Image denoising using a tight frame.
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 degrees. 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.
Shen
Lixin
L
Department of Mathematics, Western Michigan University, Kalamazoo, MI 49008, USA.
Papadakis
Manos
M
Kakadiaris
Ioannis A
IA
Konstantinidis
Ioannis
I
Kouri
Donald
D
Hoffman
David
D