利用可調式取樣及二維轉換法之心電信號編碼

Abstract

本文提出兩種新型的心電圖訊號壓縮技術。第一種方式是採取可調式取樣方法，而第二種方式則透過二維離散餘弦轉換(DCT)法。後者可提供較佳的壓縮比但前者的複雜度較低。

由於心電圖波形並不是每個地方變化都很快，因此我們根據其波形的變化率來決定它的取樣速率，在我們的演算法裡採取兩種取樣頻率，當波形變化快時，則取樣頻率高；反之，則取樣頻率低。透過可調式取樣方法不僅使得記憶體的需要量減少，並且演算複雜度也大大降低。

除此之外，我們也利用心電圖每個心跳之間的相關性來增加壓縮比。首先，先將一維的心電圖轉換成二維矩陣之後，接著做二維離散餘弦轉換法，則可得到稀疏矩陣，其中非零項的部分已非常少，我們可以只量化其中非零的部分項，所以其壓縮比大約是一維方法壓縮比的兩倍。

由於心電圖波形的重要部份在於QRS這個位置，我們為了讓醫生可以更精確的偵測此病人是否有心臟毛病，我們想出了一套方法來強調這個重要部份的精確性。首先，我們先將心電圖分成兩個部分，一個是QRS的部分，這個部分我們在量化其頻譜的值時，採用較多的位元去量化，如此一來這個部分的失真率則大為減少。反之，比較不重要的部分，我們則採取較少的位元來去作量化，透過此方法，我們的壓縮比率超過22，而在均方跟誤差百分比則達到3%以下。

The electrocardiogram (ECG) is an important biomedical signal for the diagnosis of heart diseases. Efficicient ECG waveform coding for long-term recording and effective real-time transmission have received constant intensive attention in modern clinical applications. In this thesis, we propose two new ECG waveform coding methods that require reduced memory and provide high compression ratio (CR) performance. The first approach uses a variable sampling rate analog-to-digital converter that adapts to the waveform variation rate. It reduces not only the computational complexity but also the memory requirement for subsequent discrete cosine transform as well. The second approach is based on the observation that ECG signals often exhibit a near-periodic behavior. We first convert the one-dimensional ECG waveform into a two dimensional (2D) array by the Average Magnitude Difference Function (AMDF) method then apply a two dimension time/frequency transform to increase CR as much as possible. The resulting CR is about 21.87 and the percent-root-mean-square (PRD) is 3.25% which is much better than that of the 1-D approach based on adaptive sampling. In order to further improve the performance of the 2-D approach and capture the important part of ECG signals (QRS wave), we employ a sample-dependent multi-rate quatization approach which gives an improved CR of 22.05 and PRD of 2.88%.