Prove the validity of the following properties of the Radon transform [Eq. (5.11-3)]:(a) L...

Prove the validity of the following properties of the Radon transform [Eq. (5.11-3)]:

(a) Linearity: The Radon transform is a linear operator. (See Section 2.6.2 regarding the definition of linear operators.)

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(b) Translation property: The radon transform of f(x − x0,y − y0)is g(ρ − x0cosθ − y0 sinθ, θ).

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(c) Convolution property: Show that the Radon transform of the convolution of two functions is equal to the convolution of the Radon transforms of the two functions.

(5.11-3)