A new wavelet-based approach to sharpening and smoothing of images in Besov spaces with applications to deblurring

The problem of image enhancement arises in many applications such as scanners, copiers and digital cameras. Enhancement often includes a denoising and a deblurring or sharpening step. Similar to image compression, state-of-the-art denoising techniques use wavelet bases instead of Fourier bases since wavelet domain processing provides local adaptation in smooth and non-smooth parts due to the theoretical link between wavelets and smoothness spaces. In this paper the same smoothness spaces are used to propose a way of performing sharpening and smoothing of signals with wavelets (WSS) in Besov spaces. As an application the completely wavelet-based enhancement of a scanned document is discussed