DCT快速新算法及滤波器结构研究与子波变换域图像降噪研究

【作者】 殷瑞祥；

【导师】 徐秉铮； 余英林；

【作者基本信息】 华南理工大学 ， 通信与信息系统， 2000， 博士

【摘要】 论文包括两个方面:离散余弦变换(DCT)的快速算法及滤波器实现结构,子波变换域图像门槛降噪。离散余弦变换是广泛应用于信号处理、图像处理领域的重要工具之一,已经被多个国际标准所接受,如JPEG、MPEG、H.263等。DCT应用到实际系统中的前提是具有能够快速实现的算法,自从1977第一个真正的DCT快速算法出现以来,寻求更快、更规则、更简单的DCT快速算法一直是信号处理领域的一个研究方向。论文针对应用中对DCT长度的各种需要,研究DCT的快速算法和适用于硬件和并行处理的滤波器结构。取得的主要进展有:1)提出了一种用循环卷积实现的素长度DCT快速新算法,算法具有规则的实现结构,与现有算法相比具有更低的运算复杂性,算法不仅适用于软件实现,而且适用于硬件实现。2)提出了一种非常高效率的4×4二维DCT算法,并将其作为核心模块构造在各种矩形二维DCT计算中。实验表明,新算法比行列法快4倍。3)根据DCT变换的某些数学特性,推导并提出了一种将N×N(N=2~n)二维DCT转化为N个N点一维DCT计算的快速算法。4)提出了一种新的q~m长度DCT的基q递归分解算法。根据数论关于数的分解定理,提出了一种新的任意复合长度DCT的快速算法。5)利用特别设计的快速多项式变换算法和RDFT(reduced DFT)算法,提出了计算q~n×q~m(q为奇素数,m、n为任意整数)二维DCT的快速算法。6)根据硬件实现DCT的需要,研究了各种长度的DCT用数字滤波器实现的结构。提出了(1)素长度DCT的二阶递归滤波器结构;(2)2n长度DCT并行处理一阶递归滤波器结构;(3)任意长度DCT的二阶递归滤波器结构。更多还原

【Abstract】 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.更多还原