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.

We propose a robust edge detection method based on independent component analysis (ICA). It is known that most of the basis functions extracted from natural images by ICA are sparse and similar to localized and oriented receptive fields, and in the proposed edge detection method, a target image is first transformed by ICA basis functions and then the edges are detected or reconstructed with sparse components only. Furthermore, by applying a shrinkage algorithm to filter out the components of noise in the ICA domain, we can readily obtain the sparse components of the original image, resulting in a kind of robust edge detection even for a noisy image with a very low SN ratio. The efficiency of the proposed method is demonstrated by experiments with some natural images.