Sparse geometric image representations with bandelets

By Erwan Le Pennec, Stéphane Mallat. IEEE Transactions on Image Processing, 2005

948 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/67b1cc159aacf2f30239577e6cf7a741b64f31e0

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

Citations in the corpus

Optimal approximation of piecewise smooth functions using deep ReLU neural networks (2017, methodology): “To obtain optimal approximation of two-dimensional functions with jump curves smoother than C 2 , the bandlet system was developed, [40], which is a system consisting of properly smoothly-transformed boundary-adapted wavelets that are optimally adapted to the smooth jump curves.”
Automated Visual Defect Detection for Flat Steel Surface: A Survey (2020, methodology): “Zhang et al. [78] have proposed an image fusion method based on Bandelet-PCNN (Pulse coupled neural networks) model to solve the problem of the pseudo-Gibbs phenomena around singularities.”
Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries (2006, background): “Also, with the growing realization that regular separable 1-D wavelets are inappropriate for handling images, several new tailored multiscale and directional redundant transforms were introduced, including the curvelet [11], [12], contourlet [13], [14], wedgelet [15], bandlet [ 16 ], [17], and the s”
Optimal Spatial Adaptation for Patch-Based Image Denoising (2006, methodology): “We just point out that, to our knowledge, the more competitive methods are recent wavelet-based methods [16], [17], [ 33 ], [44], [46], [54].”
Sparse directional image representations using the discrete shearlet transform (2008, background): “They include several schemes of “directional wavelets” (such as [1,3]), contourlets [12,31], complex wavelets [25,34], brushlets [9], ridgelets [6], curvelets [7], bandelets [29] and shearlets [18,20], introduced by the authors and their collaborators.”
Optimally Sparse Multidimensional Representation Using Shearlets (2007, background): “Those include contourlets, complex wavelets and other “directional wavelets” in the filter bank literature [1, 2, 11, 22, 26, 28], as well as brushlets [8], ridgelets [5], curvelets [7], and bandelets [24].”
Learning Multiscale Sparse Representations for Image and Video Restoration (2008, background): “Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA…”
Fast Discrete Curvelet Transforms (2006, positive): “Given the significance of such intermediate dimensional phenomena, there has been a vigorous research effort to provide better adapted alternatives by combining ideas from geometry with ideas from traditional multiscale analysis [17, 19, 4, 31, 14, 16].”
The SURE-LET Approach to Image Denoising (2007, background): “Bandelets [66], Grouplets [67]) have been designed to better represent the specific geometry of a given image.”
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.”
Seislet transform and seislet frame (2010, background): “Among those transforms are bandelets (Pennec and Mallat, 2005), contourlets (Do and Vetterli, 2005), curvelets (Starck et al., 2002), directionlets (Velisavljevic, 2005), shearlets (Guo and Labate, 2007), etc. Unlike isotropic wavelets, directional transforms attempt to design basis functions so…”
Image Denoising Via Learned Dictionaries and Sparse representation (2006, background): “Also, with the growing realization that regular separable 1D wavelets are inappropriate for handling images, several new tailored multi-scale and directional redundant transforms were introduced, including the Curvelet [8], Contourlet [9], Wedgelet [10], Bandlet [11], the steerable wavelet [12], and”
Double Sparsity: Learning Sparse Dictionaries for Sparse Signal Approximation (2010, methodology): “Dictionaries of this type include Wavelets [22], Curvelets [23], Contourlets [24], Shearlets [25], Complex Wavelets [26], and Bandelets [27], among others.”
Sparse Modeling for Image and Vision Processing (2014, background): “It resulted a large number of variants, such as steerable wavelets [Simoncelli et al., 1992], curvelets [Candès and Donoho, 2002], contourlets [Do and Vetterli, 2005], or bandlets [Le Pennec and Mallat, 2005].”