Fractal-wavelet image denoising

In this paper, we propose a simple yet effective fractal-wavelet scheme for edge-preserving smoothing of noisy images. Over the past decade, there has been significant interest in fractal coding for the purpose of image compression. Fractal-wavelet transforms were introduced in an effort to reduce the blockiness and computational complexity that are inherent in fractal image compression. Applications of fractal-based coding to other aspects of image processing, however, have received little attention. Recently, the authors proposed a simple yet effective fractal-based image denoising scheme that is applied in the spatial domain of the image. In this paper we extend the application of this fractal denoising scheme to the wavelet domain of the image. We find that when the wavelet transform of the noisy image is simply fractally coded, a significant amount of the noise is suppressed. However, one can go a step further and estimate the fractal code of the wavelet transform of the original noise-free image from that of the wavelet transform of the noisy image. The use of the quadtree partitioning scheme for the purpose of fractal-wavelet coding results in a significantly enhanced and restored representation of the original noisy image. The enhancement is consistent with the human visual system where extra smoothing is performed in flat and low activity regions and a lower degree of smoothing is performed near high frequency components, e.g. edges, of the image. The main advantage of the wavelet-based fractal denoising scheme over the standard fractal denoising scheme is that it is computationally less expensive.