 
Summary: Image denoising using regularized Butterworth wavelet frames
Amir Z. Averbuch Valery A. Zheludev
School of Computer Science
Tel Aviv University
Tel Aviv 69978, Israel
January 31, 2008
Abstract
We present an efficient algorithm for image restoration from highly noised originals. The algo
rithm is based on diverse library of tight and semitight wavelet frames. Unlike majority of current
denoising methods, which threshold the transform coefficients, our algorithm performs direct and
inverse multiscale transforms using properly modified frame filters. No thresholding is applied. The
processing is linear. The algorithm is fast and can be implemented in real time. It depends on one
numerical parameter, which is estimated from the noise level.
1 Introduction
Denoising is one of everactual problems in image processing. Usually, the structure of an image is
distorted by different types of noise. The goal of denoising process is to reveal the essential structure
of the image, without producing of artifacts. Currently, common approach consists in application of
a multiscale transform to the image. This is followed by manipulation of the transform coefficients.
Typically, a wavelet transform is applied and the coefficients are thresholded or shrunk (soft thresh
olding) according to a strategy that is usually based on statistical modeling of the wavelet coefficients
