Image Processing

In summary, the reconstruction algorithm based on the Fourier inversion formula has three major subprocesses:

(1)Perform 1-D transforms of the projections at angle θn(n = 1, 2, . . ., N), as in eq. (5.25).

Figure 5.8: Cartesian and polar sampling grids in the Fourier space.

(2)In the Fourier space, interpolate from a polar pattern to a Cartesian lattice.

(3)Perform the 2-D inverse transform to obtain the reconstructed image.

The third step requires a 2-D transform, so it should be performed after obtaining all the projection data.

5.2.3Phantom Reconstruction

To test the correctness of the reconstruction formulas and to study the influence of ...