Properties of the fractional (exponential) Radon transform

ABSTRACT

The fractional Radon transform defined, based on the Fourier slice theorem and the fractional Fourier transform, has many potential applications in optics and the pattern-recognition field. Here we study many properties of the fractional Radon transform using existing theory of the regular Radon transform: the inversion formulas, stability estimates, uniqueness and reconstruction for a local data problem, and a range description. Also, we define the fractional exponential Radon transform and present its inversion.

KEYWORDS:

• Fractional
• Fourier transform
• Radon transform
• exponential Radon transform
• tomography
• X-ray transform

AMS CLASSIFICATION:

• 44A12
• 42A38
• 92C55

Acknowledgments

The author would like to thank the referees for the helpful suggestions.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported by the National Research Foundation of Korea grant funded by the Korea government (MSIP) (2015R1C1A1A01051674) and the TJ Park Science Fellowship of POSCO TJ Park Foundation.