Optimal interpolation data for PDE-based compression of images with noise

We introduce and discuss shape-based models for finding the best interpolation data in compression of images with noise. The aim is to reconstruct missing regions by means minimizing a fitting term $L^2$-norm between their reconstructed counterparts using time-dependent PDE inpainting. analyze proposed framework $\Gamma$-convergence from two different points view. First, we consider continuous stationary model, obtained focusing on first iteration discretized PDE, get pointwise information "relevance" each pixel topological asymptotic method. Second, finite dimensional setting model based "fat pixels" (balls positive radius), study asymptotics when radius vanishes. Numerical computations are presented that confirm usefulness our theoretical findings non-stationary PDE-based image compression.