Many inverse problems in imaging involve measurements that are in the form of convolutions. Sparsity priors are widely exploited in their solutions for regularization as these problems are generally ill-posed. In this work, we develop image reconstruction methods for these inverse problems using patchbased and convolutional sparse models. The resulting regularized inverse problems are solved via the alternating direction method of multipliers (ADMM). The performance of the developed algorithms is investigated for an application in computational spectral imaging. Simulation results suggest that the convolutional sparse model provides similar reconstruction performance with the patch-based model; but the convolutional method is more advantageous in terms of computational cost.