Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems

By Amir Beck, Marc Teboulle. IEEE Transactions on Image Processing, 2009

2,045 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c9dcc1933139d3dce3a80cfb267fb5c02a090155

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Citations in the corpus

This is SPIRAL-TAP: Sparse Poisson Intensity Reconstruction ALgorithms—Theory and Practice (2010, background): “Regularization based on a total variation (TV) seminorm has also garnered signiﬁcant recent attention (cf. [29], [30]).”
Proximal Splitting Methods in Signal Processing (2009, methodology): “The proximal gradient method proposed in [15, 16 ] assumes the following form.”
Centralized sparse representation for image restoration (2011, methodology): “(a) Noisy and blurred; (b) FISTA [2] (PSNR=27.75 dB); (c) BM3D [11] (PSNR=28.61dB); (d) the proposed CSR (PSNR=30.30 dB).”
FISTA-Net: Learning a Fast Iterative Shrinkage Thresholding Network for Inverse Problems in Imaging (2020, methodology): “2) Comparison Study: Four state-of-the-art methods were compared against FISTA-Net, including FBP, FISTA-TV, FBP-ConvNet, and MoDL.”
Fixed-Point Algorithms for Inverse Problems in Science and Engineering (2011, neutral): “Beck [15] presented developments in the spirit of his recent work in image recovery [16, 17] that aim at improving acceleration techniques originally proposed by Nesterov [72].”
Deblurring Poissonian images by split Bregman techniques (2010, methodology): “For solving (5), we decided to use the gradient descent reprojection algorithm [10], since it outperformed the FISTA algorithm [13] due to the fact that using the inner loop initialization described above the number of iterations needed per loop decreased faster for the gradient descent reprojection”
On Nesterov acceleration for Landweber iteration of linear ill-posed problems (2016, background): “, [1, 2, 5, 8]) As far as we know, even for linear ill-posed problems (1.”
Nonlocally Centralized Sparse Representation for Image Restoration (2013, methodology): “We compared the NCSR deblurring method with four stateof-the-art deblurring methods, including the constrained TV deblurring (denoted by FISTA) method [35], the l 0 -sparsity based deblurring (denoted by l 0 -SPAR) method [36] , the TABLE I PSNR (dB) RESULTS BY DIFFERENT DENOISING METHODS.”
PyHST2: an hybrid distributed code for high speed tomographic reconstruction with iterative reconstruction and a priori knowledge capabilities (2013, positive): “In PyHST, the iterative shrinkage-thresholding algorithm [17] (ISTA) or the accelerated FISTA (fast ISTA) [18] algorithm can be used to solve the problem (3).”
A General Framework for a Class of First Order Primal-Dual Algorithms for Convex Optimization in Imaging Science (2010, background): “As discussed in [2], where this application is referred to as FGP, it can be thought of as an acceleration of gradient projection.”
Constrained 1-Spectral Clustering (2012, methodology): “The smooth dual problem can be solved efficiently using first order projected gradient methods like FISTA [2], which has a guaranteed convergence rate of O( L k2 ), where k is the number of steps, and L is the Lipschitz constant of the gradient of the objective.”
Image denoising using deep CNN with batch renormalization (2020, background): “Weighted nuclear norm minimization (WNNM) [19], markov random ﬁeld (MRF) [43, 1, 2], gradient methods [3, 69] and total-variation (TV) methods [49, 5] are also very popular image-denoising methods.”
On a generalization of the iterative soft-thresholding algorithm for the case of non-separable penalty (2011, neutral): “The combination of a gradient step with the dual algorithm (20) has been proposed several times already [10, 11]; as such that would not be an explicit algorithm as it requires infinitely many dual iterations in each outer iteration.”
Infimal convolution regularizations with discrete ℓ1-type functionals (2011, methodology): “The fast iterative shrinkage threshold algorithm (FISTA) of Beck and Teboulle [3, 4] was applied with outer and inner FISTA loops, e.”