EPR imaging: The relationship between CW spectra acquired from an extended sample subjected to fixed stepped gradients and the Radon transform of the resonance density

EPR spectroscopy can be extended to a spectroscopic imaging modality by applying magnetic field gradients across the sample to encode spatial information in the measured spectra. In this work, we present a mathematical model of the EPR imaging process in terms of the Radon transform. We describe a model for electron paramagnetic resonance imaging, derive its explicit relationship to the Radon transform, and discuss several options for reconstructing the sample absorption and dispersion densities. An important extension to previous descriptions is the incorporation of large amplitude magnetic field modulation, which can be used to improve the signal-to-noise ratio for continuous wave signal acquisition. Magnetic field modulation is shown to cause well understood changes in the shapes of spectra in the reconstructed images, but does not affect the spatial resolution achieved in these images. Since many of the novel image reconstruction strategies and noise filtering algorithms that have been developed for other modalities start from this formalism, this work allows for their direct application to EPR imaging. This promises to lead to further improvements in EPR imaging techniques.