*2.1.4 Fourier synthesis*

In many imaging systems, when using FT, it is possible to model the inverse problem with the following forward FT relation:

$$g(u,v) = \iint f(\mathbf{x}, \mathbf{y}) \exp\left[-j(u\mathbf{x} + v\mathbf{y})\right] \, \mathbf{d} \mathbf{x} \, \mathbf{d} \mathbf{y},\tag{6}$$

where the data, after an appropriate FT, can fill partially the Fourier domain *g*(*u*, *v*) of the unknown interested function *f* (*x*, *y*) [8, 9]. **Figure 5** shows the case of X-ray CT.

**Figure 5.**

*Fourier synthesis (FS) inverse problems arising in many imaging systems. Here is illustrated the FS problem in X-ray CT.*
