  This paper extends the Radon transform, a classical image processing tool for
fast tomography and denoising, to the quantum computing platform. A new kind of
periodic discrete Radon transform (PDRT), called quantum Radon transform (QRT),
is proposed. The QRT has a quantum implementation that is exponentially faster
than the classical Radon transform. Based on the QRT, we design an efficient
quantum image denoising algorithm. The simulation results show that QRT
preserves the good denoising capability as in the classical PDRT. Also, a
quantum algorithm for interpolation-based discrete Radon transform (IDRT) is
proposed, which can be used for fast line detection. Both the quantum extension
of IDRT and the line detection algorithm can provide polynomial speedups over
the classical counterparts.
