Rmage reconstruction in regions of interest from truncated radon transforms of even dimensions

It is well known that an exact image within a region of interest (ROI) can be reconstructed from truncated Radon transforms of odd dimensions. It remains, however, unclear whether exact ROI images can be reconstructed from the truncated n-dimensional (nD) Radon transform, where n >= 4 is an even number. In this work, we show that it is possible to reconstruct ROI images exactly from truncated Radon transforms of even dimensions. In particular, based upon our derived formula, two algorithms can be devised for exact reconstruction of ROI images from truncated Radon transforms of even dimensions. This work may find applications in high-dimensional tomographic imaging such as magnetic resonance spectroscopic imaging and electron paramagentic resonance imaging in which the data function can be interpreted as the 4D Radon transform.