Splines 應用於訊號與影像之多重解析度處理

Abstract

摘要 多重解析度處理(multiresolution processing)在訊號或影像研究上已證實其重要性。除了一般空間訊號的內插補點的應用外，對於任何含有需反覆疊代之演算法或演算處理時間過長的訊號分析處理方法，提供了增加其工作效率的可能性。 本論文重點在探討曲線規法(splines)及其在影像與生醫訊號(腦電波)之分析處理效能。文中將介紹近代曲線規法的擴張模型(expansion model)與縮小模型(reduction model)，並使之合併成一種適用於多重解析度處理的工具。除此，亦針對此模型進行簡化與改良，俾能降低模型於應用時(implementation)的複雜度。高品質曲線規模型HQS (High-Quality Splines model) 也基於簡化的目的產生，該模型可提供單一結構來達成擴張與縮小解析度的功能。 金字塔結構(Pyramid structure)分析是多重解析度處理的一種形式，本篇分析了兩項較常見之應用：高斯金字塔(Gaussian pyramid)與拉普拉斯金字塔(Laplacian pyramid)。在實驗方面，分成灰階影像與腦電波訊號處理兩部分，採用前述的金字塔結構對曲線規法進行分析，並與其他三種常見的多重解析度處理方式相比較，而結果顯示曲線規法在所測試之灰階影像及腦電波訊號的多重解析度處理上，均獲得最好的表現。

Abstract Multiresolution processing has proved its importance in signal and image researches. Besides solving the interpolative problem, its robustness for reliable data compression (reduction) benefits the complicated or iterative operations often required by the signal and image analysis. This thesis introduces the novel splines theorem and discusses its applications to image and electroencephalograph (EEG) signal. Two novel splines model are introduced: splines expansion model and reduction model. They are combined to be one single model for multiresolution analysis. In addition, for decreasing the complexity of implementation, the splines model is reformed to be the high-quality splines model (HQS model), which provides a unique structure for expansion and reduction. Pyramid structure is another approach used in the multiresolution analysis. Two common pyramid models are introduced in this thesis: Gaussian pyramid and Laplacian pyramid. In the experiments, we apply the pyramid concept to the splines and analyze its performance. We compare it with the other three common methods for multiresolution processing, applied to the image and EEG signal. The results show that using the splines model can achieve the best quality in the rescaling of images and EEG signals.