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The Fourier magnitude has been studied extensively, but less effort has beendevoted to the Fourier phase, despite its well-established importance in imagerepresentation. Global phase was shown to be more important for imagerepresentation than the magnitude, whereas local phase, exhibited in Gaborfilters, has been used for analysis purposes in detecting image contours andedges. Neither global nor local phase has been modelled in closed form,suitable for Bayesian estimation.  In this work, we analyze the local phase of textured images and propose alocal (Markovian) model for local phase coefficients. This model isGaussian-mixture-based, learned from the graph representation of images, basedon their complex wavelet decomposition. We demonstrate the applicability of themodel in restoration of images with noisy local phase and in image retrieval,where we show superior performance to the well-known hybrid input-output (HIO)method. We also provide a framework for application of the model in a generalsetup of image processing.

Modelling local phase of images and textures with applications in phase denoising and phase retrieval