Total Variational Robust PCA for Ultrasound Microvascular Clutter Filtering

Ultrafast ultrasound microvascular imaging significantly enhances the sensitivity of vascular resolution in blood flow imaging. Among various techniques, such as ultrafast power Doppler imaging (uPDI) and super resolution imaging, a key processing step is separating micro blood flow signals from tissue clutter and noise, which is crucial for final image quality. Robust Principal Component Analysis (rPCA) approach is widely used for spatiotemporal clutter filtering. Traditionally, nuclear norm is applied for low-rank tissue, and l<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf>-norm for blood flow in rPCA modeling. However, the complex microvasculature and variational blood flow signal intensities limit the effectiveness of the conventional rPCA clutter filters. Therefore, this study proposes a total variation regularized rPCA (TV-rPCA) clutter filtering method. In the proposed approach, microvascular imaging data are decomposed into low-rank and sparse components, constrained by nuclear norm and l<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf>-norm combined with TV regularization, respectively. By introducing TV regularization and performing partial differentiation along the two-dimensional spatial dimensions, our method extracts local spatial features to improve blood flow signal recovery, thereby enhancing the overall recovery of blood flow signals. We conducted experiments on both simulated and in-vivo rat datasets. The experimental results show that our method improves both qualitative evaluations and quantitative CNR measurements when compared with the traditional rPCA methods.