A system and method is provided for reconstructing single photon emission computed tomography data acquired with a pinhole collimator without pre-knowledge of 3D coordinates of point source markers. The system and method include reiteratively applying a downhill simplex process to determine a first parameter and a second parameter, keeping a lowest vertex from a previous iteration, randomly resetting starting values for rest vertexes for a current iteration, wherein the lowest vertex is prevented from performing a last iteration, determining whether at least one of a first threshold and a second threshold has been reached, wherein the first threshold comprises a cost function value and the second threshold comprises a predetermined number of iterations of the downhill simplex process, acquiring projection data from the first parameter, determining locations of 2D data from the projection data of the first parameter; and estimating the second parameter by fitting the forward projected data locations to the measured data locations.