Most image deblurring methods assume an over-simplistic image formation model and as a result are sensitive to more realistic image degradations. We propose a novel variational framework, that explicitly handles pixel saturation, noise, quantization, as well as non-linear camera response function due to e.g., gamma correction. We show that accurately modeling a more realistic image acquisition pipeline leads to significant improvements, both in terms of image quality and PSNR. Furthermore, we show that incorporating the nonlinear response in both the data and the regularization terms of the proposed energy leads to a more detailed restoration than a naive inversion of the non-linear curve. The minimization of the proposed energy is performed using stochastic optimization. A dataset consisting of realistically degraded images is created in order to evaluate the method.