Effective tissue clutter filtering is critical for non-contrast ultrasound imaging of slow blood flow in small vessels. Independent component analysis (ICA) has been considered by other groups for ultrasound clutter filtering in the past and was shown to be superior to principal component analysis (PCA)-based methods. However, it has not been considered specifically for slow flow applications or revisited since the onset of other slow flow-focused advancements in beamforming and tissue filtering, namely angled plane wave beamforming and full spatiotemporal singular value decomposition (SVD) (i.e., PCA-based) tissue filtering. In this work, we aim to develop a full spatiotemporal ICA-based tissue filtering technique facilitated by plane wave applications and compare it to SVD filtering. We compare ICA and SVD filtering in terms of optimal image quality in simulations and phantoms as well as in terms of optimal correlation to ground truth blood signal in simulations. Additionally, we propose an adaptive blood independent component sorting and selection method. We show that optimal and adaptive ICA can consistently separate blood from tissue better than principal component analysis (PCA)-based methods using simulations and phantoms. Additionally we demonstrate initial in vivo feasibility in ultrasound data of a liver tumor.