
Regularized Phase Estimation Methods in Interferometry ◾ 151
BOX5.1 CLASSICAL REGULARIZATION FOR
LOW-PASS FILTERING
• A noisy measured image I(x,y) may be mathematically modeled as
I(x, y) = f(x, y) + n(x, y), ∀(x, y) ∈ P.
• We can estimate f(x,y) by minimizing quadratic regularizer function-
als (using, for instance, gradient descend). The first-order regularizer
functional is given by
=−+η −− +η
∈
Uf xy fxyIxy fxyfxy fxyfxy
xy P
[(,)]{[(,) (,)] [(,) (1,)][(,)(
)] }.
(,)
The second-order (metallic thin-plate) regularizer functional is
given by
∑
=
−+η+ −+−
+η +−
+η +−−− −−−
∈
Uf xy
fxyIxy fx yfxy fx y
fxyfxy fxy
fxyfxy fx ...