Inverse Multiscale Discrete Radon Transform by Filtered Backprojection

Featured Application: The startup company Wooptix is using the inversion by filtered backprojection of the multiscale Radon transform to accelerate inverse problem solutions in the context of wavefront phase optical measurements and barcode detection. 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.