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The Study on Boundary Processing of Wavelet Transform and It’s Application

Author: LiYin
Tutor: XueJian
School: Beijing Jiaotong University
Course: Circuits and Systems
Keywords: Wavelet Transform Image boundary treatment Symmetric extension algorithm Two - channel filter banks SPIHT Coding
CLC: TP391.41
Type: Master's thesis
Year: 2009
Downloads: 184
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Abstract


The concept of wavelet transform is engaged the oil signal processing the engineers J.Morlet in 1974 first proposed by France compared with the Fourier transform, wavelet transform is a local transformation of the space (time) and frequency, and thus can be effectively extracted from the signal information to solve the Fourier transform can not solve many difficult problems in real life, the voice signal is one-dimensional or two-dimensional image signal are limited length, however, been widely used wavelet transform Mallat algorithm is based on infinite signal therefore Mallat algorithm for finite-length signal applications need the signal continuation, extension algorithm plays a decisive role in the quality of the recovery image. In this paper, the first to study the wavelet transform and Mallat algorithms, filter banks, sampling and interpolation basic theory, then theoretically prove that the use of symmetric periodic continuation algorithm can accurately reconstruct the signal in the case of the wavelet transform coefficients increase and a detailed analysis of the case of the one-dimensional two-channel signal by the symmetry of the symmetry of the signal, the signal is twice the sampling filter symmetry, signal reconstruction filter after the continuation of several symmetric periodic extension algorithm wavelet transform key technologies, different signal required intercepted twice the sampling point determination method, and the coefficient is not more accurate reconstruction of the conditions, the signal decomposition and reconstruction boundary extension required the shortest Points effectively reduce the degree of complexity of the algorithm and the computational complexity of the algorithm itself. Matlab simulation either for the odd long or even long signal, symmetric periodic extension algorithm appropriate selection of filters and signal the two ends of decomposition and reconstruction continuation can be accurately reconstructed image is given the symmetric cycle extension algorithm flowchart wavelet transform extension possible way, and specific wavelet transform coefficients are given in the figure, an example to illustrate the precise weight of the signal in the wavelet transform coefficient increase structure. Subsequently, through the comparative analysis of the experimental data, found and pointed out that the lack of the symmetric extension algorithm used by Matlab, improvement ideas and methods, the preparation of the relevant procedures, improved symmetric extension algorithm to restore the image of the peak noise ratio (PSNR, PeakSignaltoNosieRation). At the end of this article, the symmetric periodic extension algorithm is applied to image two-dimensional wavelet transform, introduced the EZW and SHIHT algorithm based on wavelet transform coefficients of the image in accordance with the the SPIHT algorithm coding standard codec verified to symmetric extension algorithm to decompose, the higher PSNR reconstructed image at the same time from the point of view of the energy is concentrated in the transformed symmetric extension algorithm is more suitable for image coding. Symmetric extension algorithm in the case of the wavelet transform coefficients increase accurate reconstructed signal after the transformation of the energy is more concentrated, the reconstructed image has a higher PSNR than other extension algorithm reconstructed image in the field of image compression certain practical application significance.

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CLC: > Industrial Technology > Automation technology,computer technology > Computing technology,computer technology > Computer applications > Information processing (information processing) > Pattern Recognition and devices > Image recognition device
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