Application of partial differential equation‐based inpainting on sensitivity maps

Abstract

Inpainting is an image interpolation method. Partial differential equation (PDE)-based digital inpainting techniques are finding broad applications. In this paper, PDE-based inpainting techniques are applied to the field of MR parallel imaging. A novel model and its corresponding numerical method are introduced. This model is then applied to sensitivity maps. Coil sensitivity maps are important for parallel imaging, and they often require extrapolation and hole filling (holes being dark regions of low signal in MR images). These problems can be solved simultaneously by the application of inpainting techniques. Experiments for determining coil sensitivity maps for phantoms and cardiac MR images demonstrate the accuracy of the proposed model. Images generated using sensitivity encoding (SENSE) that utilizes inpainted sensitivity maps, thin-plate spline (TPS) estimated sensitivity maps, and Gaussian kernel smoothed (GKS) sensitivity maps are compared. From the experimental results, it can be seen that inpainted sensitivity maps produce better results than GKS sensitivity maps. The TPS method generates results similar to those of the inpainting technique but is much more time-consuming.