Fractal based spatial domain techniques for image de-noising

Abstract

An image is often corrupted by noise in its acquisition and transmission. Hence, noise reduction is a required step for any sophisticated image processing algorithm. Denoising or noise reduction has been a permanent research topic for engineers and scientists and one reason for it is the lack of a single technique, which is able to achieve denoising for a wide class of images. Though, traditional linear noise removal techniques like Wiener filtering, has been existing for a long time for their simplicity and are able to achieve significant noise removal when the variance of noise is low, they cause blurring and smoothening of the sharp edges of the image. Hence, in recent years there has been a fair amount of research on non-linear noise removal techniques and prominent among them are the wavelet based denoising techniques. The idea of wavelet thresholding relies on the assumption that the signal magnitudes of the noise in wavelet representation are such that wavelet coefficients can be set to zero if their magnitude are less than a predetermined threshold. More recent developments focus on more sophisticated methods, like local or context-based thresholding in wavelet domain. A new approach to image denoising is using fractal compression for denoising. As fractal image coding is performed in spatial domain it is also possible to carry out the fractal image denoising. The task of fractal image denoising is to construct a fractal code for noisy image such that either the collage or the attractor is closer to the original noise-free image than the non encoded noisy image. This paper analyzes, implements and compares the fractal image denoising methods to find the best one for denoising a wide variety of gray scale images. It also proposes a fractal based coding method, which accomplishes simultaneous denoising as well as compression.