I wanted to know if practically the inverse radon transform operation is considered linear and would be a good candidate for the application of compressed sensing. To my understanding it should be linear since it is just an integral transform, but I have only basic knowledge about compressed sensing and the inverse radon transform. Any knowledge or resources would be appreciated.
For an operator $R$ to be linear, it has to satisfy two conditions:
- $R(f+g) = Rf + Rg$ for any two operands $f,g$;
- $R(\alpha f) = \alpha Rf$ for any operand $f$ and (real or complex) number $\alpha$.
This is true for the Radon transform, as one easily verifies. Whether compressed sensing can be applied to it is something beyond my realm of knowledge.