| Summary: | 碩士 === 國立臺灣大學 === 電信工程學研究所 === 100 === In this thesis, we mainly focus on the applications of discrete orthogonal polynomials, including time series approximation and segmentation, build of time-variant autoregressive (TVAR) process model and implementation of Savitzky-Golay filter (S-G filter) for image and signal processing. Besides, I also introduce the Finite difference time domain (FDTD) method, a numerical method used for solving electromagnetic wave equation originally, and its applications to path planning and image segmentation.
About the structure of this thesis, first, the definition and common properties of discrete orthogonal polynomials are introduced. Then using discrete orthogonal polynomials as bases, we apply them for time series approximation and segmentation with new developed fast update equation of weighting coefficients, estimation of parameters of time-variant autoregressive model and realization of Savitzky-Golay smoothing filter.
Also, I summary the main applications and properties of Savitzky-Golay filter, such as digital differentiator, image enhancement and image denoising. I further proposed the multi-scale adaptive image denosing method based on the concept of Savitzky-Golay filter. Compared with traditional image denosing using Savitzky-Golay filter, the proposed method can maintain the detail of image better when denosing.
May this thesis will be useful for you.
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