Exploiting redundancy to solve the Poisson equation using local information

This paper proposes a novel method of solving the Poisson equation used in image processing techniques that are based on computations in the gradient domain. The Poisson equation is used to perform an inverse gradient transform; it back-solves to find an image that is closest to having a particular gradient. The traditional methods for back-solving require access to the entire gradient-domain image; in a real-time embedded implementation, this implies high hardware complexity, large latency, and large memory buffers. We propose a method that produces high quality results visually and is based on a small sliding window with specially chosen boundary conditions. The method has been simulated as a proof of concept, and should result in much faster and smaller digital hardware than traditional approaches.