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We propose in this paper a novel two-stage Projection Correction Modeling(PCM) framework for image reconstruction from (non-uniform) Fouriermeasurements. PCM consists of a projection stage (P-stage) motivated by themulti-scale Galerkin method and a correction stage (C-stage) with an edgeguided regularity fusing together the advantages of total variation (TV) andtotal fractional variation (TFV). The P-stage allows for continuous modeling ofthe underlying image of interest. The given measurements are projected onto aspace in which the image is well represented. We then enhance thereconstruction result at the C-stage that minimizes an energy functionalconsisting of a fidelity in the transformed domain and a novel edge guidedregularity. We further develop efficient proximal algorithms to solve thecorresponding optimization problem. Various numerical results in both 1Dsignals and 2D images have also been presented to demonstrate the superiorperformance of the proposed two-stage method to other classical one-stagemethods.

PCM-TV-TFV: A Novel Two Stage Framework for Image Reconstruction from Fourier Data