The problem of obtaining 3-D tomographic images from geometries involving sparse sets of illuminators and detectors arises in applications like digital breast tomosynthesis, security inspection, non-destructive evaluation and other similar applications. In these applications, the acquired projection data is highly incomplete, so traditional reconstruction approaches such as filtered backprojection (FBP) lead to significant distortion and artifacts in the reconstruction. In this work, we describe an iterative reconstruction algorithm that exploits regularization to obtain well-posed inverse problems. However, the computations associated with these iterative algorithms are significantly greater than the FBP algorithms. We describe how we structure those computations to exploit GPU architectures to reduce the computation time of the iterative reconstruction algorithm. We illustrate the results on data computed from an experimental 3-D imaging system.