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

The Fourier magnitude has been studied extensively, but less effort has been devoted to the Fourier phase, despite its well-established importance in image representation. Global phase was shown to be more important for image representation than the magnitude, whereas local phase, exhibited in Gabor filters, has been used for analysis purposes in detecting image contours and edges. 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 a local (Markovian) model for local phase coefficients. This model is Gaussian-mixture-based, learned from the graph representation of images, based on their complex wavelet decomposition. We demonstrate the applicability of the model 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 general setup of image processing.