Research On Wavelet Compression Based On The Multiscale Geometric Analysis

In recent decades, with the development of computer technology, the higher demand is put forward by people in terms of the quality and volume of the digital image, therefore, the amount of image data increasing quickly, which brings big problems for data storage and transport. It's necessary to compress the image to meet the needs of various applications. Lots of useful information contained in the image details, such as textures and contours. Different types of images contain different details, how to retain the useful information has become a hotspot of the current study. This research is aimed at the problem.Wavelet transform achieves great success in the image compression, but due to limitations of its theory, the ability of impress the details of high dimensional space is limited. This article introduces the basic theory of wavelet transform in details, and analyzes the characteristics of wavelet transform deeply. On the basis of wavelet transform, multiscale geometric analysis (MGA) theory achieves great development, and it has become one hot direction of the digital image compression research. MGA has the characteristics of anisotropy, and it can approach a high dimensional function containing line singularity effectively. This novel introduces the effective MGA tool——Contourlet transform. In a sense, Contourlet transform is a real 2D image sparse representation. It can impress the singularities of image effectively, and it performs well in image processing. Contourlet transform adopted double filter bank structure:first, using Laplace pyramid transform to do image multi-resolution analysis; second, using direction filter bank to do direction decomposition. LP decomposition is a redundant decomposition, so Contourlet transform does not suitable for image compression. To overcome this shortcoming, a new kind of MGA tool WBCT was proposed. WBCT combines wavelet transform and direction filter together realizes a no redundant transformation. Then, this article introduces two classic embedded coding methods:EZW and SPIHT.The WBCT-based SPIHT compression coding method restores the image directional character much better. It performs good to the image with more details, but for the image with little details, multiple directions decomposition will reduce the effect of decoded image. Therefore, this article puts forward the concept of smoothness, and the direction decomposition of wavelet sub-bands depend on smooth. According to the structure of coefficients from the algorithm proposed in this article, SPIHT algorithm was improved. Experiments show that the proposed algorithm can made different degree of direction decomposition to different types of images, and the decoded image is better than that form wavelet transform and WBCT.