where
is a diagonal operator composed of the elements of
,
is a diagonal operator composed of the elements of
. Note that in equations 26-28,
,
, and
denote vectorized 2D matrices. Equations 27 and 28 can be solved using shaping regularization with a local-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
.
Plane-wave orthogonal polynomial transform for amplitude-preserving noise attenuation