The Study On Boundary Processing Of Wavelet Transform And It's Application

The concept of wavelet transform is first proposed by the French oil signal processing engineer J.Morlet in 1974.Compared with the Fourier transform,the wavelet transform is a local transform of space(time) and frequency,which can effectively extract the information from the signal.The wavelet transform can solve a lot of problems which the Fourier transforam can not slove.In real life,both one-dimensional voice signal and two-dimensional image signal have the limited length,however,the widely used Mallat algorithm orders that the length of the signal must be infinite.Therefore,the problems have been arised to extend a length-limited signal to be infinite.Different ways of extension have a great effect on the quality of the the reconstructed image.In this paper,first of all,a brief introduction is given to explain the concept of wavelet transform,Mallat algorithm,filter bankersm,the decimaltion and the interpolation of the filter banks.And then,it is proved that the signal can be perfectly reconstructed through the symmetric extension at the situation of non-expansion of the wavelet coefficients.After detailedly analysing the symmetry of the signal,the symmetry of the signal after sampling and the symmetry of the filter banks,this paper proposes a different way to incept the signal and the theory of the shortest length of the signal needs to be extended,which effectively reduce the computational complexity of the algorithm.Through Matlab simulation,it is verified that whatever the singal length is,if only choosing the right extension modes,the image can be perfectly reconstructed.And the flow chat is given to explain the process..Subsequently,through comparing the experiment data,a disadvantage of the symmetric extension which Matlab takes is pointed out.Through compiling procedures strictly according to the algorithm,the PSNR of the reconstructed image has been improve.At the end of this paper,the symmetric extension is applied to two-dimensional wavelet image transform.After coding and decoding the wavelet coefficients according to the SPIHT standard,it is found the PSNR of the reconstructed image extend by symmetric is higher than the other images extend through other ways.The symmetric extension algorithm can perfect reconstruct the image at the situation of non-expansion of the wavelet coefficients and gets the better reconstructed image.It has a certain meaning of a practical application.