SHAH: SHape-Adaptive Haar wavelets for image processing
(2016) Journal of Computational and Graphical Statistics — Vol. 25, n° 3, p. 879-898 (2016)
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- Abstract
- 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.
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Citations
Fryzlewicz, P., & Timmermans, C. (2016). SHAH: SHape-Adaptive Haar wavelets for image processing. Journal of Computational and Graphical Statistics, 25(3), 879-898. https://doi.org/10.1080/10618600.2015.1048345 (Original work published 2016)