The relative importance of local phase and local amplitude in patchwise image reconstruction

Abstract

Natural images were subjected to patchwise Fourier analysis, and the local amplitude and phase spectra were swapped between different images. When the patches were large relative to the image size, the appearance of the reconstructed image was similar to that of the image from which the phase information had been derived, in agreement with previous reports of phase-dominance in the global Fourier Transform. However, when the patch size was made sufficiently small, the appearance of reconstructed images was dominated by amplitude rather than phase. This was not simply due to the DC component of the amplitude spectrum. Prior low-pass filtering of the images enhanced the dominance of amplitude information in the patchwise transform. We conclude that patchwise-reconstructed images contain two quite distinct kinds of information for the human observer. The first is the positional information ("local sign") of the patches themselves; the second is the textural information within patches, which is dominated by amplitude rather than phase. The reason why the global Fourier Transform is dominated by phase is that in the absence of any other information about local sign, phase is necessary to reconstruct localised features such as edges.