醫用超音波成像系統可將回音信號產生的機制區分為線性與非線性兩種系統，線性系統產生的回音信號會具有加法特性，亦即發射數種波形所產生之回音信號的總合會等於數種波形先總和再發射所產生之回音信號，然而非線性系統則否。在臨床使用上由於一般人體組織產生的信號偏屬於線性非時變系統，而用以注入血液提昇灌流區信號強度的超音波顯影劑(ultrasound contrast agents)則歸屬於非線性時變系統，故可使用脈衝相減法(pulse subtraction)對超音波顯影劑進行非線性偵測促使臟器腫瘤或心臟腔室等顯影劑灌流區域之影像對比有效提升。基於前述線性系統的加法特性，在本研究中我們嘗試從頻域上進行發射信號的分割以產生脈衝相減法之發射脈衝序列來區分線性組織信號與非線性顯影劑信號，首先設計一高斯封包的載波，稱之為全波形，再將全波形由低通濾波器進行分割程序後產生兩個總和會等於全波形之子波形，且將全波形之回傳信號與加總後的各子波形之回傳信號經相減後所殘留之信號即為超音波非線性系統的成像特徵。本研究之模擬分析與實驗結果指出，該方法確實可以有效區別超音波成像中的組織與顯影劑之區域，且區別能力和pulse inversion amplitude modulation (PIAM) 與pulse subtraction time delay (PSTD) 相差不多，故此藉由該設計方式而提出頻域之脈衝相減法以提升醫用超音波之非線性顯影劑區域的偵測能力。

The medical ultrasound imaging system can be utilized to differentiate between linear echo and non-linear echo. In linear system, the addition property holds and thus the sum of the echoes from several transmit waves are equal to the echo from the sum of these transmit waves. In non-linear system, however, the addition property fails and residual signal will be produced when the sum of the echoes is subtracted from the echo from the sum of transmit waves. Clinically, the acoustic response from native tissue resembles the linear system while that from ultrasound contrast agent (UCA) appears to be more non-linear. Therefore, the pulse subtraction (PS) method can highlight the UCA perfused region such as the myocardium and tumor by using the residual signal from nonlinear contrast responses for imaging. In this study, since the nonlinear oscillation of UCA is highly sensitive to the impinging frequency, the frequency-domain design of the transmit waveforms in the PS method was proposed by spectrally extracting subband components from the original wave. Then, the echoes from the sub-waves are subtracted from the echo from the original wave to generate specific residual signal for the non-linear microbubbles. Our simulation and experimental results indicate that the residual signal can efficiently distinguish bubbles from background tissue. The performance of our frequency-domain pulse subtraction method (FDPS) is comparable to pulse inversion amplitude modulation (PIAM) and pulse subtraction time delay (PSTD) in terms of CTR improvement.

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