28 May 2004 The fast parametric slantlet transform with applications
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Transform methods have played an important role in signal and image processing applications. Recently, Selesnick has constructed the new orthogonal discrete wavelet transform, called the slantlet wavelet, with two zero moments and with improved time localization. The discrete slantlet wavelet transform is carried out by an existing filterbank which lacks a tree structure and has a complexity problem. The slantlet wavelet has been successfully applied in compression and denoising. In this paper, we present a new class of orthogonal parametric fast Haar slantlet transform system where the slantlet wavelet and Haar transforms are special cases of it. We propose designing the slantlet wavelet transform using Haar slantlet transform matrix. A new class of parametric filterbanks is developed. The behavior of the parametric Haar slantlet transforms in signal and image denoising is presented. We show that the new technique performs better than the slantlet wavelet transform in denoising for piecewise constant signals. We also show that the parametric Haar slantlet transform performs better than the cosine and Fourier transforms for grey level images.
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Sos S. Agaian, Khaled Tourshan, Joseph P. Noonan, "The fast parametric slantlet transform with applications", Proc. SPIE 5298, Image Processing: Algorithms and Systems III, (28 May 2004); doi: 10.1117/12.518302; https://doi.org/10.1117/12.518302

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