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When noniterative methods without adequate regularization are applied to correct for the effects of attenuation and distance-dependent spatial resolution in three-dimensional (3-D) single-photon emission computed tomography (SPECT) at clinical noise levels, they often yield images with conspicuous artifacts, thereby significantly limiting the usefulness of these reconstruction methods. In this work, we extend a regularized inverse-filtering approach that allows the incorporation of an a priori random image field of nonzero mean, as well as an estimated noise level of the SPECT data, for effective suppression of noise and artifacts without significantly compromising the resolution. Our results indicate that the proposed approach can substantially improve the visual quality and the quantitative accuracy of 3-D SPECT images. In combination with its speed advantage, the proposed method may be useful in 3-D SPECT clinical applications.