Least-squares reconstruction of an image from its noisy observations using the bispectrum

The observed images are allowed to be spatially shifted with respect to one another, and the observation noise is assumed to be Gaussian. An algorithm is proposed that recovers the image by separately reconstructing its Fourier phase and Fourier log-magnitude, in the least-squares sense, from the modulo-2π phase and log-magnitude of the bispectrum of the image estimated from the given noisy observations. A technique proposed by the authors is used to unwrap the modulo-2π bispectral phase and to reconstruct the Fourier phase of the image. Experimental results demonstrate the performance of the proposed algorithm