where
is a diagonal operator composed from the elements of
:
and
is a diagonal operator composed from the elements of
:
.
Least-squares problems B-2 and B-3 can be solved with the help of shaping regularization with a smoothness constraint:
where
is a smoothing operator, and
and
are two parameters controlling the physical dimensionality and enabling fast convergence when inversion is implemented iteratively. These two parameters can be chosen as
and
(Fomel, 2007a). The definition of
and
are equivalent to definition of LOW in this paper.
Random noise attenuation using local signal-and-noise orthogonalization