On microlocal artifacts arising in tomography modeled by a class of generalized Radon transforms

In this paper, we provide a unified framework for understanding how and why artifacts arise in limited data tomography, using precise microlocal analysis of the underlying generalized Radon transforms (gRT). Our insights facilitate a more accurate assessment of reconstructions and eventually enable practical artifact reduction strategies in real-world imaging applications. To this end, we consider gRTs as Fourier integral operators whose propagation of singularities is governed by their canonical relations. Thus, we can discern various types of singularities in the reconstructions, including visible singularities (present in both the ground truth and its reconstruction), invisible singularities (present in the ground truth but not in the reconstruction), and artifacts (singularities present in the reconstruction but not in the ground truth). Several concrete examples illustrate the theoretical results: in photoacoustic tomography, mirror artifacts, a special kind of artifacts, arise due a non-injectivity property of the canonical relation (the Bolker condition is violated). In classical X-ray computerized tomography, we consider region of interest (ROI) tomography, where object independent artifacts, a further subtype of artifacts, may manifest at the boundaries of the ROI. Lastly, we investigate artifact formation in linearized seismic imaging (Kirchhoff migration), which depends on the underlying pressure wave velocity model used in the linearization process.