Design And Application Of Directional Filters And Filter Banks

Due to the ability of extracting information directly and efficiently, digital filter have been widely used in many applications, such as communications, system identification, image processing, etc. Recently, a large amount of attention has been paid to two-dimensional (2-D) directional filters, since they can extract directional information efficiently. The design of 2-D directional filters and checkerboard-shaped directional filter banks (DFBs) as well as their applications in image processing are investigated in detail in this dissertation. The main work can be summarized as follows:Firstly, a brief review of the development of directional filters is given. Through the analysis of them, we summarize that the methods available have the following disadvantages: a) complicated optimization, that is, the coefficients of the final filters are always obtained by complicated optimization; b) limited number of directions, that is, due to the limitation of various constraints and optimization, directional filters with arbitrary orientation cannot be obtained by the existing methods. In this paper, we use polar Fourier transform to design directional filters. By rotation modulating a wedge-shaped prototype filter in the polar Fourier domain, we can obtain directional filters with various orientations. The corresponding coefficients are obtained by the inverse transform. Since no complicated optimization is involved, the filters can be obtained simply and efficiently. Further, by employing these designed directional filters, we can detect the directions of texture images exactly. Experiment results show the potential power of the proposed method.Secondly, another focus concerned is the sparse representation of texture images. The sparse representation of texture images plays an important role in the areas of image compression and image denoising. In this thesis, with the analysis on the disadvantages of employing conventional 2-D wavelet in texture image processing, we propose a class of non-redundant DFBs. The proposed DFB is constructed by using one-dimensional (1-D) M-channel linear-phase filter banks and 2-D quadrant filter banks, leading to low design complexity and easy implementation. Furthermore, the non-redundancy property makes the proposed DFB suitable for those applications requiring economical representations. The experiment results on nonlinear approximation show that the proposed DFBs have higher PSNR than the conventional wavelet and contourlet.