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Regularization of the one-step gradient method

The one-step gradient iteration is:
O(n+1) (x,y) = O(n) (x,y) + P(-x,-y) * R(n)(x,y)     (14.117)

with R(n)(x,y) = I(x,y) - P(x,y) * O(n) (x,y). The regularization by the significant structures leads to:
$\displaystyle O^{(n+1)} (x,y) = O^{(n)} (x,y) + P(-x,-y) * {\bar{R}}^{(n)}(x,y)$     (14.118)

Petra Nass