Biomedical Engineering Reference
In-Depth Information
Fig. 8
Representation of the simple backprojection method. The value of a given projection is
uniformly distributed on the image that are being calculated. (
a
) Represents the process for only
three views; (
b
) the same process for a large number of views (Adapted from [
16
])
Analytical methods can be classified into three groups: simple backprojection,
filter of the backprojection and backprojection of filtered projections [
15
]. The iter-
ative methods can be divided into statistical and non-statistical methods. Statistical
methods do not make assumptions about the nature of the noise presented in the data.
Conversely, statistical methods assume that noise contaminating the data follows
either a Gaussian or a Poisson distribution, resulting from there a logical division
within the statistical methods.
In the simple backprojection the measurements are uniformly distributed along
the line of projection. Proceeding similarly for all projections at different angles an
estimate of the activity distribution will be obtained.
Although being a fairly simple process, the results are not accurate, as can be
observed in Fig.
8
where the reconstructed image of a point source appears blurred.
The filtered backprojection (FBP) corrects this problem by filtering the projections
before backprojection [
17
](Fig.
9
).
Although in clinical practice the analytical methods are usually preferred, the
iterative methods have characteristics that make them more attractive to those who
are looking for accuracy and versatility (even at the expense of more processing
time). Iterative methods allow incorporating models that are more realistic and
therefore correct several effects that occurred during data acquisition.
In general, iterative methods involve four basic steps, outlined in Fig.
10
.
