Multidimensional All Phase Digital Filtering Theory And Image Multiscale Geometric Representation

Multiscale geometric representation is considered to be optimal in capturing multidimensional singularities and representing multidimensional function. In terms of digital filtering, multiscale geometric representation of images is in fact a multidimensional filtering problem. This paper proposed a series of design theory of all phase multidimensional multirate digital filter and all phase biorthogonal quincunx filter bank base on multidimensional all phase digital filtering theory, and explored its application in multiscale geometric representation of images. The researches are of great theoretical significance and open new prospect of application. The dissertation is proved innovational in the following respects:Firstly,a general method for designing multidimensional all phase digital filter (APDF) was proposed starting from an one-dimensional prototype APDF, which laid the foundation of multidimensional all phase digital filtering theory. The method is applicable to arbitrary rational decimation/expansion matrix H, and able to design and implement high-performance APDF with an arbitrary parallelepiped-shaped passband support. Besides, the parameter estimation formulas for the passband and stopband ripples and transition band vector of resulting filters were derived.Two-channel Quincunx filter bank (QFB) is the key filter bank in multiscale geometric representation of images. A design scheme for QFB was presented with high performance and simple implementation. While retaining linear phase and perfect reconstruction, all phase biorthogonal quincunx filter bank (apbQFB) was constructed from all phase diamond transformation kernel function, taking quasi-QMF model and CDF family of biorthogonal wavelet as one-dimensional prototype filter bank. Typeâ… apbQFB and Typeâ…¡apbQFB was designed and used to generate two new Contourlet transforms.A new class of biorthogonal wavelet filter banks, namely equal-even length anti-symmetric biorthogonal wavelet was studied to enhance the theories of wavelet transform and multiscale geometric representation. Both analysis and synthesis filters in each of these wavelet filter banks have the same even length, and wavelet function is anti-symmetric with many characteristics such as differential operator property.Due to the direct current leakage of conventional DFB, overcompleteness of Contourlet and limited directional selectivity of DWT, it is vitally necessary to explore multiresolution DFBs with brand-new frequency plane division and implementation to combine multiscale, multidirection and nonredundancy efficiently. This paper discussed systematically quincunx multiresolution DFBs, and all phase nonuniform quincunx DFB (apnuqDFB) were constructed on the basis of apbQFB. Nonredundant multiscale and multidirectional hybrid structures were implemented by combining apnuqDFB with DWT successfully. Compared to DWT and Contourlet, apnuqDFB demonstrates certain superiority in representing directional detail and high texture of images.