The Study And Realization About Adaptive Wavelet Transforms Via Lifting

Wavelet analysis has attracted many researchers' attentions in recent twenty years. It becomes one of the important tools in signal analysis fields. As the second generation wavelet with the special algorithm structure, the lifting wavelet is proposed for improving the operation speed of traditional wavelet and reducing the memory requirement. It is also fit for adaptive, nonlinear and integer to integer transform, so it becomes a research hotspot in the information science field.In the traditional wavelet transform, because the wavelet filter and coefficient is fixed, and it can not change by the input signals. As a result, when the discontinuous signal is analyzed, it will produce a lot of big wavelet coefficients in the sharp transitions. In the image processing, some images have sharp edges, smooth or oddity in parts and there are some letters in them. When we use traditional wavelet analyzing these images, the processing effects are very bad. To solve this problem, with the advantage of the lifting, the adaptive wavelet transforms via lifting is proposed. In the transform, update filter is selected by the signal's character. Perfect reconstruction is possible without any overhead cost. The goal of selecting update filter is to hold the edge's definition and small wavelet coefficients. To make sure the system's stability, in the lifting scheme of adaptive wavelet, update step is placed before prediction step. In this framework, prediction step doesn't affect update step, so it will not affect the next transform. And the condition is applied for the adaptive by the framework. The Adaptive wavelet transforms via lifting is benefit for the image compression, because of the high stability, the small coefficients of high frequency parts, and the perfect reconstruction. With the adaptive wavelet transforms via lifting and the SPIHT, the image compression is realized in this paper, and the result is pleasant.To validate the practicability of this algorithm, the algorithm is simulated in the last part of this paper. The results of the simulating indicate that The Adaptive wavelet transforms via lifting is effective to the image compression.