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Iterative least-squares reconstruction of the Fourier phase of an image from the modulo-2π phase of its bispectrum

We propose a novel technique for the least-squares reconstruction of the Fourier phase of an image from the modulo-2(pi) phase of its bispectrum. The proposed technique unwraps the given bispectral phase and reconstructs the Fourier phase of the image iteratively through alternating projections onto two particular constraint sets: (1) the set of bispectral phase functions that differ from the given modulo-2(pi) bispectral phase by only integral multiples of 2(pi) at every sample point, and (2) the set of bispectral phase functions that correspond to deterministic signals. We formally define the above sets and their corresponding projection operators. We describe the iterative algorithm in detail, and provide experimental results to demonstrate its performance.