Image restoration with multiple DirLOTs

A directional lapped orthogonal transform (DirLOT) is an orthonormal transform of which basis is allowed to be anisotropic with the symmetric, real-valued and compact-support property. Due to its directional property, DirLOT is superior to the existing separable transforms such as DCT and DWT in expressing diagonal edges and textures. The goal of this paper is to enhance the ability of DirLOT further. To achieve this goal, we propose a novel image restoration technique using multiple DirLOTs. This paper generalizes an image denoising technique in [1], and expands the application of multiple DirLOTs by introducing linear degradation operator P. The idea is to use multiple DirLOTs to construct a redundant dictionary. More precisely, the redundant dictionary is constructed as a union of symmetric orthonormal discrete wavelet transforms generated by DirLOTs. To select atoms fitting a target image from the dictionary, we formulate an image restoration problem as an ℓ₁- regularized least square problem, which can efficiently be solved by the iterativeshrinkage/thresholding algorithm (ISTA). The proposed technique is beneficial in expressing multiple directions of edges/textures. Simulation results show that the proposed technique significantly outperforms the nonsubsampled Haar wavelet transform for deblurring, super-resolution, and inpainting.