透過精確計算對分段連續訊號進行高效率的基底擴展

Abstract

在日常生活中，分段連續訊號無所不在，例如生物醫學訊號（心電訊號）、數位影像訊號、半導體測量訊號等。然而，此類訊號，特別是在奇異點(singular point)附近的訊號，特別難近似，常常會出現失真或需要過多的儲存資源。 因此在本篇論文中，我們採用了時頻分析和基於基底擴展的訊號處理的概念，提出了一種基於訊號分段連續性的分類演算法，對訊號進行預處理並將其分割為高頻區間和低頻區間；隨後，我們還提出了三種對於這些分段信號做相對應處裡的信號壓縮方式。 最後，我們建立了一個測試壓縮方法的平台，使用累積合比(Cumulative Sum ratio)作為信號經壓縮後，還原能力的評斷依據(evaluation criteria)，並使用20種壓縮方法和我們所提出的三種方法做比較，並加入權重排名機制(weighted ranking)使比較更具參考價值，由最後的測試結果可看出，我們提出的壓縮方法是可以應用於準確的尋找ECG信號R峰值(R peak)區間和影像信號的壓縮。

In daily life, piecewise continuous signals are ubiquitous, including biomedical signals (ECG signals), digital image signals, semiconductor measurement signals, etc. However, these signals, especially in the location near singular points, often suffer from distortion due to approximation difficulties or require excessive storage resources. In this thesis, we employ the concepts of time-frequency analysis and signal processing based on basis expansion. We propose a classification algorithm based on the piecewise continuity of signals to preprocess and segment them into high-frequency and low-frequency parts. Subsequently, we propose three methods for decomposing each segmented signal. Finally, we established a platform for testing compression methods, utilizing the Cumulative Sum ratio as the evaluation criterion for the signal''s restoration ability after compression. We compared 20 compression methods with the three methods we proposed, incorporating a weighted ranking mechanism for a fairer and more informative comparison. The final test results show that our proposed compression methods can accurately locate the R-peak intervals in biomedical ECG signals and compress one row of image signals.