A method and apparatus are disclosed for high-sensitivity Single-Photon Emission Computed Tomography (SPECT), and Positron Emission Tomography (PET). The apparatus includes a two-dimensional (2D) gamma detector array that moves to different positions in a three-dimensional (3D) volume space near an emission source and records a data vector g. In particular, the 3D volume space in which emission data g is measured extends substantially along a radial direction r pointing away from the emission source and each photon detector element in the 2D gamma detector array is provided with a very large collimator aperture. Data g is related to the 3D spatial density distribution f of the emission source, noise vector n, and a system matrix H of the SPECT/PET apparatus through the linear system of equations g=Hf+n. This equation is solved for f by a method that reduces the effect of noise.