Image denoising with union of directional orthonormal DWTS

A novel image denoising technique is proposed by using directional lapped orthogonal transforms (DirLOTs). DirLOTs satisfy orthogonality and the bases are allowed to be anisotropic with the fixed-critically-subsampling, overlapping, symmetric, real-valued and compact-support property. In this work, DirLOTs are used to construct directional symmetric orthonormal discrete wavelet transforms and then the bases are adopted to generate a redundant dictionary with several directions. The multiple directional property is suitable for representing natural images which contain diagonal edges and textures. The proposed dictionary is applied to solve the basis pursuit denoising problem. The denoising performance is evaluated for several images through the heuristic shrinkage and block-coordinate-relaxation algorithm. It is verified that the proposed technique is simple but yields perceptually preferable results.