Recovering edges in ill-posed inverse problems: optimality of curvelet frames

By E.J. Candes, David L. Donoho. 2002

344 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/601ba02449e03c7b36e882b80de24c42b887aa4d

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In Computational Mechanics

In Computer Vision and Pattern Recognition

In Radiology, Nuclear Medicine and Imaging

Citations in the corpus

Why Simple Shrinkage Is Still Relevant for Redundant Representations? (2006, background): “A new trend in recent years has been the use of overcomplete transforms, replacing the traditional unitary ones—see [14]–[24], [28]–[32] for representative works.”
From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images (2009, methodology): “They used a dictionary combining two representations: curvelets [146, 12, 13] for representing the cartoon part, and local overlapped DCT for the texture.”
New multiscale transforms, minimum total variation synthesis: applications to edge-preserving image reconstruction (2002, methodology): “Then, the thresholding of curvelet coefficients is provably optimal for estimating objects of that class as this procedure yields near-minimax rates of convergence over F , see [11] for details.”
New tight frames of curvelets and optimal representations of objects with C² singularities (2002, methodology): “Our theoretical results, see the companion paper [8], show that, because images have edges, many of the standard approaches to image restoration and enhancement (e.”
Fast Discrete Curvelet Transforms (2006, background): “The statistical optimality of the curvelet shrinkage extends to other situations involving indirect measurements as in a large class of ill-posed inverse problems [9].”
A Douglas–Rachford Splitting Approach to Nonsmooth Convex Variational Signal Recovery (2007, background): “Discretized versions of curvelets [11], dual-tree wavelet decompositions [14], Gabor frames [26], [49], and contourlets [29] constitute tight frames under suitable hypotheses.”
An iterative thresholding algorithm for linear inverse problems with a sparsity constraint (2003, positive): “In order to obtain more eﬃcient (sparser) expansions of this type of functions, other expansions have to be used, using e.g. ridgelets or curvelets ([16], [5]).”
Learning Multiscale Sparse Representations for Image and Video Restoration (2008, background): “Such attempts include wavelets [28], curvelets [5, 6], contourlets [15, 16], wedgelets [17], bandlets [24, 29], and steerable wavelets [21, 39].”
Sparse Representation for Color Image Restoration (2008, background): “If we consider the case where is the set of natural images, dictionaries such as wavelets of various sorts [4], curvelets [5], [6], contourlets [7], [8], wedgelets [9], bandlets [10], [11], and steerable wavelets [12], [13], are all attempts to design dictionaries that fulﬁll the above model…”
Sharpness-Aware Low-Dose CT Denoising Using Conditional Generative Adversarial Network (2017, neutral): “discrete gradient, contourlet [48], curvelet [10].”
New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities (2004, methodology): “This and other facts together with the complicated index structure make any kind of mathematical and quantitative analysis especially delicate; see, for instance, the structure of the proof in [8].”
From Heuristic Optimization to Dictionary Learning: A Review and Comprehensive Comparison of Image Denoising Algorithms (2014, background): “are a large number of variations in this category, such as discrete cosine transform (DCT), wavelets [51], wedgelets [52], curvelets [53], [54], bandlets [34], [55], contourlets [56], and steerable wavelets [57], [58], wavelets based methods are still dominant.”