Pruned Simple Model Sets for Fast Exact Recovery of Image

Reconstruction of image can be defined as the general problem of estimating a two-dimensional object from a partial version of this object (a limited set of "projections"). In this paper, we propose new approach for image reconstruction based onsimple quasicrystals and L1 minimisation. We discuss the exact reconstruction of an image supposed to have small spectra. We show that simple model sets may be used as sampling set for exact recovery. Moreover, by eliminating a finite number of points from the simple model sets we still have exact recovery. This last aspect is very important for practical applications, e.g. lossy compression. We run our approch on benchmark images data sets and show that the quasicrystal sampling is more performant than the random uniform in terms of time execution when the dimension of the input image increases.