Non-Separable Wavelet Theory And Applications In Image Compression

Multivariate non-separable wavelet is an important research field in the developing of wavelet theory. It has great significance both in theory and application. The paper starts with the point of application, mainly studying the construction of bivariate non-separable wavelet and its applications in image compression.First, the paper studies the property of orthogonal MRA based on a general dilation matrix from the beginning of multi-scale analysis in multidimension. And it discusses the multi-dimensional sampling, the decomposition and reconstruction of multi-dimensional signals using non-separable wavelet. The perfect reconstruction condition of multi-band wavelet in multi-dimension is also given.Next, the problems of construction of non-separable wavelet bases are studied. From the frame of multivariate orthogonal MRA, we discuss the construction of bivariate non-separablewavelet with compact support based on dilation matrix and get severalconclusions. The construction of bivariate bi-orthogonal non-separable wavelet is also realized using the CBC algorithm and McCllean transform.At last, the paper studies the application of non-separable wavelet in image compression. The character of quincunx wavelet transform and non-separable wavelet transform based ondilation matrix is studied first. Then combining with the character of the twoclasses of non-separable wavelet and the wavelet zero tree structure, using the ways of changing the mode of image decomposition, we give the experiments result of the two classes of wavelet combining with SPIHT coding in image compression. And we compare their performance with the typical CDF97 wavelet.