Interior SPECT- Exact and Stable ROI Reconstruction from Uniformly Attenuated Local Projections

Single photon emission computed tomography (SPECT) is an important biomedical imaging modality. However, since gamma cameras are expensive and bulky, truncated projection data are either preferred or unavoidable. Inspired by the recent results on interior tomography in the x-ray CT field, here we present the interior SPECT approach for exact and stable reconstruction of a region of interest (ROI) from uniformly attenuated local projection data, aided by prior knowledge of a sub-region in the ROI. First, by analytic continuation we prove that interior SPECT is both exact and stable, and by singular value decomposition (SVD) we establish the stability of interior SPECT. Then, given the constant attenuation coefficient and object boundary, our interior SPECT reconstruction is achieved by inverting a generalized truncated Hilbert transform using the SVD technique. Preliminary numerical simulation data demonstrate that our work has practical utilities. The theoretical generalization of our work to the variable attenuation case is underway, and the same numerical approach can be applied.