Abstract : Arterial Spin Labeling (ASL) is a noninvasive perfusion technique which allows the absolute quantification for Cerebral Blood Flow (CBF). The perfusion is obtained from the difference between images with and without magnetic spin labeling of the arterial blood and the captured signal is around 0.5-2% of the magnitude of the labeling images, so the noise is one of the main problems for further data analysis. Classical method, Mono-TI, for CBF quantification is averaging repetitions with only one Inversion Time (TI) - the time delay between labeling and acquisition to allow the labeled blood to arrive the imaging slice. It improves the robustness to noise, however, cannot compensate the variety of Arterial Arrival Time (AAT). In this paper, Diverse-TI is proposed to exploit different TI sampling instants (sampling diversity) to improve the robustness to variety of AAT and simultaneously average repetitions with each TI (sampling repetitions) to improve the robustness to noise. Generally, the sampling diversity is relatively small and can be considered as compressed measurements, thus the Compressive Matched Filter (CMF) enlightened from sparsity is exploited to directly reconstruct CBF and AAT directly from compressed measurements. Meanwhile, regarding the CBF quantification performance, the compromise between the sampling repetition and sampling diversity is discussed and the empirical protocol to determine the sampling diversity is proposed. Simulations are carried out to highlight our discussions.