Image restoration with union of directional orthonormal DWTs

This work proposes to apply directional lapped orthogonal transforms to image restoration. A DirLOT is an orthonormal transform of which basis is allowed to be anisotropic with the symmetric, real-valued and compact-support property. In this work, DirLOTs are used to generate symmetric orthonormal discrete wavelet transforms and then a redundant dictionary as a union of unitary transforms. The multiple directional property is suitable for representing natural images which contain diagonal edges and textures. The performances of deblurring, super-resolution and inpainting are evaluated for several images with the iterative-shrinkage/thresholding algorithm. It is verified that the proposed dictionary yields comparable or superior restoration performance to the non-subsampled Haar transform.