  We introduce regularised diffusion--shock (RDS) inpainting as a modification
of diffusion--shock inpainting from our SSVM 2023 conference paper. RDS
inpainting combines two carefully chosen components: homogeneous diffusion and
coherence-enhancing shock filtering. It benefits from the complementary synergy
of its building blocks: The shock term propagates edge data with perfect
sharpness and directional accuracy over large distances due to its high degree
of anisotropy. Homogeneous diffusion fills large areas efficiently. The second
order equation underlying RDS inpainting inherits a maximum--minimum principle
from its components, which is also fulfilled in the discrete case, in contrast
to competing anisotropic methods. The regularisation addresses the largest
drawback of the original model: It allows a drastic reduction in model
parameters without any loss in quality. Furthermore, we extend RDS inpainting
to vector-valued data. Our experiments show a performance that is comparable to
or better than many inpainting methods based on partial differential equations
and related integrodifferential models
