Lifting Frame Work In Image Processing

As a effective tools for image processing ,wavelet has been widely used in different area. And the second generation wavelet the lifting frame work has been use in JPEG2000 as a standardization, the lifting frame work is based on the tradition wavelet, and use predicting and update to realize the second generation wavelet. And the detail process will be showed as followed .first we split the signal in to tow parts the even sting en and the odds sting on . And we can predict the odds with the even. Just because the even is quite similar to his neighbor odds. The difference Ad between the prediction and the real odds will be much smaller than the odds. So we can use the even and the difference Ad to rebuilt the whole signal. After the prediction we need to use â–³d to update the even . Update means to find a en so that in a standard Q() ,the Q(en)=Q(en-1).that is to find out the similarity of the different even in the stings. How make all the theory into realty. We know that the lifting frame work is base on the first generation wavelet, we can transform the group of filters of the tradition wavelet into a matrix of multinomial .by the theoremof Euclid ,we can factorize the matrix into some simple triangular matrix . Then we can get the coefficient for prediction and update.This article show the lifting frame work of Daubechies97 wavelet ,and base on this ,we adjust the coefficient so that we can get better SNR .we can see that if we use different coefficient to different image there will be higher SNR in the processing .we have three ways to adjust the coefficient. The first one is to adaptive pace of tracing searching . first we should identify a area for large pace searching .when the best coefficient is on the edge of the area ,we move the searching center to that number ,and go on with the same pace searching with the same large area .when the best coefficient is in the searching area ,we cut down the length of pace ,and go on with the little pace searching . the second way is 8 point searching plus 4 point searching . First we should identify the first searching point ,and searching the all 9 point include the start point .after the searching , we can get the best point from the all 9 point,if the best one is in the middle ,we change into small pace searching to search 4 point around this point .if the best point is on the edge ,we move the searching center to that point and add some point to complement the square and go on searching .when the best point turn out to be the center one .change into small pace and search the 4 point around this point .The third method is composed of the other two, we search with the first way by large pace and then we use the second way by small pace in detail searching .