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Applications such as Magnetic Resonance Tomography acquire imaging data by point samples of their Fourier transform. This raises the question of balancing the efficiency of the sampling strategies with the approximation accuracy of an associated reconstruction procedure. In this paper, we introduce a novel sampling-reconstruction scheme based on a random anisotropic sampling pattern and a compressed sensing type reconstruction strategy with a variant of dualizable shearlet frames as sparsifyingdoi:10.1137/16m1098541 fatcat:v5ne3q25hjhz5hgyrytc7omyte