This paper presents a threshold-free maximum a posteriori (MAP) super resolution (SR) algorithm to reconstruct high resolution (HR) images with sharp edges. The joint distribution of directional edge images is modeled as a multidimensional Lorentzian (MDL) function and regarded as a new image prior. This model makes full use of gradient information to restrict the solution space and yields an edge-preserving SR algorithm. The Lorentzian parameters in the cost function are replaced with a tunable variable, and graduated nonconvexity (GNC) optimization is used to guarantee that the proposed multidimensional Lorentzian SR (MDLSR) algorithm converges to the global minimum. Simulation results show the effectiveness of the MDLSR algorithm as well as its superiority over conventional SR methods.
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