
Mathematical and Statistical Aspects of Inverse Problems 93
4
−5000
0
5000
Residuals vs Model
Model Solution
Residuals
4
−40
−30
−20
−10
0
10
20
30
40
Modified (sqrt) Residuals vs Model
Model Solution
Modified (sqrt) Residuals
FIGURE 3.13: Truncated residual plots for models N
j
k
= I[n](t
j
, z
j
k
; θ
0
) +
(I[n](t
j
, z
j
k
; θ
0
))
γ
e
E
kj
with γ = 0 (top) vs. γ = 1/2 (bottom) where γ = 1/2
works well!!
by
ˆw
j,k
=
I[n](t
j
, z
j
k
;
ˆ
θ
(l)
)
1/2
, I[n](t
j
, z
j
k
;
ˆ
θ
(l)
) > I
0
(I
0
)
1/2
, I[n](t
j
, z
j
k
;
ˆ
θ
(l)
) ≤ I
0
.
(3.81)
The cuto ff value I
0
> 0 is determined by the experimenter so that the resulting
residuals appear random. In the work that follows, I
0
= 1 × 10
4
.
Truncated ...