Critical to accurate reconstruction of sparse signals from low-dimensional low-photon count observations is the solution of nonlinear optimization problems that promote sparse solutions. In this work, we explore recovering high-resolution sparse signals from low-resolution measurements corrupted by Poisson noise using a gradient-based optimization approach with non-convex regularization. In particular, we analyze zero-finding methods for solving the p-norm regularized minimization subproblems arising from a sequential quadratic approach. Numerical results from fluorescence molecular tomography are presented.