This paper presents a non-iterative regularized inverse solution to the image interpolation problem. This solution is based on the segmentation of the image to be interpolated into overlapping blocks and the interpolation of each block, separately. The purpose of the overlapping blocks is to avoid edge effects. A global regularization parameter is used in interpolating each block. In this solution, a single matrix inversion process of moderate dimensions is required in the whole interpolation process. Thus, it avoids the large computational cost due to the matrices of large dimensions involved in the interpolation process. The performance of this approach is compared to the standard iterative regularized interpolation scheme and to polynomial based interpolation schemes such as the bicubic and cubic spline techniques. A comparison of the suggested approach with some algorithms implemented in the commercial ACDSee software has been performend in the paper. The obtained results reveal that the suggested solution has a better performance as compared to other algorithms from the MSE and the edges preservation points of view. Its computation time is relatively large as compared to traditional algorithms but this is acceptable when image quality is the main concern.