Sparse directional image representations using the discrete shearlet transform
By Glenn R. Easley, Demetrio Labate, Wang-Q Lim. 2008
1,088 citations recorded by the source corpus.
Abstract In spite of their remarkable success in signal processing applications, it is now widely acknowledged that traditional wavelets are not very effective in dealing multidimensional signals containing distributed discontinuities such as edges. To overcome this limitation, one has to use basis elements with much higher directional sensitivity and of various shapes, to be able to capture the intrinsic geometrical features of multidimensional phenomena. This paper introduces a new discrete multiscale directional representation called the discrete shearlet transform. This approach, which is based on the shearlet transform, combines the power of multiscale methods with a unique ability to capture the geometry of multidimensional data and is optimally efficient in representing images containing edges. We describe two different methods of implementing the shearlet transform. The numerical experiments presented in this paper demonstrate that the discrete shearlet transform is very competitive in denoising applications both in terms of performance and computational efficiency.
Subfields: Computer Vision and Pattern Recognition, Media Technology
View Paper: https://www.semanticscholar.org/paper/6364f81147db1da9e8b12c4b201e6ef2ff13c016
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computer Vision and Pattern Recognition
In Media Technology
Citations in the corpus
- Fast Finite Shearlet Transform: a tutorial (2012, background): “The construction of the shearlets is based on ideas from [11] and [22].”
- Resolution of the wavefront set using continuous shearlets (2006, background): “We refer to [13, 15, 16, 17, 18, 22, 21] for more detail about the research about shearlets.”
- Pixel-level image fusion: A survey of the state of the art (2017, background): “I Multi-scale decomposition pyramid[4], wavelet [5, 11, 12], complex wavelet [13], curvelet[14, 15], contourlet [16–23], shear-let [24–26], edge-preserving decompositions[27– 29], anisotropic heat diffusion[30], log-Gabor transform[31], support value transform [32, 33], optimal scale transform [34,…”
- Full length article: Compactly supported shearlets are optimally sparse (2011, neutral): “, [9, 15] for the continuum theory, [16, 8, 18] for the digital theory, and [10, 7] for recent applications.”
- Optimally Sparse Multidimensional Representation Using Shearlets (2007, background): “The theory of composite wavelets, recently proposed by the authors and their collaborators [14, 15, 16], provides a most general setting for the construction of truly multidimensional, efficient, multiscale representations.”
- Medical Image Fusion With Parameter-Adaptive Pulse Coupled Neural Network in Nonsubsampled Shearlet Transform Domain (2019, methodology): “of ST, known as NSST, has been introduced based on nonsubsampled pyramid filters (NSPFs) and shift-invariant shearlet filter banks (SFBs) [36].”
- A Shearlet Approach to Edge Analysis and Detection (2009, positive): “We refer to [19] for more details about the comparison of shearlets and other orientable multiscale transforms.”
- An introduction to continuous optimization for imaging (2016, methodology): “The case α = 0 was suggested by Eckstein (1989) for primal–dual iterations, referred to as the ‘alternating step method for monotropic programming’.”