Sectioned Convoluion for Discrete Wavelet Transform
Date Issued
2008
Date
2008
Author(s)
Shen, Nu-Chuan
Abstract
Discrete wavelet transform (DWT) is a very popular mathematical tool. It has been widely applied in engineering, signal processing and image processing, etc. n this thesis, we will introduce the DWT and the application of it and then I will use a method called sectioned convolution that proposed in this thesis to reduce the complexity of the DWT. The sectioned convolution is a fast algorithm of convolution by splitting the input of signal into section by section with sectioned length L, so we do not have to do the convolution until all the signal is received. It not only finds out a way to solve the delay problem but also reduces the computation time and computation complexity very much.he sectioned convolution discrete wavelet transform (SCDWT) is an application of sectioned convolution. It replaces all the traditional convolution computation in the DWT into the sectioned convolution. The efficiency implementation sectioned convolution discrete wavelet transform (EISCDWT) is an efficient way to implement the DWT. Its concept just likes the efficient implementation discrete wavelet transform but we use the sectioned convolution to instead of the traditional convolution. By this replacement, we can reduce the computation complexity and computation time. Beside the advantages that we mention above, there is another advantage that we also reduce the system complexity. Because we split the signal into the same length L, the point of FFT is fixed, the complexity of system is reduced. ecently, there are many research works about the DWT. The DWT has been used for many applications. We believe that the algorithm that we proposed in this thesis can make the DWT more powerful and have a lot of potentiality in the future. n this thesis, I will introduce the research works about the DWT systematically, including the research works of my professor and I and do a detailed comparison to the previous works. n Chap. 1, I will introduce the basic ideas and history of the wavelet transform. n Chap. 2, I will introduce the definition and the computation complexity of the DWT, including the detailed derivation, property.n Chap. 3, I will introduce the applications of the DWT simply.n Chap. 4, I will introduce the EIDWT and compare it to the traditional DWT in computation complexity.n Chap. 5, I will introduce the sectioned convolution and compare it to the traditional convolution on computation time and computation complexity. Considering the fair competition, all the programmings in my thesis are written by myself. n Chap. 9, I will do a detailed analysis of SCDWT and EISCDWT and a comparison between the DWT, SCDWT and EISCDWT. In the end of this chapter, I will compare the JPEG2000 with EISCDWT and JPEG wit DCT. n Chaps. 7, 8, I will introduce other researches of method to improve the efficiency of DWT ay this thesis be helpful for you.
Subjects
convoluiton
discrete wavelet transform
Type
thesis
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