A simplified and accelerated implementation of SVD for filtering ultrafast power Doppler images

Ultrafast Power Doppler (UPD) is a growing ultrasound modality for imaging and diagnosing microvasculature disease. A key element of UPD is using singular value decomposition (SVD) as a highly selective filter for tissue and electronic noise. However, two significant drawbacks of SVD are its computational burden and the complexity of its algorithms. These limitations hinder the development of fast and specific SVD algorithms for UPD imaging. This study introduces power SVD (pSVD), a simplified and accelerated algorithm for filtering tissue and noise in UPD images.pSVD exploits several mathematical properties of SVD specific to UPD images. In particular, pSVD allows the direct computation of blood-related SVD components from the temporal singular vectors. This feature simplifies the expression of SVD while significantly accelerating its computation. After detailing the theory behind pSVD, we evaluate its performances in several in vitro and in vivo experiments and compare it to SVD and randomized SVD (rSVD).pSVD strongly decreases the running time of SVD (between 5 and 12 times in vivo) without impacting the quality of UPD images. Compared to rSVD, pSVD can be significantly faster (up to 3 times) or slightly slower but gives access to more estimators to isolate tissue subspaces.pSVD is highly valuable for implementing UPD imaging in clinical ultrasound and provides a better understanding of SVD for ultrasound imaging in general.