Color image restoration via the lattice Boltzmann method for anisotropic nonlinear diffusion

The work proposes a method for restoring damaged regions of color three-channel images (the inpainting problem) based on the equation of nonlinear anisotropic diffusion. As the numerical solution algorithm, the lattice Boltzmann equation with five discrete velocities and multiple relaxation times is employed. The direction and intensity of the smoothing are determined using the structure matrix. A parallel implementation of the algorithm has been developed using MPI (Message Passing Interface) technology with image domain decomposition in a Cartesian topology. The application of the proposed method to images with defects of various shapes and sizes is examined. The results demonstrate the correctness of structural and color information restoration in the damaged regions. The accuracy of the method is evaluated on a test set of 10,000 images, and the execution times of sequential and parallel versions of the algorithm are compared.