Frequency guided phase unwrapping for improved AM-FM reconstruction

We introduce a new phase unwrapping algorithm that makes it possible to obtain high fidelity image reconstructions from computed AM-FM models without the need for storing multiple boundary conditions such as phase samples from the original image in order to reconstruct the phase from the estimated FM field. This is important to the development of general modulation domain filters because the phase initial conditions are unknown after a filtering operation that modifies the FM functions, making reconstruction of the filtered image hard. In the new approach, frequency information from an initial least squares estimate of the unwrapped phase is used to guide selection of refined phase values that are congruent with the principal phase of the image. The selection process applies a queue-based region growing strategy to compute the final unwrapped phase solution with sparse branch cuts that tend to be placed only in areas with low visual impact. This final solution for the unwrapped phase leads to new solutions for the frequency modulations of the image that are in good agreement with visual perception and provide high quality reconstruction of the original image.