Tomographie reconstruction for single photon emission computed tomography (SPECT) with simultaneous compensation for attenuation, scatter, and distance dependent collimator resolution is provided by an Inverse Monte Carlo (IMOC) reconstruction algorithm. A detection probability matrix is formed by Monte Carlo solution to the photon transport equation for SPECT acquisition from a unit source activity in each reconstruction source voxel. The measured projection vector will equal the product of this detection probability matrix with the unknown source distribution vector. The resulting large, nonsparse system of equations is solved for the source distribution using an iterative Maximum Likelihood EM estimator. Reconstruction of experimentally acquired projections from phantoms shows quantitative compensation for scatter and attenuation. Comparison with filtered backprojection (FBP) reconstruction shows an improvement in resolution recovery, contrast, and signal-to-noise for the IMOC algorithm. Reconstruction of clinical studies shows improved contrast, structural resolution, and noise characteristics.