Multiple Basis Wavelet Denoising using Besov Projections
Baraniuk, Richard G.
wavelet; denoising; Besov projections
Wavelet-based image denoising algorithm depends upon the energy compaction property of wavelet transforms. However, for many real-world images, we cannot expect good energy compaction in a single wavelet domain, because most real-world images consist of components of a variety of smoothness. We can relieve this problem by using multiple wavelet bases to match different characteristics of images. In this paper, we propose a novel image denoising algorithm that uses multiple wavelet bases. By establishing a new relationship between the deterministic Besov space theory and the wavelet-domain statistical models, we generalize the Besov theory for finite sampled data. After defining convex sets in Besov spaces that contain the true image, we obtain an estimate of the true image by the method of projection onto convex sets. The algorithm outperforms existing multiple wavelet basis denoising algorithms; in particular, it shows excellent performance at low signal-to-noise ratios.