High-Order Total Variation-Based Image Restoration

By Tony F. Chan, Antonio Marquina, P. Mulet. SIAM Journal on Scientific Computing, 2000

809 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/3b965ae9beb7e173d4b25474f7bc99ee61259bee

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In Computer Vision and Pattern Recognition

1. Wotao Yin
2. Stanley J. Osher
3. Yin Zhang
4. Xuecheng Tai
5. Junfeng Yang
6. Chunlin Wu
7. Jian-Feng Cai
8. Zuowei Shen

Citations in the corpus

• Iterative Image Restoration Combining Total Variation Minimization and a Second-Order Functional (2005, methodology): “However, both from a theoretical (Weickert, 1998; Ring, 2000) and experimental (Lysaker et al., 2003; Chambolle and Lions, 1997; Chan et al., 2000) point of view, it has been shown that the TV-norm transforms smooth signal into piecewise constants, the so-called staircase effect.”
• A Fast Algorithm for Edge-Preserving Variational Multichannel Image Restoration (2009, background): “, [12, 23], which indicates the effect of preventing staircasing caused by TV.”
• Fractional-Order Anisotropic Diffusion for Image Denoising (2007, background): “To reduce the blocky effect, while preserving sharp jump discontinuities (edges), many other non-linear filters have been suggested in the literature [10]–[18] and during the last few years, fourth-order PDEs have been of special interest [13]–[18].”
• Image restoration: Total variation, wavelet frames, and beyond (2012, background): “Another approach reducing the staircase effect without multi-layer assumptions of the images is adding a higher order regularization term to the original ROF model by [29].”
• A Combined First and Second Order Variational Approach for Image Reconstruction (2012, neutral): “Another attempt to combine first and second order regularisation originates from Chan, Marquina, and Mulet [26], who consider total variation minimisation together with weighted versions of the Laplacian.”
• Variable Exponent, Linear Growth Functionals in Image Restoration (2006, methodology): “We also refer the reader to the work in [15, 16, 26, 35] for an alternate variational approach for reducing staircasing by minimizing second order functionals.”
• Missing Information Reconstruction of Remote Sensing Data: A Technical Review (2015, background): “, the curvature-driven diffusion (CDD) models [9], high-order TV [30], and spectral-spatial adaptive TV [31].”
• Recent Developments in Total Variation Image Restoration (2004, methodology): “Another method that utilizes total variation and higher order derivatives to suppress stair-casing is by Chan, Marquina, and Mulet in [13].”
• Augmented Lagrangian Method, Dual Methods, and Split Bregman Iteration for ROF, Vectorial TV, and High Order Models (2010, methodology): “As well known, the TV restoration models (e.g., ROF and vectorial TV) su(cid:11)er from staircase e(cid:11)ect; see [45, 41, 13, 15, 5] and references therein.”
• Infimal convolution regularizations with discrete ℓ1-type functionals (2011, neutral): “For various other variational and PDE approaches involving higher order derivatives, see [11, 15, 22, 24, 30, 41, 43].”
• Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time (2003, neutral): “Different functionals can be used to measure the oscillations in an image and a general formulation of the noise removal problem (cf. [18], [10]) is to solve (2) We search for a new image by minimizing subject to constraints involving the statistics of the noise.”