The Classical And Novel Wavelet Theory With Application In The Field Of Image Processing

This thesis aims to study the application of wavelet family in image processing, especially in remote sensing image. The main innovative contributions of this dissertation are as follows:Firstly, the author gives a thorough introduction on the history of classical wavelet analysis, including the source from Fourier analysis, and the background of signal processing. Also on the main idea of the wavelet transform, MRA, especially the Daubechies wavelets.The success of wavelets is mainly due to the good performance for piecewise smooth functions in one dimension. Unfortunately, such is not the case in two dimensions. The ridgelet system is very well at representing the smooth functions with line singularities. The curvelet has the best ability at representing the smooth functions with curvilinear singularities. Abilities of ridgelet and curvelet make them superior to the classical wavelets for image processing.Texture is an important attribute in the image, which provides substantial information for the recognition and interpretation of this image.Contourlet transform has good multi-resolution, localized and directional characteristics. The method based on Contourlet+IHS transform is proposed to fuse SAR image and multi-spectral images. A global dual frame(GDF) and the local dual frame (LDF) representation for the digital ridgelet reconstruction algorithm is discussed.Combing the basic theory of multi-scale Gabor and BP neural net, Gabor filter recognization algorithm is designed, which can solve bottle-neck problem namely Gabor feature vector dimension is relatively high, as well as large computational complexity. A construction method of edge detection function and a curvelet-based Geodesic snake(CGS) is proposed, and applied to complex image segmentation of multiple objects.