延遲相乘加總(DMAS)成像使用通道對的乘法耦合來獲得接收孔徑的空間同調性，因此相較傳統延遲加總(DAS)成像具有較高影像解析度和對比度。然而現有之DMAS成像是基於射頻通道信號進行乘法耦合，因此射頻通道信號必須預先進行過取樣處理以避免頻域混疊並搭配帶通濾波以隔離出二次諧波的成像分量。
本論文提出了基於基頻通道信號的DMAS成像演算法(BB-DMAS)，由於基頻通道信號的乘法耦合不會造成頻譜上移，BB-DMAS無須上述過取樣和帶通濾波即可得到高品質的超音波影像成像，BB-DMAS成像保留時間延遲後的複數通道信號相位並調整其振幅為p次方根值，在通道加總之後進行p次方以恢復其原始信號維度，其中 p值可為任意有理數來提供彈性可調的影像品質。BB-DMAS除適用固定發射聚焦的成像模式之外，也可實施於平面波複合之發射合成聚焦影像。
研究結果顯示BB-DMAS和RF-DMAS之間的成像結果是相仿的，且BB-DMAS成像可以視為DAS成像與通道域相位同調因子(PCF)的相乘，其可適性同調權重特性可以衰減旁瓣及雜波等低同調分量。隨著BB-DMAS成像中有理數p值的增加，抑制橫向旁瓣、柵瓣和隨機雜訊的能力提高，發射聚焦實驗結果之影像對比度從DAS的-24.8 dB減小到BB-DMAS的-34.3 dB (p=1.5)，-43.0 dB (p=2.0)和-51.4 dB (p=2.5)。但由於發射聚焦區域中信號同調性較高，DMAS成像會在焦深處呈現明亮區域而導致固定發射聚焦成像下之影像均勻性低。對於依賴多角度平面波同調複合之合成聚焦影像，BB-DMAS亦可實施於由發射角和接收通道兩個維度構成的回波矩陣中來產生輸出影像，與文獻中僅在單一維度上進行延遲相乘加總計算的方法相較，本論文提出的二維延遲相乘加總(2D-DMAS)成像可直接提取二維信號同調性以進一步提高影像品質。實驗結果顯示影像橫向寬度從DAS的0.53 mm減小到2D-DMAS的0.42 mm (p=1.5)，0.36 mm (p=2.0)，0.31 mm (p=2.5)及0.28 mm (p=3.0)，且同一p值下之2D-DMAS成像橫向寬度均較文獻中僅在單一維度上提取信號同調性的方法更低。
但DMAS成像會增加超音波影像斑點變異程度，影像對比雜訊比反而隨p值增加而減小，因此在未來的工作可以結合其他抑制斑點技術以找到對比度和對比雜訊比之間的最佳平衡。

Compared to conventional Delay-and-Sum (DAS) beamforming, Delay-Multiply-and-Sum (DMAS) imaging uses multiplicative coupling of channel pairs for spatial coherence of receiving aperture to improve image resolution and contrast. However, present DMAS imaging is based on the radio-frequency (RF) channel signals (RF-DMAS) and thus requires large oversampling to avoid aliasing and switching of band-pass filtering to isolate the corresponding spectral components for imaging.
Baseband DMAS (BB-DMAS) beamforming in this study is based on the demodulated channel signals to provide similar results but with simplified signal processing. The multiplicative coupling in BB-DMAS always renders baseband signal and thus the need for oversampling is eliminated. The BB-DMAS beamforming scales the magnitude of time-delayed channel signal by p-th root while maintaining the phase. After channel sum, the output dimensionality is restored by p-th power. The BB-DMAS can use any rational p value to provide flexible image quality. Besides, BB-DMAS is applicable to both fixed transmit focused imaging and synthetic focused imaging such as plane wave compounding.
Our results show that the image characteristics between BB-DMAS and RF-DMAS are similar. BB-DMAS beamforming can be seen as the adaptively weighted DAS beamforming with the phase coherence factor (PCF) among receive channels. The suppression of lateral side lobe level, grating lobe level and uncorrelated random noises gradually increases with the p value in BB-DMAS beamforming. The image contrast decreases from -24.8 dB in DAS to -34.3 dB, -43.0 dB and -51.4 dB in BB-DMAS, respectively with p value of 1.5, 2.0 and 2.5.
The DMAS beamforming would exhibit bright region at the focal depth due to higher signal coherence in the transmit focal zone and thus compromise the image uniformity. Therefore, this study attempts to overcome this problem by using unfocused plane wave imaging. For plane-wave (PW) imaging, multi-angle coherent compounding relies on two-dimensional (2D) summation of echo matrix in both dimensions of transmit angle and receive channel to produce the image output. Previously, Delay-Multiply-and-Sum (DMAS) beamforming has been combined with multi-angle PW imaging but only in either one dimension. In this study, a novel 2D-DMAS operation is proposed for multi-angle PW imaging to extract the 2D spatial coherence of echo matrix for further improvement of image quality. Our results show that the lateral width (LW) decreases from 0.53 mm in DAS to 0.42 mm, 0.36 mm, 0.31 mm and 0.28 mm in 2D-DMAS, respectively with p value of 1.5, 2.0, 2.5 and 3.0. Moreover, 2D-DMAS consistently provides the lowest LW when compared with the aforementioned reference methods.
However, DMAS beamforming exhibits a lower CNR caused by obvious granular speckle pattern and thus noticeably elevate the speckle variation. Future work may focus on the combination of DMAS beamforming with the speckle suppression techniques to find the best trade-off between image CR and CNR.

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