1. A method for reconstructing an image of an object, the image including image elements, said method comprising: accessing measurement data associated with the image elements; introducing an auxiliary variable to transform an original problem of reconstructing the image to a constrained optimization problem; solving the constrained optimization problem using a method of multipliers to create a sequence of sub-problems and solve the sequence of sub-problems, wherein solving the sequence of sub-problems comprises reconstructing the image by optimizing a first objective function, wherein the first objective function is optimized by iteratively solving a nested sequence of approximate optimization problems, and wherein an inner loop iteratively optimizes a second objective function approximating the first objective function, and an outer loop utilizes the solution of the second objective function to optimize the first objective function.