Guaranteed reconstruction for image super-resolution

This paper presents a new reconstruction operator to be used in a super-resolution scheme. Here, by reconstruction in super-resolution, we mean the back-projection operation, i.e. the way K low resolution (LR) images are aggregated to obtain a smooth high resolution (HR) image. Within this method, we replace the usual reconstruction procedure by a non-additive reconstruction operation based on the nice properties of fuzzy partitions. This non-additive reconstruction operator represents a convex family of usual additive reconstruction operators. The obtained reconstructed image is thus a convex family of usual reconstructed images. It allows the super-resolution method to be less sensitive to the choice of the reconstruction method. To make the reading of this method easier, it is presented with 1D signals. We present some experiments to illustrate the proved properties of this new operator.