Image deblurring is an important task for digital cameras. This paper introduces spatial-variant upper and lower bound constraints to regularize Total Variation blind deconvolution. The local upper and lower bound constraints are computed based on the local structure of the observed image. We demonstrate that the proposed spatial-variant constraints can be useful in PSF estimation and image blind deconvolution. Secondly, as other traditional deblurring techniques, the TV blind deconvolution can also produce ringing artifacts. This paper study the GMM-based method to learn the ringing patch distributions. The learned distribution function is then incorporated into the deblurring objective function to suppress the ringing artifacts. Experiments demonstrated the efficacy of the proposed method.