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
fDate :
5/1/2006 12:00:00 AM
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;
Journal_Title :
Image Processing, IEEE Transactions on
DOI :
10.1109/TIP.2005.864240