In this paper we propose a new deterministic algorithm for solving sparse data image restoration problem in presence of noise. This problem consists in estimating the original image given just some noisy value of its pixels. By regularization techniques the solution of the problem is define as the minimum of an energy function. Such an energy function is not convex. We define the local energy of a column or of a row by fixing the values of image in the other columns or in the other rows, respectively. In order to minimize the total energy function, we apply the following algorithm: we minimize iteratively each local energy by reducing the problem to the shortest path problem, until we arrive at a fixed point. The experimental results confirm the goodness of this technique.