grandes-ecoles 2015 QV.B.2

grandes-ecoles · France · centrale-maths1__mp Indefinite & Definite Integrals Definite Integral Evaluation (Computational)
We model the density of tissues by an unknown function $f$ zero outside the zone to be studied. Assuming that each incident X-ray beam is carried by an affine line $\Delta$, and denoting by $I_e$ and $I_s$ its intensity measured on either side of the targeted zone: $$\ln\left(\frac{I_e}{I_s}\right) = \int_\Delta f$$
Explain how the Radon inversion formula allows us in principle to know the density of tissues in the radiographed zone.
We model the density of tissues by an unknown function $f$ zero outside the zone to be studied. Assuming that each incident X-ray beam is carried by an affine line $\Delta$, and denoting by $I_e$ and $I_s$ its intensity measured on either side of the targeted zone:
$$\ln\left(\frac{I_e}{I_s}\right) = \int_\Delta f$$

Explain how the Radon inversion formula allows us in principle to know the density of tissues in the radiographed zone.