Design Algorithms Of Two-dimensional NPR Cosine Modulated Filter Banks

Two-dimensional(2-D) multirate filter banks have been used widely in image compression, computer vision and texture discrimination and classification, etc. In practical applications, we desire that 2-D filter banks have some properties, such as linear phase, nonseparable and nonuniform, etc. This paper mainly studies the design of 2-D cosine modulated filter banks with nearly perfect reconstruction(NPR). This dissertation consists of two parts.Part one presents a design method of 2-D linear phase nearly perfect reconstruction (LP-NPR) filter banks based on cosine modulation. Firstly, the Parks-McClellan algorithm is adopted for designing the prototype filter. And then, by employing a new class of cosine modulation, 1-D NPR filter bnaks with linear phase(LP) property can be obtained. Next, we cascade two 1-D LP-NPR filter banks in the form of tree structure to design a separable 2-D filter banks. Finally, with the unimodular transformation, a nonseparable 2-D LP filter banks is constructed, which meets the requirement of NPR. Experimental results indicate the proposed method is feasible, and the designed filter banks can obtain the satisfying reconstructive precision.In part two, in many practical applications, ones desire the different frequency bands have different resolution when analysing the signals or images. So filter banks are required to have nonuniform freguency tilng. Based on the scaling algorithm, we analyse the structure of the 2-D nonuniform filter banks. Further, using the unimodular transformation, we give a simple method for designing 2-D nonseparable nonuniform filter banks. In some constrained conditions, the whole system achieves NPR. Finally, an example is given to demonstrate the given method.