This paper is concerned with solving the image interpolation problem as an inverse problem using a regularized interpolation algorithm. The objective of the paper is how to solve the image interpolation problem as an inverse problem in an efficient manner. The paper suggests a new implementation for the regularized image interpolation algorithm. In this suggested implementation, a single matrix inversion process of small dimensions is required in the interpolation process avoiding the large computational complexity due to the matrices of large dimentions involved in the interpolation process. The performance of this suggested image interpolation algorithm is compared to the standard polynomial interpolation algorithm such as the bilinear, the bicubic and the cubic spline algorithms. Results iluustrate that the suggested implemetation of the regularized image interpolation algorithm is superior to the traditional implementation from the mean square error point of view and the computational complexity point of view as well.