The digital TV filter and nonlinear denoising

By Tony F. Chan, Stanley J. Osher, Jianhong Shen. IEEE Transactions on Image Processing, 2001

549 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition, Media Technology

View Paper: https://www.semanticscholar.org/paper/f81c5a0647754d128af29319c0e54a5c22ea2f27

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In Computer Vision and Pattern Recognition

In Media Technology

Citations in the corpus

Kernel Regression for Image Processing and Reconstruction (2007, unknown): “However, the data-adapted kernel regression in its simplest form (bilateral filter) exploits the (PDE-based) total variation (TV) regularization [28], [43].”
On the origin of the bilateral filter and ways to improve it (2002, background): “[18] proposed a new filter named digital total-variation for noise removal.”
Mathematical Models for Local Nontexture Inpaintings (2002, methodology): “Numerical investigations and discussions can be found in [2, 8, 15, 41], and more recent ones in [9, 29, 38].”
Chromatogram baseline estimation and denoising using sparsity (BEADS) (2014, methodology): “Most sparse modeling techniques arose from the “least absolute shrinkage and selection operator” (better known under the lasso moniker [50, 40]), basis pursuit methods [10], total variation [8], and compound regularization [2].”
The SURE-LET Approach to Image Denoising (2007, unknown): “12) is finally obtained by gradient descent [29]: ∂ ∂t U(x, y, t) = div { ∇U(x, y, t) |∇U(x, y, t)| } + λ (I0(x, y)− U(x, y, t)) (1.”
Edge-preserving and scale-dependent properties of total variation regularization (2003, unknown): “has been put into developing faster numerical schemes for solving the TV regularization problem [10, 12, 13, 25, 28, 33, 41], and to a lesser extent into the existence and uniqueness of solutions to (2)–(4) [1, 9, 19, 20], a relatively limited amount of study has been devoted to understanding more p”
Despeckling of medical ultrasound images (2006, background): “specified in [ 44 ] (such a formulation stems from explicit discretization of the Euler-Lagrange equation”
Nonlocal Operators with Applications to Image Processing (2008, background): “Total variation type regularizations on graphs were ﬁrst proposed in [15] and later by [57] and [7].”
Fast and robust multiframe super resolution (2004, background): “The most useful property of TV criterion is that it tends to preserve edges in the reconstruction [22]–[ 24 ], as it does not severely penalize steep local gradients.”
Multiframe demosaicing and super-resolution of color images (2006, methodology): “[ 32 ] and a related method called the bilateral filter 9 [33], [34], a robust regularizer called Bilateral-TV”
Nonlocal Discrete Regularization on Weighted Graphs: A Framework for Image and Manifold Processing (2008, methodology): “(11) If the graph is unweighted ( , ), corresponds to the curvature operator proposed in [41] and [42] in the context of image restoration.”
Edge and line oriented contour detection: State of the art (2011, background): “Other extensions concern vector-valued images [45,46], images defined on graphs [46], deblurring application [47,48], and decomposition of an image into three components (filtered image, texture, and noise) [37].”
Discrete Signal Processing on Graphs: Frequency Analysis (2013, methodology): “They have been used for signal denoising, deblurring and recovery [42], [43], [44], [45].”