In this paper, we propose a new approach for structured illumination microscopy image reconstruction. We first introduce the principles of this imaging modality and describe the forward model. We then propose the minimization of nonsmooth convex objective functions for the recovery of the unknown image. In this context, we investigate two data-fitting terms for Poisson-Gaussian noise and introduce a new patch-based regularization method. This approach is tested against other regularization approaches on a realistic benchmark. Finally, we perform some test experiments on images acquired on two different microscopes.