In many fast MR imaging techniques, K-space is sampled sparsely in order to gain a fast traverse of K-space. These techniques use non-Cartesian sampling trajectories like radial, zigzag, and spiral. In the reconstruction procedure, usually interpolation methods are used to obtain missing samples on a regular grid. In this paper, we propose an iterative method for image reconstruction which uses the black marginal area of the image. The proposed iterative solution offers a great enhancement in the quality of the reconstructed image in comparison with conventional algorithms like zero filling and neural network. This method is applied on MRI data and its improved performance over other methods is demonstrated.