Implementation of 2-D Biorthogonal Wavelet Transform Using 2-D APDF

다국어 초록 (Multilingual Abstract)

All phase digital filter (APDF) is a new type of linear phase FIR digital filter which was proposed in recent years, and a general method to design 2-D FIR digital filters called 2-D APDF is presented in this paper. Firstly, the theory of biorthogonal wavelet transform and 2-D APDF is expounded. Secondly, a novel algorithm is proposed to implement biorthogonal wavelet transform by using 2-D APDF based on DFT and IDCT. The relations between two kinds of filters are discussed. As an important application of biorthogonal wavelet transform, multi-resolution analysis of 2-D image signal could be used to test the feasibility and applicability of the proposed algorithm. Finally, the test image can be reconstructed perfectly in the multi-resolution analysis of 2-D image experiment using MATLAB tool in this paper, and the analysis indicates that the proposed method performs well.

목차 (Table of Contents)

• Abstract
• 1. Introduction
• 2. Biorthogonal Wavelet Transform
• 2.1. One-dimensional Mallat Algorithm
• 2.2. Two-dimensional Mallat Algorithm
• 3. The Method to Design 2-D APDF Based on DFT
• 3.1. The Principle of All Phase Digital Filter (APDF) Based on DFT
• 3.2. Derivation of Transition Matrix GN
• 3.3. The Method to Design a 2-D APDF Based on DFT Using Transition Matrix
• 3.4. 2-D APDF Filtering Realized in Transform Domain
• 4. Algorithm Design of Biorthogonal Wavelet Transform Using 2-D APDF
• 4.1. Process of 2-D Biorthogonal Wavelet Transform Using 2-D APDF
• 4.2. The Process of a 2-D Signal through the 2-D APDF Realized in Transform Domain
• 4.3. Solving the Sequency Response Matrix in the 2-D APDF
• 5. Experimental Results
• 6. Conclusion
• Acknowledgements
• References