A TIME-FREQUENCY ADAPTIVE SIGNAL MODEL-BASED APPROACH FOR PARAMETRIC ECG COMPRESSION 14th European Signal Processing Conference (EUSIPCO 2006), Florence, Italy, September 4-8, 2006, copyright by EURASIP N. Ruiz-Reyes, P. Vera-Candeas, P.J. Reche-L´opez and F. Ca˜nadas-Quesada 報告者 葛書銓 指導教授 陳福坤

Outline Introduction Atomic decompositions and matching pursuit Principles of atomic modelling Matching pursuit The compression algorithm Preprocessing Encoding Decoding Results and discussion

Introduction 提出一個新的ECG信號編碼方法基於時頻原子信號表示法(time-frequency atomic signal representations) 適應性訊號參數模型時頻原子的過完備字典(overcomplete dictionaries) 過完備擴展利用匹配追蹤演算法(matching pursuit algorithm)求解

Atomic decompositions and matching pursuit Principles of atomic modelling A signal model of the form can be expressed in matrix notation as With where the signal x is a column vector (N x 1), a is a column vector of expansion coefficients (M x 1), and D is an (N x M) matrix whose columns are the expansion functions [n].

The matrix D is square (N = M) and invertible, and the Expansion coefficients for a signal x are uniquely given by

Overcomplete 定義 (1) 稱為基底函數， 為展開集合是這類函數的基底 展開集合的封閉展延，表示成 稱為基底函數， 為展開集合是這類函數的基底 展開集合的封閉展延，表示成 如果展開集合不是 的一個基底，但符合定義(1)式中的展開，且其中對任意 有超過一組以上的

Matching pursuit 為一種貪婪演算法 : 求區域最佳解 (2) At the m-th iteration, the residue is: (2)

The orthogonality principle gives the weight associated to each atom at the m-th iteration: (3)

The norm of can be expressed as: (4) which is minimized by maximizing (5)

Therefore, the optimum atom (and its weight ) at the m-th iteration are obtained from (6): (6)

The computation of correlations for all at each iteration is highly computational consuming. This computation can be substantially reduced using an updating formula based on equation (2). The correlations at the m-th iteration are given by: (7)

The compression algorithm Preprocessing The P and T waves are filtered with a 0.01-50 Hz bandpass FIR filter The QRS section with a 0.1-100 Hz bandpass FIR filter. The last step of preprocessing is baseline removal.

Encoding stage of the proposed ECG compression system

In order to achieve the same PRD value at the encoder and the decoder, the optimum weight at each iteration of matching pursuit must be quantized and the reconstructed value applied to achieve the residue:

Decoding stage of the proposed ECG compression system

Results and discussion Example of reconstructed ECG signals (record 202 of MIT-BIH Arrhythmia database). (a) Original signal; (b) Reconstructed signal with PRD = 12% (bit rate = 51.48 bits/s);

(c) Reconstructed signal with PRD = 7% (bit rate = 97.80 bits/s)