Image Restoration with Multiple Directional Transforms

This thesis deals with the application of multiple directional transforms to image restoration, and discusses two cases of image restoration, image denoising and image fusion. In Chapter 1, the background of image restoration is described. First, image denoising problems are addressed. Image denoising is a principal problem of image processing and the purpose is to obtain an original picture as an ideal one. For photon acquisition systems, low-light image denoising is becoming in use in optical imaging applications such as astronomical imaging, fluorescence microscopy appliances, magnetic resonance imaging. In this case, the noises are strongly dependent on the signals and approximately obeys Poisson distribution, which leads difficulties in denoising process. The denoising problem for Poisson noise can be modeled by a modular fashion through variance stabilization. Using the variance stabilization, denoising techniques for additive Gaussian noises become available for Poisson denoising. This chapter summarizes some of such existing methods. Next, image fusion problems are dealt with. Image fusion is a technique to synthesize a full focused picture, in which all the contents are focused, from a set of partially focused images with different focal lengths. At present, there are several types of image fusion techniques. Those include spatial domain, feature space and transform domain techniques. In the spatial domain and feature space approaches, the synthesis performance heavily depends on the adopted segmentation algorithm, and they prone to fail fusion at object edges, while the transform domain approach is influenced by the adopted transform. In order to improve the quality of fused image, some disadvantages of existing methods are discussed in this chapter. This chapter mentions the possibility of improving the performance of Poisson denoising and image fusion from viewpoints different form existing researches. In Chapter 2, from comparison with Discrete Cosine Transform (DCT) and Discrete Wavelet Transform (DWT), the features of directional lapped orthogonal transforms (DirLOTs) are discussed and emphasized For preparation of Chapter 3 and later, explanations on DirLOTs are given through some figures and expressions. Based on the relationship between directivity of DirLOT and slant edge and texture of image, the possibility of the performance improvement of image restoration is described. In Chapter 3, a Poisson denoising method is proposed. Various discrete wavelet transforms have been used for Poisson image denoising. However, the transforms have disadvantages such as shift variance, aliasing, and lack of directional selectivity. PURE-LET is known as an efficient Poisson denoising