MR. TOMP : Inversion of the Modulo Radon Transform (MRT) via Orthogonal Matching Pursuit (OMP)

In the recent years, practitioners in the area of tomography have proposed high dynamic range (HDR) solutions that are inspired by the multi-exposure fusion strategy in computational photography. To this end, multiple Radon Transform projections are acquired at different exposures that are algorithmically fused to facilitate HDR re-construction. A single-shot alternative to multi-exposure fusion approach has been proposed in our recent line of work which is based on the Modulo Radon Transform (MRT). In this case, Radon Transform projections are folded via modulo non-linearity. This folding allows HDR values to be mapped into the dynamic range of the sensor and, thus, avoids saturation or clipping. The folded measurements are then mapped back to their ambient range using algorithms. The main goal of this paper is to introduce a novel, Fourier domain recovery method, namely, the OMP-FBP method, which is based on the Orthogonal Matching Pursuit (OMP) algorithm and Filtered Back Projection (FBP) formula. The proposed OMP-FBP method offers several advantages; it is agnostic to the modulo threshold or the number of folds, can handle much lower sampling rates than previous approaches and is empirically stable to noise and outliers. Computer simulations as well as hardware experiments in the paper validate the effectivity of the OMP-FBP recovery method.