## Materials and Methods
### Principle of H-Doppler Flow Imaging  
Figure 1 shows the schematic description of the H-Doppler working sequence. 1 Parallel convolution filter for H-scan  
Two parallel convolution filters (\(\text{G}H_{2}(t)\) and \(\text{G}H_{8}(t)\)), normalized by the signal energy \(\sqrt{E_{n}}\), are applied to the plane wave Radio Frequency (RF) raw data (7 coherent angles ranging from \(-11^{\circ}\) to \(11^{\circ}\)) to gauge the relative strength of the received signals. The relative strengths of these filter outputs are color-coded: the large layer scattering (\(\text{G}H_{2}\) convolution outputs) and the Rayleigh scattering (\(\text{G}H_{8}\) convolution outputs) signals are assigned to the R and B channels, respectively. The original unfiltered compounded data is assigned to the G channel. 2 Compound plane wave beamforming  
The compound plane wave (CPW) imaging sequence is then performed for the multi-channel signals of RGB with parallelized beamforming (delay and sum). For each spatial image location, the post-beamformed RF data of each channel is separately achieved by averaging the acquisitions over all coherent plane wave transmissions. Then the signal envelope for each of these compounded convolution outputs is calculated via a Hilbert transformation to produce a stable H-scan image display. Next, the ratio of the \(\text{G}H_{2}(t)/\text{G}H_{8}(t)\) and \(\text{G}H_{8}(t)/\text{G}H_{2}(t)\) are utilized to separately weight the R and B channels after the normalization of R and B channels data (i.e., range from 0 to 1). Lastly, the envelope of the original unfiltered data is assigned to the G channel to achieve the RGB color-coded H-scan display image. Note that the H-scan image display sequence is not needed for the H-Doppler approach; this is only for process display purposes. 3 Singular value decomposition (SVD) clutter filtering  
With a total of 2100 ensembles in the slow time direction, which corresponds to 672 milliseconds ultrafast data acquisition, the typical data for small vessel flow imaging is a 3D matrix, with one dimension  
Figure 1: Schematic description of the H-Doppler, including scattering and reflection identification with H-scan, and power Doppler imaging with spatiotemporal singular value decomposition clutter filtering. By applying the compounding plane waves (CPW) beamforming to the 2 nd order Gaussian-weighted Hermite polynomials [\(\text{G}H_{2}(t)\)] and the 8 th Gaussian-weighted Hermite polynomials [\(\text{G}H_{8}(t)\) ] convolution filter output, ultrasound signals containing large layer scatterers are input into the R channel and the Rayleigh scattering signals contributed by blood flow are input into the B channel to obtain the H-scan image of the biological tissue. Doppler blood flow imaging was then performed with the multi-channel signals of the H-scan with the spatiotemporal singular value decomposition clutter filtering. The background noise corresponding to the R channel was removed by the B channel Doppler signals to obtain high-quality blood flow imaging results. SVD: singular value decomposition. in time (\(N_{t}\)) and two dimensions in space (\(N_{x}\) and \(N_{z}\)) [6; 15]. This 3D matrix was then reorganized into a 2D Casorati matrix with dimensions of \(N_{x}\)-\(N_{z}\) by \(N_{t}\), in which one dimension is time and the other dimension is space (both lateral and axial) [10]. The singular value decomposition (SVD) could be performed for this spatiotemporal 2D Casorati matrix (\(S\)) by [10]:  
\[S=U\Delta V^{*} \tag{16}\]  
where \(\Delta\) is the non-square diagonal singular value matrix, \(U\) is the singular vector matrix of space and \(V\) is the singular vector matrix of time and \({}^{*}\) stands for the conjugate transpose. Based on the definition of SVD and principal component analysis (PCA), \(S\) can be expressed as the sum of a series of weighted, ordered signal components [10].