Fast Incremental Image Reconstruction with CNN-enhanced Poisson Interpolation

Abstract

We present a novel image reconstruction method from scattered data based on multigrid relaxation of the Poisson equation and convolutional neural networks (CNN). We first formulate the image reconstruction problem as a Poisson equation with irregular boundary conditions, then propose a fast multigrid method for solving such an equation, and finally enhance the reconstructed image with a CNN to recover the details. The method works incrementally so that additional points can be added, and the amount of points does not affect the reconstruction speed. Furthermore, the multigrid and CNN techniques ensure that the output image resolution has only minor impact on the reconstruction speed. We evaluated the method on the CompCars dataset, where it achieves up to 40% error reduction compared to a reconstruction-only approach and 9% compared to a CNN-only approach.