Article (Scientific journals)
SHAH: SHape-Adaptive Haar wavelets for image processing
Fryzlewicz, Piotr; Timmermans, Catherine
2015In Journal of Computational and Graphical Statistics, 25 (3), p. 879-898
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Keywords :
Adaptive transformations; Greedy algorithms; Multiscale; Sparsity; Statistical learning
Abstract :
[en] We propose the SHAH (SHape-Adaptive Haar) transform for images, which results in an orthonormal, adaptive decomposition of the image into Haar-wavelet-like components, arranged hierarchically according to decreasing importance, whose shapes reflect the features present in the image. The decomposition is as sparse as it can be for piecewise-constant images. It is performed via an stepwise bottom-up algorithm with quadratic computational complexity; however, nearly-linear variants also exist. SHAH is rapidly invertible. We show how to use SHAH for image denoising. Having performed the SHAH transform, the coefficients are hard- or soft-thresholded, and the inverse transform taken. The SHAH image denoising algorithm compares favourably to the state of the art for piecewise-constant images. A clear asset of the methodology is its very general scope: it can be used with any images or more generally with any data that can be represented as graphs or networks.
Disciplines :
Mathematics
Author, co-author :
Fryzlewicz, Piotr;  London School of Economics
Timmermans, Catherine ;  Université catholique de Louvain
Language :
English
Title :
SHAH: SHape-Adaptive Haar wavelets for image processing
Publication date :
2015
Journal title :
Journal of Computational and Graphical Statistics
ISSN :
1061-8600
eISSN :
1537-2715
Publisher :
Taylor & Francis, United Kingdom
Volume :
25
Issue :
3
Pages :
879-898
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBi :
since 11 January 2019

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