The curvelet transform for image denoising

By Jean-Luc Starck, E.J. Candes, David L. Donoho. Proceedings 2001 International Conference on Image Processing (Cat. No.01CH37205), 2001

2,599 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition, Media Technology

View Paper: https://www.semanticscholar.org/paper/90d788e4da8347335d63c73d11ec789d1ab959ff

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Citations in the corpus

Transforms and Operators for Directional Bioimage Analysis: A Survey. (2016, background): “2015), image denoising (Starck et al. 2002), contrast enhancement (Starck et al.”
Directional multiresolution image representations (2002, methodology): “In [64, 159, 6], different interpolation approaches were proposed to solve the polar versus rectangular coordinate transform problem, all requiring overcomplete systems.”
A New Benchmark Based on Recent Advances in Multispectral Pansharpening: Revisiting Pansharpening With Classical and Emerging Pansharpening Methods (2021, background): “Also, in this case, it is possible to trace these methods back to fusion approaches based on general-purpose decompositions, performed by means of a simple low-pass filter, or by more complex iterative approaches, such as Laplacian pyramids [36], wavelets [37]–[39], curvelets [40], and contourlets [”
Radon transform orientation estimation for rotation invariant texture analysis (2005, methodology): “Ridgelet transform is also used to implement curvelet decomposition, which is used for image denoising [ 27 ].”
Gray and color image contrast enhancement by the curvelet transform (2003, background): “3) Calculate the noise standard deviation for each band of the curvelet transform (see [12] for more details on this step).”
A Review of Wavelet Analysis and Its Applications: Challenges and Opportunities (2022, background): “Its performance in image denoising, texture classiﬁcation, and image retrieval is lower than that of multi-directional wavelet [41].”
Local adaptivity to variable smoothness for exemplar-based image denoising and representation (2005, neutral): “However, we do not draw into comparison both the wavelet-based methods [24, 74, 62, 22, 60, 47] since they process the input data in the transformed domain, and the fractal denoising methods [32] also rooted in wavelet theory.”
Wave atoms and sparsity of oscillatory patterns (2007, background): “An example of quantitative success story is curvelets, which were designed for the purpose of providing a sparse expansion of curved edges [8,9,31], bandlimited wavefronts [7] and other geometric features in images.”
The dual-tree complex wavelet transform (2005, methodology): “Examples include steerable pyramids [41], [96], directional FBs and pyramids [10], [31], curvelets [15], [100], and directional wavelet transforms based on complex FBs [36], [39], [55], [57].”
Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA) (2005, background): “Instead, we can rely on years’ results on the role of sparsity and over-completeness in signal and image processin respect to the wavelet transform, and its advanced versions such as the curvelet [24], and m can also pose these as assumptions we build upon, and see whether the results agree.”
$rm K$-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation (2006, neutral): “In denoising, wavelet methods and shift-invariant variations that exploit overcomplete representation are among the most effective known algorithms for this task [2]–[5].”
Simultaneous image fusion and denoising with adaptive sparse representation (2015, methodology): “First, in image denoising applications, the advantages of the CVT [33], NSCT [34] and SR [17] based methods over traditional multi-resolution (e.g. DWT) methods have been widely veri ﬁ ed.”
Hyperspectral and Multispectral Image Fusion Based on a Sparse Representation (2014, methodology): “ dictionary with columns referred to as atoms is proposed as a basis for the image patches. In many applications, the dictionary D is predeﬁned and can be constructed from wavelets [47], curv elets 7 [48] or discrete cosine transform (DCT) vectors [49]. However, these bases are not necessarily well ”
Directionlets: anisotropic multidirectional representation with separable filtering (2006, methodology): “The obtained results are comparable to the current best results [23; 68; 87], while the computational complexity of directionlets is lower than the complexity of other denoising methods based on non-separable transforms.”