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:

$$O^{(n+1)} (x,y) = O^{(n)} (x,y) + P(-x,-y) * {\bar{R}}^{(n)}(x,y)$$ (14.118)