Image Super-Resolution via Filtered Scales Integral Reconstruction Applied to GOCE Geoid Data

abstract

In this paper a new approach is presented for enhancing image super-resolution via a filtered scale integral reconstruction. Based on the concept that any sensed quantity (from an instrumental point of view) must be necessarily considered as an averaged value in a suitable time and space continuum, the local reconstruction approach expects to map a space of average values onto another one (filtered scales) with a reduced extension and possibly, in an asymptotic limit, onto the space of points. The only assumption is that measurements are given in the integral average sense i.e., for some reason, they have to be considered as integral average values for given computational domains or cells. The proposed algorithm can be used to correlate averaged values to point values; yet the most reliable results, in a probabilistic sense, can be obtained if the ratio between input and output scales is not too high. The essential concept of this working methodology is the possibility to correlate average measurements to point-wise measurements upon suitably weighting the contribution of the molecules surrounding the inspected one