Image Processing Reference

In-Depth Information

The difference between
v
and computed expectation of real signal, given the measured sig-

nal. Finally, the distribution
U
is estimated applying a deconvolution filter as follows:

(11)

In which * defines complex conjugate,

is the Fourier transform of
F
,
Z
is a constant term for

limiting the magnitude of
G
.

This estimation is then used to estimate a corresponding ield.

In addition to processing stages were described above, there are some steps for practical im-

pletion of applied algorithm.

(12)

(13)

In which
h
is the distance between

,
x
i
is the location,
N
is the set of measurements
v
(
x
i
),

is the centers of the bins

• Smoothing the bias field by using the B-spline technique [
25
]. For doing this stage, the MRI

data should resample into subsamples (coarser resolution). This step is carried out because

smoothing the bias field at full resolution is computationally diicult.

The smoothing stage is a challenging stage and the manner of smoothing, effects on bias

field correction performance. The proposed approach for smoothing is approximating data

by using linear combination of smooth basis functions. B-spline is a suitable basis, which

is compactly supported spline. In comparison with conventional filtering approaches the

proposed technique is superior regarding to missing data. Filtering methods are not suit-

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