Abstract
The Radon transform is a valuable tool in inverse problems such as the ones present in electromagnetic imaging. Up to now the inversion of the multiscale discrete Radon transform has been only possible by iterative numerical methods while the continuous Radon transform is usually tackled with the filtered backprojection approach. In this study, we will show, for the first time, that the multiscale discrete version of Radon transform can as well be inverted with filtered backprojection, and by doing so, we will achieve the fastest implementation until now of bidimensional discrete Radon inversion. Moreover, the proposed method allows the sacrifice of accuracy for further acceleration. It is a well-conditioned inversion that exhibits a resistance against noise similar to that of iterative methods.
Highlights
IntroductionDirect Radon transform performs integrals along lines while the inverse Radon transform takes the values in the transformed domain and must find out what values of the measure domain gave place to these already integrated values
The Radon transform is of great importance in the field of medical imaging and in general in problems where a magnitude cannot be directly sensed, and instead what is available is the magnitude integrated along a line, in which a beam of energy interacted with the physical medium [1,2].Direct Radon transform performs integrals along lines while the inverse Radon transform takes the values in the transformed domain and must find out what values of the measure domain gave place to these already integrated values
The projection-slice theorem or Fourier-slice theorem links the Radon transform with the Fourier transform, and has made it possible to solve the inverse Radon transform by means of the so-called filtered backprojection method. This method consists of placing Radon angular projections as one-dimensional slices of the Fourier bidimensional transform domain, performing the inverse Fourier transform to obtain the bidimensional Radon inversion after high pass filtering has been applied [3]
Summary
Direct Radon transform performs integrals along lines while the inverse Radon transform takes the values in the transformed domain and must find out what values of the measure domain gave place to these already integrated values This is a much harder problem to solve, as there may be many or no solutions (in the presence of noise), which makes the reverse path notably more complicated than the direct path. The projection-slice theorem or Fourier-slice theorem links the Radon transform with the Fourier transform, and has made it possible to solve the inverse Radon transform by means of the so-called filtered backprojection method. This method consists of placing Radon angular projections as one-dimensional slices of the Fourier bidimensional transform domain, performing the inverse Fourier transform to obtain the bidimensional Radon inversion after high pass filtering has been applied [3]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
