Robust clutter filtering is essential for ultrasound small vessel imaging. Eigen-based clutter filtering techniques have recently shown great improvement in clutter rejection over conventional clutter filters in small animals. However, for in vivo human imaging, eigen-based clutter filtering can be challenging due to the complex spatially-varying tissue and noise characteristics. To address this challenge, we present a novel block-wise adaptive singular value decomposition (SVD) based clutter filtering technique. The proposed method divides the global plane wave data into overlapped local spatial segments, within which tissue signals are assumed to be locally coherent and noise locally stationary. This, in turn, enables effective separation of tissue, blood and noise via SVD. For each block, the proposed method adaptively determines the singular value cutoff thresholds based on local data statistics. Processing results from each block are redundantly combined to improve both the signal-to-noise-ratio (SNR) and the contrast-to-noise-ratio (CNR) of the small vessel perfusion image. Experimental results show that the proposed method achieved more than two-fold increase in SNR and more than three-fold increase in CNR in dB scale over the conventional global SVD filtering technique for an in vivo human native kidney study. The proposed method also showed substantial improvement in suppression of the depth-dependent background noise and better rejection of near field tissue clutter. The effects of different processing block size and block overlap percentage were systematically investigated as well as the tradeoff between imaging quality and computational cost.