Iterative multiresolution algorithm for image reconstruction from the magnitude of its Fourier transform

Abstract

Iterative algorithms are currently the most effective approaches to solving a number of difficult signal reconstruction and recovery problems, and all of these algorithms suffer from stagnation and computational complexity. We propose a new multiresolution iterative approach that employs the concept of a multiresolution pyramid. This method attempts to solve the problem of image reconstruction from the measurement of the image’s Fourier modulus by decomposing the problem onto different resolution grids, which enables the iterative algorithm to avoid stagnation by providing a better initial guess and enabling a higher likelihood of arriving at a global minimum while dramatically reducing the computational cost. Results on both synthetic and real-world images are shown; a performance comparison with the direct iterative algorithm demonstrates the effectiveness of our approach in terms of convergence, robustness and computational efficiency.