A method for reconstructing an image of an object that includes a plurality of image elements. The method includes accessing image data associated with a plurality of image elements, and reconstructing an image of the object by optimizing an objective function, where the objective function is optimized by iteratively solving a nested sequence of approximate optimization problems. The algorithm is composed of nested iterative loops, in which an inner loop iteratively optimizes an objective function approximating the outer loop objective function, and an outer loop that utilizes the solution of the inner loop to optimize the original objective function.