Combined quadratic optimization/median filtering technique for image restoration

Recently, we have introduced a new iterative technique for signal and image restoration. The technique solves a bound-constrained quadratic optimization problem with preconditioning. Although this technique yields a good solution in just few iterations, the error starts increasing after it reaches a minimum. This is a common problem in iterative techniques where the first few iterations restore the low frequency components of the signal and as the number of iterations increases the algorithm attempts to restore the high frequency components, which are dominated by noise. In this article we combine the proposed new iterative technique with median filtering. Median filtering helps maintain a low error by preserving the edge information while reducing the frequency noise.