## 3 Materials and Methods
### Data Processing  
The RF data, both simulated and experimentally acquired, were processed in different combinations to study image quality. The multi-transducer beamforming was performed as described in Section 2, Equations (1)-(3), and the optimum beamforming parameters, calculated as described in Section 2 (Equation (5)), were used to generate CoMTUS images. For the simulated RF data, where the actual position of the arrays in space is known, an additional image, noted as 2 probes, was beamformed by assuming an SOS of 1540 m/s and using the spatial location of the array elements. Note that, in the experimental case, this is not possible because the actual position of the arrays in space is not accurately known. Finally, the data corresponding to the sequence when the array T1 transmits and receives, i.e., \(T_{1}R_{1}\), and noted here as one probe, was used as a baseline for array performance, providing a point of comparison to the current coherent PW compounding method [15] in both simulated and experimental scenarios. Note that, for all the cases except CoMTUS, an assumed value of the SOS was used to beamform the data (1540 m/s for simulated data and 1450 m/s for experimental data).  
In order to achieve a comparison between imaging modalities that is as fair as possible in terms of transmitted energy, the CoMTUS and the 2 probes images are obtained by compounding only six different PWs, while the one probe system images are generated compounding the total number of the transmit PWs, i.e., seven PWs from \(-15^{\circ}\) to \(15^{\circ}\), in \(5^{\circ}\) steps. Specifically for the CoMTUS and 2 probe images, the results use compounded RF data when the array T1 transmits PW at zero and positive angles (\(0^{\circ}\), \(5^{\circ}\),\(10^{\circ}\)) and the array T2 transmits PW at zero and negative angles (\(0^{\circ}\), \(-5^{\circ}\), \(-10^{\circ}\)). An even number of transmissions was set because the CoMTUS optimization is based on pairs of transmissions, one per array (Equation (6)). In addition, firing at opposite angles with the two arrays guarantees the CoMTUS performance since an overlap of the isonated regions is mandatory to determine the relative probe-to-probe position [10].  
For each resulting image, lateral resolution (LR), contrast and the contrast-to-noise ratio (CNR) were measured to quantify the impact of both the aperture size and the clutter. LR was calculated from the point-spread-function (PSF) of the middle point target. An axial-lateral plane for 2D PSF analysis was chosen by finding the location of the peak value in the elevation dimension from the envelope-detected data. Lateral and axial PSF profiles were taken from the centre of the point target and aligned with the principal resolution directions. LR was then assessed by measuring the width of the PSF at the \(-6\) dB level. The contrast and CNR were measured from the envelope-detected images [32]. Contrast and CNR were calculated as: \(\text{Contrast}=20\log_{10}(\mu_{i}/\mu_{o})\) and \(\text{CNR}=\mid\mu_{i}-\mu_{o}\mid/\sqrt{\mu_{i}^{2}+\mu_{o}^{2}}\), where \(\mu_{i}\) and \(\mu_{o}\) are the means of the signal inside and outside of the region, respectively, and at the same imaging depth. A circular region of 10 mm in diameter was used for these calculations.