A deterministic model-based restoration procedure is presented. The algorithm is effective for the restoration of coarsely sampled images degraded by diffraction and noise. The a priori information, an assumed parametric object model, is used to arrive at the solution. The object model is convolved with the optical system and sensing mechanism degradations and then matched against the limited number of available samples. The unknown parameters are then estimated using a numerical least mean square error optimization procedure. The method has been tested with a double delta function model via digital simulations. A zero-mean, additive, white Gaussian background noise process was assumed. The technique requires a high signal-to-noise ratio (SNR) to resolve the doublet with a separation distance smaller than the detector width. With increasing separation, good restoration can be achieved at low SNR. The procedure is applicable to restore generalized objects.
John A. Saghri,
Andrew G. Tescher,
"Model-Based Restoration Procedure For Small, Low Resolution Optical Images," Optical Engineering 23(3), (1 June 1984). https://doi.org/10.1117/12.7973282