than 80% of the light from a point source to be spread into a halo of radius of 2–3 arcsec. The point spread function (PSF) is both time variant (resulting from spacecraft jitter and desorption of the secondary mirror support structure) and space variant (owing to the Cassegrain repeater optics in the Wide Field / Planetary Camera). A variety of image restoration algorithms have been utilized on HST data with some success, although optimal restorations require better modeling of the PSF and the development of efficient restoration algorithms that accommodate a spacevariant PSF. The first HST servicing mission (December 1993) will deploy a corrective optics system for the Faint Object Camera and the two spectrographs and a second generation WF/PC with internal corrective optics. As simulations demonstrate, however, the restoration algorithms developed now for aberrated images will be very useful for removing the remaining diffraction features and optimizing dynamic range in post-servicing mission data.

scholarly journals An adaptive model combining a total variation filter and a fractional-order filter for image restoration

2019 ◽  
Vol 13 ◽  
pp. 174830181983305 ◽  
Author(s):  
Yafeng Yang ◽  
Donghong Zhao
Keyword(s):  
Image Restoration ◽  
Total Variation ◽  
Fractional Order ◽  
Gradient Algorithm ◽  
Remarkable Effect ◽  
Order Filter ◽  
Model Combining ◽  
Proposed Model ◽  
Primal Dual ◽  
Image Edges

In this paper, we propose a model that combines a total variation filter with a fractional-order filter, which can unite the advantages of the two filters, and has a remarkable effect in the protection of image edges and texture details; simultaneously, the proposed model can eliminate the staircase effect. In addition, the model improves the PSNR compared with the total variation filter and the fractional-order filter when removing noise. Zhu and Chan presented the primal-dual hybrid gradient algorithm and proved that it is effective for the total variation filter. On the basis of their work, we employ the primal-dual hybrid gradient algorithm to solve the combined model in this article. The final experimental results show that the new model and algorithm are effective for image restoration.

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