| The goal of this thesis is the solution of constrained minimization problems that originate in applications from image reconstruction. These applications include microscopy, medical imaging and, our particular application, astronomical imaging. Constraints arise from the fact that the objects we are imaging are photon densities, or light intensities, and are therefore nonnegative. These minimization problems are ill-conditioned, and, since high resolution images are desired, are large-scale. Consequently, efficient numerical techniques are required. We minimize both quadratic and strictly convex functions. Existing algorithms are implemented for the quadratic minimization problem, and ideas from these algorithms are extended to the problem of minimizing the convex function. A detailed analysis and numerical study of these algorithms is presented. |
