The Nonlocalp‐Laplacian Evolution for Image Interpolation
Yi Zhan · Mathematical Problems in Engineering · 2011
This paper presents an image interpolation model with nonlocalp‐Laplacian regularization. The nonlocalp‐Laplacian regularization overcomes the drawback of the partial differential equation (PDE) proposed by Belahmidi and Guichard (2004) that image density diffuses in the directions pointed bylocalgradient. The grey values of images diffuse along image feature direction not gradient direction under the control of the proposed model, that is, minimal smoothing in the directions across the image features and maximal smoothing in the directions along the image features. The total regularizer combines the advantages of nonlocalp‐Laplacian regularization and total variation (TV) regularization (preserving discontinuities and 1D image structures). The derived model efficiently reconstructs the real image, leading to a natural interpolation, with reduced blurring and staircase artifacts. We present experimental results that prove the potential and efficacy of the method.