The Role of Fourier Phase in Image Representation and Reconstruction

abstract: The Fourier representation of a signal or image is equivalent to its native representation in the sense that the signal or image can be reconstructed exactly from its Fourier transform. The Fourier transform is generally complex-valued, and each value of the Fourier spectrum thus possesses both magnitude and phase. Degradation of signals and images when Fourier phase information is lost or corrupted has been studied extensively in the signal processing research literature, as has reconstruction of signals and images using only Fourier magnitude information. This thesis focuses on the case of images, where it examines the visual effect of quantifiable levels of Fourier phase loss and, in particular, studies the merits of introducing varying degrees of phase information in a classical iterative algorithm for reconstructing an image from its Fourier magnitude. (abstract