Regularization is a common technique used to improve image quality in inverse problems such as MR image reconstruction. In this work, we extend our previous Graphics Processing Unit (GPU) implementation of MR image reconstruction with compensation for susceptibility-induced field inhomogeneity effects by incorporating an additional quadratic regularization term. Regularization techniques commonly impose the prior information that MR images are relatively smooth by penalizing large changes in intensity between neighboring voxels. However, the associated computations often increase data access and the overall computational load, which can lead to slower image reconstruction. This motivates us to adopt a GPU-enabled implementation of spatial regularization using sparse matrices. This implementation enables the computations for the entire reconstruction procedure to be done on the GPU, which avoids the memory bandwidth bottlenecks associated with frequent communications between the GPU and CPU. Both the CPU and GPU code of this implementation will be available for release at the time of the conference.