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:
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.
• Estimating V distribution by using an equal-size bins histogram and Parzen window [ 24 ] .
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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