Neural Networks for Image Restoration from the Magnitude of Its Fourier Transform
IWANN '01 Proceedings of the 6th International Work-Conference on Artificial and Natural Neural Networks: Bio-inspired Applications of Connectionism-Part II
The self-duality of discrete short-time Fourier transform and its applications
IEEE Transactions on Signal Processing
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The discrete phase retrieval problem is to reconstruct a discrete time signal whose support is known and compact from the magnitude of its discrete Fourier transform. We formulate the problem as a linear system of equations; our methods do not require polynomial rooting, tracking zero curves of algebraic functions, or any sort of iteration like previous methods. Our solutions obviate the stagnation problems associated with iterative algorithms, and our solutions are computationally simpler and more stable than alternative noniterative algorithms. Furthermore, our methods can explicitly accommodate noisy Fourier magnitude information through the use of total least squares type techniques. We assume either of the following two types of a priori knowledge of the signal: (1) a band of known values (which may be zeros) or (2) some known values of a subminimum phase signal (whose zeros lie inside a disk of radius greater than unity). We illustrate our methods with nonminimum-phase one-dimensional (1-D) and two-dimensional (2-D) signals