Complex Wavelets for Shift Invariant Analysis and Filtering of Signals
TLDR
In this article, a dual tree of wavelet filters is proposed to obtain real and imaginary parts of the wavelet transform. And the dual tree can be extended for image and other multi-dimensional signals.About:
This article is published in Applied and Computational Harmonic Analysis.The article was published on 2001-05-01 and is currently open access. It has received 1767 citations till now. The article focuses on the topics: Complex wavelet transform & Discrete wavelet transform.read more
Citations
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Proceedings ArticleDOI
Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network
Wenzhe Shi,Jose Caballero,Ferenc Huszar,Johannes Totz,Andrew Peter Aitken,Rob Bishop,Daniel Rueckert,Zehan Wang +7 more
TL;DR: This paper presents the first convolutional neural network capable of real-time SR of 1080p videos on a single K2 GPU and introduces an efficient sub-pixel convolution layer which learns an array of upscaling filters to upscale the final LR feature maps into the HR output.
Journal ArticleDOI
The contourlet transform: an efficient directional multiresolution image representation
Minh N. Do,Martin Vetterli +1 more
TL;DR: A "true" two-dimensional transform that can capture the intrinsic geometrical structure that is key in visual information is pursued and it is shown that with parabolic scaling and sufficient directional vanishing moments, contourlets achieve the optimal approximation rate for piecewise smooth functions with discontinuities along twice continuously differentiable curves.
Journal ArticleDOI
Image denoising using scale mixtures of Gaussians in the wavelet domain
TL;DR: The performance of this method for removing noise from digital images substantially surpasses that of previously published methods, both visually and in terms of mean squared error.
Journal ArticleDOI
The dual-tree complex wavelet transform
TL;DR: Several methods for filter design are described for dual-tree CWT that demonstrates with relatively short filters, an effective invertible approximately analytic wavelet transform can indeed be implemented using the dual- tree approach.
Journal ArticleDOI
Wavelets on graphs via spectral graph theory
TL;DR: A novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite weighted graph using the spectral decomposition of the discrete graph Laplacian L, based on defining scaling using the graph analogue of the Fourier domain.
References
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Journal ArticleDOI
A theory for multiresolution signal decomposition: the wavelet representation
TL;DR: In this paper, it is shown that the difference of information between the approximation of a signal at the resolutions 2/sup j+1/ and 2 /sup j/ (where j is an integer) can be extracted by decomposing this signal on a wavelet orthonormal basis of L/sup 2/(R/sup n/), the vector space of measurable, square-integrable n-dimensional functions.
Book
A wavelet tour of signal processing
TL;DR: An introduction to a Transient World and an Approximation Tour of Wavelet Packet and Local Cosine Bases.
Journal ArticleDOI
De-noising by soft-thresholding
TL;DR: The authors prove two results about this type of estimator that are unprecedented in several ways: with high probability f/spl circ/*/sub n/ is at least as smooth as f, in any of a wide variety of smoothness measures.
Journal ArticleDOI
The Laplacian Pyramid as a Compact Image Code
Peter J. Burt,Edward H. Adelson +1 more
TL;DR: A technique for image encoding in which local operators of many scales but identical shape serve as the basis functions, which tends to enhance salient image features and is well suited for many image analysis tasks as well as for image compression.
Journal ArticleDOI
Shiftable multiscale transforms
TL;DR: Two examples of jointly shiftable transforms that are simultaneously shiftable in more than one domain are explored and the usefulness of these image representations for scale-space analysis, stereo disparity measurement, and image enhancement is demonstrated.