Efficient image restoration with the Huber-Markov prior model

Image restoration is an ill-posed problem that must be regularized in order to reduce noise amplification in the restored image. Although quadratic penalty terms allow for fast restoration algorithms based on the fast Fourier transform (FFT), they often lead to images whose discontinuities are not well preserved. On the other hand, edge-preserving penalty terms can produce better results at the expense of computational efficiency. A restoration technique exploiting the Woodbury matrix identity was recently presented. However, its performance decreases when the number of discontinuities becomes significant. To overcome this problem, we propose a simple preconditioner to be employed in conjunction with the preconditioned nonlinear conjugate gradient method. Experiments are employed to demonstrate the effectiveness of our approach.