A new algorithm for three-dimensional image reconstruction in nuclear medicine in which scattered radiation rather than multiple projected images is used for determination of the source depth within the body is proposed. Images taken from numerous energy windows are combined for the reconstruction of the source distribution in the body. In the first paper of this series Gunter et al. [ IEEE Trans. Nucl. Sci. 37, 1300 ( 1990)] examined simple linear algorithms for recovering source depth information from scattered radiation. These linear algorithms were unsuccessful because the scattering process produces little signal in the low-energy images at high spatial frequencies. As a result, the reconstructed source distributions exhibited nodal patterns and blurring. The scattering kernel that was measured and reported in the first paper is now examined more carefully. The singular-value decomposition of the kernel matrices is used to break the reconstruction problem into distinct channels that relate energy spectra to source depth distributions. Based on this analysis, a new nonlinear reconstruction algorithm that avoids the earlier problems is proposed. The new algorithm does not degrade spatial resolution in the imaging plane and provides depth resolution with a standard deviation of 4 cm for point sources without requiring any camera motion. The algorithm also provides significant attenuation correction and, therefore, improved quantitation of the source distribution.
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