Procedure for digital image restoration

Claim 1

An image restoration method including image sensor wherein image degradation creates a degraded image g(x,y) of the form Pf=g, wherein p is an integral operator applied upon an ideal image f(x,y), w(x,y,0)=P 0 f represents the ideal image at time t=0 prior to the operation of p upon f, and w(x,y,1)=Pf=g(x,y) represents the degraded image at time t=1, the restoration method comprising the steps of: (a) providing an image system described by said operator p; (b) transmitting said ideal image f(x,y) through an image blurring and degrading transmission medium of said imaging system to provide said degraded image g(x,y); (c) receiving said degraded image g(x,y) from said transmission medium by said image sensor; (d) digitizing said received degraded image by said digitizer for comparison with said ideal image f(x,y); (e) requiring the magnitude of the difference between the ideal image f and a blurred version of f to be less than a preassigned tolerance value by performing the following steps: (f) constraining said magnitude of said difference by minimizing ∥f-P s f∥ wherein P s f represents the image at time t=s and s is a substantially small value; (g) imposing the constraint ∥f-P s f∥≦Kε, where K is a constant and ε is representative of at least one image restoration parameter; (h) imposing the constraint ∥Pf-g∥≦ε, wherein ε is representative of at least one image restoration parameter; (i) imposing the constraint ∥f∥≦M, wherein M>>ε; (j) determining a restored image f(x,y) which minimizes the quantity {∥Pf-g∥.sup.2 +∥(ε/M)f∥.sup.2 +∥(1/K)(f-P.sup.2 f)∥.sup.2 } in accordance with said selected image; (k) adjusting said image in accordance with steps (f)-(j) to provide a plurality of adjusted images; and (l) selecting an adjusted image of said plurality of adjusted images.