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Title: Data-driven tight frame construction and image denoising
Authors: Cai, J.-F.
Ji, H. 
Shen, Z. 
Ye, G.-B.
Keywords: Image de-noising
Sparse approximation
Tight frame
Wavelet thresholding
Issue Date: 2014
Citation: Cai, J.-F., Ji, H., Shen, Z., Ye, G.-B. (2014). Data-driven tight frame construction and image denoising. Applied and Computational Harmonic Analysis 37 (1) : 89-105. ScholarBank@NUS Repository.
Abstract: Sparsity-based regularization methods for image restoration assume that the underlying image has a good sparse approximation under a certain system. Such a system can be a basis, a frame, or a general over-complete dictionary. One widely used class of such systems in image restoration are wavelet tight frames. There have been enduring efforts on seeking wavelet tight frames under which a certain class of functions or images can have a good sparse approximation. However, the structure of images varies greatly in practice and a system working well for one type of images may not work for another. This paper presents a method that derives a discrete tight frame system from the input image itself to provide a better sparse approximation to the input image. Such an adaptive tight frame construction scheme is applied to image denoising by constructing a tight frame tailored to the given noisy data. The experiments showed that the proposed approach performs better in image denoising than those wavelet tight frames designed for a class of images. Moreover, by ensuring that the system derived from our approach is always a tight frame, our approach also runs much faster than other over-complete dictionary based approaches with comparable performance on denoising. © 2013 Elsevier Inc.
Source Title: Applied and Computational Harmonic Analysis
ISSN: 1096603X
DOI: 10.1016/j.acha.2013.10.001
Appears in Collections:Staff Publications

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