This paper proposes a Poisson denoising method with a union of directional lapped orthogonal transforms (DirLOTs). DirLOTs are 2-D non-separable lapped orthogonal transforms with directional characteristics under the fixed-critically-subsampling, overlapping, orthonormal, symmetric, real-valued and compact-support property. In this work, DirLOTs are used to generate symmetric orthogonal 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 textures and edges. Multiple DirLOTs can overcome a disadvantage of separable wavelets in representing diagonal components. In addition to this feature, multiple DirLOTs make transform-based denoising performance better through the redundant representation. Experimental results show that the combination of the variance stabilizing transformation (VST), Stein's unbiased risk estimator-linear expansion of threshold (SURE-LET) approach and multiple DirLOTs is able to significantly improve the denoising performance.

This letter proposes an image fusion method which adopts a union of multiple directional lapped orthogonal transforms (DirLOTs). DirLOTs are used to generate symmetric orthogonal discrete wavelet transforms and then to construct a union of unitary transforms as a redundant dictionary with a multiple directional property. The multiple DirLOTs can overcome a disadvantage of separable wavelets to represent images which contain slant textures and edges. We analyse the characteristic of local luminance contrast, and propose a fusion rule based on interscale relation of wavelet coefficients. Relying on the above, a novel image fusion method is proposed. Some experimental results show that the proposed method is able to significantly improve the fusion performance from those with the conventional discrete wavelet transforms.