An Iterative Regularization Method for Total Variation-Based Image Restoration

By Stanley J. Osher, Martin Burger, Donald Goldfarb, Jinjun Xu, Wotao Yin. 2005

1,957 citations recorded by the source corpus.

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

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Citations in the corpus

Context Encoders: Feature Learning by Inpainting (2016, background): “Inpainting and hole-filling It is important to point out that our hole-filling task cannot be handled by classical inpainting [4, 32] or texture synthesis [2, 11] approaches, since the missing region is too large for local non-semantic methods to work well.”
Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising (2016, background): “Over the past few decades, various models have been exploited for modeling image priors, including nonlocal self-similarity (NSS) models [1], [2], [3], [4], sparse models [4], [5], [6], gradient models [7], [8], [9] and Markov random ﬁeld (MRF) models [10], [11], [12].”
NTIRE 2017 Challenge on Single Image Super-Resolution: Dataset and Study (2017, background): “Single image super-resolution as well as image restoration research literature spans over decades [36, 20, 4, 13, 16, 3, 15, 14, 6, 32, 54, 30, 17, 23, 12, 47, 48, 10, 21].”
Total-Variation-Regularized Low-Rank Matrix Factorization for Hyperspectral Image Restoration (2016, methodology): “The TV-based algorithm is a very popular denoising approach because of its effectiveness in preserving edge information and the spatial piecewise smoothness [13], [14].”
A Nonlinear Inverse Scale Space Method for a Convex Multiplicative Noise Model (2008, methodology): “It differs from the minimization in [5, 21], because in [17] the authors replaced λ by λ2k−1, resulting in the following TV minimization: (5.”
Image Super-Resolution by TV-Regularization and Bregman Iteration (2008, methodology): “This procedure is based on an original idea by Bregman [1] and is similar to the one suggested and implemented in [7, 13] for image restoration problems.”
A Probabilistic Method for Image Enhancement With Simultaneous Illumination and Reflectance Estimation (2015, methodology): “This operation is the similar to “adding back the noise” used in TV denoising [40].”
Beyond Deep Residual Learning for Image Restoration: Persistent Homology-Guided Manifold Simplification (2016, background): “Over the last few decades, various algorithms have been developed, which include non-local self-similarity (NSS) models [2], total variation (TV) approaches [22], and sparse dictionary learning models [9].”
A Harmonic Extension Approach for Collaborative Ranking (2016, methodology): “To solve the above optimization problem, we first use the Bregman iteration to enforce the constraint [15].”
Sparsity-based image denoising via dictionary learning and structural clustering (2011, methodology): “If we choose to model both α⃗ and γ⃗ by i.i.d. Laplacian distribution, the prior model is given by P (α⃗, β⃗) = ∏ i 1√ 2σα exp(−||α⃗i||1 σα )× ∏ k ∏ i 1√ 2σγ exp(−||α⃗i − β⃗k||1 σγ ).”
Deep Generalized Unfolding Networks for Image Restoration (2022, background): “, total variation [49], sparse representation [15, 18, 42], low-rank [23], and self-similarity [7,12].”
Fast algorithms for nonconvex compressive sensing: MRI reconstruction from very few data (2009, methodology): “Bregman iterations were first used in image restoration [ 16 ]; the basic approach is that one can enforce a data constraint more and more tightly by adding the residual back to the data at each iteration.”
A Fast Alternating Direction Method for TVL1-L2 Signal Reconstruction From Partial Fourier Data (2010, methodology): “Bregman iterative algorithm [ 36 ], [46], a split Bregman method was proposed in [31] for a class of inverse problems, which is equivalent to the ALM.”