The Dct Fast Algorithm And Filter Structure Of The Wavelet Transform Domain Image Noise Reduction

The thesis includes two parts: the research for fast algorithms and filterimplementation structure of discrete cosine transform (DCT), research forwavelet-based image threshold de-noising. The discrete cosine transform is one ofthe important tools in signal processing and image/video processing, which isaccepted by several international standards, such as JPEG, MPEG, H.263. Theprecondition for using DCT in practical system is the algorithms for fastimplementation of DCT existing. Since the first true DCT fast algorithm isproposed in 1977, looking for the faster, more structured and simpler algorithm forDCT is one of research topics in signal processing fields. According to therequirement for various lengths of DCT in applications, the thesis deals with thefast algorithms and filter implementation structures suited for implementing inhardware and parallel processing. The main achievements includes:1) A new fast algorithm for computing prime length DCT using cyclicconvolutions is proposed. The algorithm possesses regular implementationstructure and lower operational complexity compared with existing algorithms.It is suited for both software and hardware implementation.2) A very efficient algorithm for 4×4 two-dimensional DCT is presented. Thealgorithm is also used in various rectangle two-dimensional DCT as a kernelmodel. The experiment results indicate that the algorithm is four times fasterthan row-column algorithm.3) According to the mathematic properties of DCT, a new algorithm of N×N(N=2~n) two-dimensional DCT implementing by N N-point one-dimensionalDCT.4) A new recursive decomposition algorithm for q~m length DCT is proposed.According to the number decomposition theorem in number theory, using theabove algorithms proposed, a new fast algorithm for computation of compositelength DCT is constructed.5) By special designed fast polynomial transform algorithm and reduced DFTalgorithm, a new algorithm for computing q~n×q~m ( q is odd prime, m and n arearbitrary integers) two-dimensional DCT is proposed.6) Meeting the requirements of hardware-implementing DCT, we deal with thedigital filter implementation structure of DCT with various lengths and propose(1) second-order recursive filter structure for prime length DCT;(2) parallel processing first-order recursive filter structure for length 2n DCT;(3)second-order recursive filter structure for DCT with arbitrary length.Wavelet transform is a new signal processing tool developed in 1980's, whichhas good time-frequency localization and signal-noise separation properties.Recently, wavelet transform is widely used in signal, image/video de-noising. Thethreshold filtering is a simple and practical method for wavelet-based imagede-noising. The thesis deals with the modification of the image thresholdde-noising by using some properties of the wavelet transform. The main workincludes1) Adjusting the de-noising threshold adapted to the energy of image signal, thedistribution of image energy in wavelet transform domain and the inheritproperty between wavelet coefficients in parent and child sub-bands, weconstruct a new adapted threshold image de-noising system. The PSNR ofrecovered image in the system is increased 1~2db than the fix thresholdde-noising system. The observation shows that there is more detail informationreserved in the recovered image of our system.2) Considering the selectivity of wavelet base in the wavelet transform, we havetested and analyzed the performance of different wavelet base used in thresholdde-noising system. It is shown that there are mutual supplement betweendifferent wavelet bases. Based this fact we propose two multi-channelthreshold image de-noising system. The experiment results shows that thePSNR of recovered image is further increased 1~2db than the single channelsystem.3) Combining the adapted threshold filtering and the multi-channel thresholdimage de-noising system, we construct an adapted multi-channel parallelthreshold image de-noising system. The de-noising ability of the system isimproved further. The PSNR of the system is increased 1~2db than the singlechannel adapted system.