Regularized Least-Squares SPECT Image Reconstruction Using Multiresolution Spatial B-Splines and a Negativity Penalty

We investigated the benefit of incorporating a negativity penalty into a least-squares criterion used to reconstruct 3-D radiotracer distributions in cardiac SPECT studies. B-spline spatial basis functions were used to provide a continuous model for the 3-D tracer distribution. Spline coefficients that tended to have negative values were identified and were constrained to stay near zero with use of a quadratic penalty that penalized nonzero contributions to the projection data model. To test the method we used trilinear B-splines to reconstruct volumetric images for a 99mTc-sestamibi cardiac SPECT/CT patient study. Spline coefficients were estimated by minimizing a least-squares criterion by direct matrix inversion via Cholesky decomposition. Volumetric images were reconstructed both with and without the negativity penalty, using (1) a higher-resolution spline basis and (2) a multiresolution basis composed of higher-resolution splines in the heart volume and lower-resolution splines elsewhere. Reduced image noise and good myocardial resolution were obtained with use of the multiresolution basis. Use of the penalty dramatically reduced image noise for the higherresolution basis and yielded good resolution throughout the body. Encouraged by these results, we are using multiresolution 4-D spatiotemporal B-splines and penalized weighted least-squares inversion to reconstruct dynamic SPECT data from rest/stress cardiac patient studies.