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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.

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    $\begingroup$ It is linear (although not continuous -- which is why you'd rather formulate things as an equation involving the forward transform), and compressed sensing is routinely applied (usually in the wavelet domain, since medical images are rarely sparse in the pixel domain) -- you'd be pretty late to the game... (Googling "compressive sensing Radon" gives about 100000 hits.) $\endgroup$ – Christian Clason Apr 20 '17 at 16:26
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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.

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