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Image deblurring and denoising are the main steps in early vision problems. A common problem in deblurring is the ringing artifacts created by trying to restore the unknown point spread function (PSF). The random noise present makes this task even harder. Variational blind deconvolution methods add a smoothness term for the PSF as well as for the unknown image. These methods can amplify the outliers correspond to noisy pixels. To remedy these problems we propose the addition of a first order reaction term which penalizes the deviation in gradients. This reduces the ringing artifact in blind image deconvolution. Numerical results show the effectiveness of this additional term in various blind and semi-blind image deblurring and denoising problems.