WAVELET CHARACTERIZATION OF DYADIC BMO NORM AND ITS APPLICATION IN IMAGE DECOMPOSITION FOR DISTINGUISHING BETWEEN TEXTURE AND NOISE

Abstract

Following the oscillating theory of Meyer, many image decomposition models have been proposed to split an image into two parts: structures and textures. But these models are not effective in the case of a noisy image, because both textures and noise are oscillating patterns. In this paper, we use the local variance measure to separate noise from textures. Firstly, we examine the relationship between dyadic BMO norm and local variance. Then, we give the wavelet representation of dyadic BMO norm and local variance, and further propose a method to distinguish between texture and noise in wavelet domain. In high frequency wavelet domain, we propose a decomposition model using local variance as constraints, while in low frequency domain, we use the shrinkage scheme to distinguish them. Finally, we present various numerical results on images to demonstrate the potential of our method.