An imaging problem: Restoration of blurred digital characters

Abstract

The restoration or sharpening of blurred images of letters or other characters differs from the general restoration problem in that the original object is known to be quantized to just two levels, 0 and 1. Two nonlinear modifications of a classical method for the solution of integral equations are suggested as candidates for a fast, accurate, restoration algorithm. Letters defined by a digital matrix were blurred by spreading each matrix element uniformly over the area of four matrix elements. Under this type of blurring, van Cittert's solution by the method of successive substitutions is apparently unsuited because it generates a noncorvergent series. However, successive stages have been shown to sometimes improve before ultimately diverging; therefore one or two stages of correction followed by requantization has practical potential. Alternatively, theory shows that convergence could be reinstated by further deliberate blurring before restoration. Ordinarily deliberate blurring would be avoided on the grounds that the signal-to-noise ratio would deteriorate; but subsequent requantization to the levels might invalidate these grounds. Tests of the latter idea, using block capitals digitized on a 7 × 5 matrix, which is about as coarse as one can use, have proved favorable. The 2-stage version of the procedure is rather complicated when arrived at via the conceptual approach described, but a simple negative feed-forward flow diagram has been found which is equivallent and which greatly simplifies the restoration procedure.