The Research And Applications Of Symmetric Extension Transforms On Wavelet Image Processing

In recent years wavelet transform has received substantial attention in image processing. It can combine the time domain and the frequency domain. It analyses the images by Multi-Resolution Analysis. At the same time, it can decompose the image into different independent bands administering to be encoded by different methods, which have been proved an effective technique for high quality coding at low bit rate.The image is finite-length sequence. When an image, which is decomposed by wavelet, is reconstructed, sub-band signal data points will increase, at the same time, the boundary distortion will be introduced. In order to reduce the information lost or distortion of image, in the wavelet transform, we need make extension of the boundary of the original signal.In this paper, after the analysis and comparison of the common extension, we use symmetric extension transform to solve the problem. After the detailed analysis of symmetric extension types and the symmetric types of filter, we derived the symmetrical relationship of the convoluted and decimated signals with finite length. We build the multi-level two-dimensional wavelet transform system for any symmetric types of images and filters and also build the interface of the system. And we introduce two kinds of optimization strategy to reduce the complexity of the algorithm: Based on the principle of convolution and decimate, only half of the data are calculated in the process of decomposition; the extension length of input signal and sub-band signal only equal to the maximum length of filter banks. At the same time, the realization of algorithm by convoluting in time domain and the establishment of index matrix for the decomposition vector make the algorithm simpler. This structure will be applied to the image coding, it make coding on wavelet decomposition coefficient with SPIHT algorithm, then make decoding and reconstruction, compare the PSNR between the reconstructed image and the original image.The results show that the image can be perfectly reconstructed without any boundary distortion in this way. And it is obvious that the reconstructed image with symmetric extension methods can always be better than that reconstructed with periodic extension method. It proved to have improved the PSNR of the reconstructed image comparing with the method of periodic extension. It is also proved to have improved the PSNR of the compressed images by simulation in Matlab. Experiments show that the symmetric extension algorithm comparing with other methods is more effective in resolving the problem of signal extension during the decomposition of sub-band signal, and it is worthy of application.