
Local Polynomial Phase Modeling and Estimation ◾ 227
BOX6.5 2-D PHASE-DIFFERENCING OPERATOR
Consider the following two-dimensional (2-D) signal:
Γ(x,y) = exp[jϕ(x,y)] + η(x,y) {(x,y) ∈ [0,255]}
with a bivariate quadratic phase, given as
φ= +++++xy ccyc xc yc xy
(,)(0,0) (0,1)(1, 0) (0,2)(1, 1) (2,0)
where the coefficients c(0,0) = 0, [c(0,1),c(1,0)] = [0.3, 0.2] and
[c(0,2),c(1,1),c(2,0)] = [−0.003, −0.002, 0.001], and the noise standard
deviation σ
η
= 0.2. This equation indicates that the phase can be viewed as
having three layers. The simulated phase is shown in Figure6.14a.
For the phase-differencing operator method, we proceed by ...