Multigrid algorithm for image reconstruction from Fourier modulus

Two new iterative multigrid algorithms for image reconstruction from Fourier magnitude data are proposed. The first algorithm is based on the error reduction algorithm and the second is based on a quasi-Newton´s method. Both algorithms take advantage of a multigrid scheme to speed up the convergence rate of the iterations. Furthermore, they recover more high frequency components of the image than their non-multigrid counterpart. Experimental study has shown the great potential of both algorithms