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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.

Wooptix

Light Field team

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.

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.

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.

https://www.mdpi.com/2076-3417/11/1/22/htm