On Infimal Convolution of TV-Type Functionals and Applications to Video and Image Reconstruction

The infimal convolution of total (generalized) variation-type functionals and its application as regularization for video and image reconstruction is considered. The definition of this particular type of regularization functional is motivated by the need of suitably combining spatial and temporal regularity requirements for video processing. The proposed functional is defined in an infinite dimensional setting, and important analytical properties are established. As applications, the reconstruction of compressed video data and of noisy still images is considered. The resulting problem settings are posed in function space, and suitable numerical solution schemes are established. Experiments confirm a significant improvement compared to standard total variation-type methods, which originates from the introduction of spatio-temporal and spatial anisotropies.