【作者】 曹春红；

【导师】 高协平；

【作者基本信息】 湘潭大学 ， 计算机软件与理论， 2005， 硕士

【摘要】 小波框架理论是信号处理的一种有效工具,目前已经广泛应用于小波分析、信号分析、图像处理数值计算等理论和应用领域。本文阐述了小波分析与框架的一些基本理论,并且在已有的最小能量框架理论的基础上,构造了L~2 [0,1]上的区间最小能量框架,这样构造的框架对于限制于一个区间或一个紧致区域K 中的信号,不但能解决逼近空间L~2 (R)与信号空间L~2 (K)不匹配的而产生“边界效应”的问题,而且它有比较好的时频局部化特性和平移不变性,以及更大的设计自由度,在实际应用中可以把光滑性,紧支性,对称性等完美结合在一起,易于实现,对信号的重构较正交小波有更好的稳定性; 给出了L~2 [0,1]上区间最小能量框架的充分必要条件; 得到了L~2 [0,1]上的区间最小能量框架的分解和重构算法; 并通过实验验证了区间最小能量框架的优越性。更多还原

【Abstract】 Frame theory is one of efficient tools in the signal processing. At present frame theories have been widely used in wavelet analysis, image processing, numerical analysis, etc. In this paper, we first elaborates on the basic principles of frames and wavelet transforms, and constructs a class of minimum energy frames in L~2 [0,1], which not only allow the design more freedom, can have the properties in the applications with symmetry and (or) anti-symmetry, compact supports, good time–frequency localized representations and shift-invariance, but also can solve the un-matching between the space of L~2 (R) and the signal space of L~2 (K) . And then, we obtain the necessary and sufficient conditions of the minimum energy frames in L~2 [0,1]. In the final, we give the decomposition algorithm.The results of the experiments indicate that the frames constructed by us are more useful than the orthonormal wavelets in the application of signal de-noising.更多还原