With the advent of positron emission tomography (PET), a variety of techniques have been developed to measure local cerebral blood flow (LCBF) noninvasively in humans. A potential class of techniques, which includes linear least squares (LS), linear weighted least squares (WLS), linear generalized least squares (GLS), and linear generalized weighted least squares (GWLS), is proposed. The statistical characteristics of these methods are examined by computer simulation. The authors present a comparison of these four methods with two other rapid estimation techniques developed by Huang et al. (1982) and Alpert (1984), and two classical methods, the unweighted and weighted nonlinear least squares regression. The results show that these methods can take full advantage of the contribution from the fine temporal sampling data of modern tomographs, and thus provide statistically reliable estimates that are comparable to those obtained from nonlinear LS regression. These methods also have high computational efficiency, and the parameters can be estimated directly from operational equations in one single step. Therefore, they can potentially be used in image-wide estimation of local cerebral blood flow and distribution volume with PET.