Non-iterative methods have been developed for image reconstruction in 3D SPECT with uniform attenuation and distance-dependent spatial resolution. It was observed that these methods can, in general, be susceptible to data noise and other errors, yielding conspicuous image artefacts. In this work, we developed and evaluated a regularized inverse-filtering approach for effective suppression of noise and artefacts in 3D SPECT images without significantly compromising image resolution. The proposed approach allows the incorporation of a priori random image field and data information and can thus robustly control the degree of suppression of noise and artefacts in 3D SPECT images. Using computer simulations, we evaluated and compared quantitatively images reconstructed from data sets of various noise levels by the use of the proposed methods and the existing non-iterative methods. These numerical results clearly demonstrated that the proposed regularized inverse-filtering approach can effectively suppress image noise and artefacts that plague the existing non-iterative methods, thus yielding quantitatively more accurate 3D SPECT images. The proposed regularized inverse-filtering approach can also be generalized to other imaging modalities.