Fourier reconstruction as a valid alternative to filtered back projection in iterative applications: implementation of Fourier spectral spatial EPR imaging

The qualitative equivalence between the Fourier reconstruction (FR) algorithm and the filtered back projection (FBP) algorithm is demonstrated when all the different phase errors that can occur in FR are eliminated. The causes of phase errors are underlined and methods to eliminate them are presented. The practical comparison between FR and FBP has been evaluated on a numerical test image and the results are reported, demonstrating the qualitative equivalence. FR has the advantage of being very computationally efficient. In fact, the time spent to obtain the FR image was 1/20 of that used to obtain the FBP image. Because of the computational efficiency of FR and the good quality of the results obtained, an iterative version of FR has been used to implement the spectral–spatial imaging (SSI) algorithm in the field of electron paramagnetic resonance imaging (EPRI). An experimental example, demonstrating its good performance, is reported.