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