14.4.3 Regularization frequency list

As extrapolation is forbidden, and interpolation only allowed to a certain extent in the frequency gaps of the frequency coverage to be synthesized, the experimental frequency list  $\mathcal{L}_e$should be completed by high-frequency points. These points, located outside the frequency coverage to be synthesized  $\mathcal{H}_s$, are those for which the high-frequency components of the image to be reconstructed are practically negligible.

The elements of the regularization frequency list  $\mathcal{L}_r$are the frequency points  u_r located outside the frequency coverage to be synthesized  $\mathcal{H}_s$at the nodes of the Fourier grid  $\text{\boldmath $G$\unboldmath}\,\delta u$:

$$\mathcal{L}_r = \{ \mathbf{u}_r=\mathbf{q}\,\delta u, \mathbf... ...unboldmath }: \mathbf{q}\,\delta u \not\in \mathcal{H}_s \}.$$ (14.8)

The global frequency list  $\mathcal{L}$ is then the concatenation of  $\mathcal{L}_e$ with  $\mathcal{L}_r$.