Non-convex Sparse Optimization for Photon-limited Imaging

While convex optimization for low-light imaging has received some attention by the imaging community, non-convex optimization techniques for photon-limited imaging are still in their nascent stages. In this thesis, we developed a stagebased non-convex approach to recover high-resolution sparse signals from low-dimensional measurements corrupted by Poisson noise. We incorporate gradient-based information to construct a sequence of quadratic subproblems with an `p-norm (0 ≤ p < 1) penalty term to promote sparsity. The proposed methods lead to more accurate and high strength reconstructions in medical imaging applications such as bioluminescence tomography and fluorescence lifetime imaging.