Superresolving signal and image restoration using a linear associative memory

The long-standing problem of the superresolving reconstruction (restoration) of an object of known finite spatial extent from a noisy linearly degraded image is considered. The resolution of two-point sources (objects) spaced less than one Rayleigh distance apart is an ill-posed problem. To determine a superresolving inverse of an ill-conditioned linear degradation operator with a known set of input/output training signals, a linear associative memory (LAM) technique is employed. By limiting the set of reconstructable signals, an exceptionally robust inverse filter has been obtained. This filter is based on a new constrained LAM matrix operator technique. Superresolving restoration of 1-D and 2-D two-point sources as well as some typical edge-type signals in the presence of considerable measurement noise is demonstrated.