On stability of reconstruction from Fourier transform modulus

The lower bound on the condition number of reconstruction of two classes of sequences from their Fourier transform magnitude (FTM) is derived. The lower bound for one class is shown to be 1, and for the other class to be 1/2 N/sup Q/2/, where Q is the dimensionality of the sequence and N is the number of nonzero elements in each dimension. Stability of reconstruction from the FTM and the space-domain phase is discussed. It is found that randomizing the space-domain phase improves reconstruction robustness. Experimental results are presented to verify theoretical predictions.<
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