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for an optimal filter. The Backus-Gilbert method [24, 25] is a regularization method that differs from others in that it seeks to maximize stability of the solution rather than, in the first instance, its smoothness. The Backus-Gilbert method seeks to make the mapping from f and f as close to the identity as possible in the limit of error-free data. Although the Backus-Gilbert philosophy is rather different from standard linear regularization methods, in practice the differences between the

Equation (35) shows that Abramatic and Silverman's model can be seen as a linear combination of a stationary lowpass component and a nonstationary highpass component [16]. Inserting H for the stationary Wiener solution we can write the filter in Eq. (35) as

Original MR data Filtered MR data

FIGURE 5 Filtering MR data through the pelvis using Lee's method. Note how the background noise the original image (left) has effectively been suppressed in the result image (right). Note how the motion related artifacts are reduced, but blurring is introduced.

Original MR data Filtered MR data

FIGURE 5 Filtering MR data through the pelvis using Lee's method. Note how the background noise the original image (left) has effectively been suppressed in the result image (right). Note how the motion related artifacts are reduced, but blurring is introduced.

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