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SHAH: SHape-Adaptive Haar wavelets for image processing

Fryzlewicz, Piotr ORCID: 0000-0002-9676-902X and Timmermans, Catherine (2016) SHAH: SHape-Adaptive Haar wavelets for image processing. Journal of Computational and Graphical Statistics, 25 (3). pp. 879-898. ISSN 1061-8600

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Identification Number: 10.1080/10618600.2015.1048345


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.

Item Type: Article
Official URL:
Additional Information: © 2016 The Authors
Divisions: Statistics
Subjects: T Technology > TK Electrical engineering. Electronics Nuclear engineering
T Technology > TR Photography
Date Deposited: 04 Jun 2015 14:07
Last Modified: 29 May 2024 05:06
Projects: EP/L014246/1, P06/03, EP/L014246/1, P06/03
Funders: Engineering and Physical Sciences Research Council, IAP research network grant of the Belgian Government, Engineering and Physical Sciences Research Council, IAP research network grant of the Belgian Government

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