DocumentCode :
900789
Title :
Image denoising using a tight frame
Author :
Shen, Lixin ; Papadakis, Manos ; Kakadiaris, Ioannis A. ; Konstantinidis, Ioannis ; Kouri, Donald ; Hoffman, David
Author_Institution :
Dept. of Math., Western Michigan Univ., Kalamazoo, MI, USA
Volume :
15
Issue :
5
fYear :
2006
fDate :
5/1/2006 12:00:00 AM
Firstpage :
1254
Lastpage :
1263
Abstract :
We present a general mathematical theory for lifting frames that allows us to modify existing filters to construct new ones that form Parseval frames. We apply our theory to design nonseparable Parseval frames from separable (tensor) products of a piecewise linear spline tight frame. These new frame systems incorporate the weighted average operator, the Sobel operator, and the Laplacian operator in directions that are integer multiples of 45°. A new image denoising algorithm is then proposed, tailored to the specific properties of these new frame filters. We demonstrate the performance of our algorithm on a diverse set of images with very encouraging results.
Keywords :
Laplace equations; image denoising; mathematical operators; piecewise linear techniques; splines (mathematics); Laplacian operator; Sobel operator; image denoising; nonseparable Parseval frames; piecewise linear spline tight frame; weighted average operator; Chemistry; Discrete wavelet transforms; Filtering theory; Filters; Image denoising; Laboratories; Mathematics; Minimax techniques; Noise reduction; Tensile stress; Image denoising; tight frame; wavelets; Algorithms; Computer Simulation; Image Enhancement; Image Interpretation, Computer-Assisted; Information Storage and Retrieval; Models, Statistical; Numerical Analysis, Computer-Assisted; Pattern Recognition, Automated; Signal Processing, Computer-Assisted;
fLanguage :
English
Journal_Title :
Image Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1057-7149
Type :
jour
DOI :
10.1109/TIP.2005.864240
Filename :
1621246
Link To Document :
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