PET 1/r-blurring

The direct back projection introduces as error in the sence that blurring of the activity of the source occurs. This is illustrated using fig. 1.

Figure 1: 1/r-blurring. See text below figure for details.

1. The original distribution with, in this case, one source.
2. The parallel projection measured along the vertical. Roughly halfway down a signal is detected.
3. The back projection of the parallel projection. Somewhere along the bar (at posituion r0) the source is located. In the back projection this is represented by a constant value across the whole line.
4. The sum of two back projections, which results in constant values across two bars under different angles. At the overlapping part the intensity values double.
5. The effect of three and four back projections. The intensity values near the source becomes larger and larger.
6. The effect of many projections. At the location of the source there is a high intensity, but this is partly covered by a blurr which extends radially from the source.

At the location r from the source the contributions of N back projections are distributed over the circumference of the circle. Hence, the blurring reduces with 1/r. That's why it is called 1/r-blurring.