Modeling Spatial Smoothness in Fully 3-D SPECT Image Reconstruction Using Multiresolution B-Splines

We investigated the use of B-spline spatial basis functions to model continuous 3-D tracer distributions in cardiac SPECT studies. This approach is motivated by goals of achieving a well-posed image reconstruction problem and computational efficiency. Uniform B-spline basis functions have the noteworthy property that splines having larger spatial support can be composed from a linear combination of splines having smaller support, thus facilitating creation of a multiresolution spatial model. B-splines can be evaluated quickly when calculating projection data models or displaying reconstructed images, and there is no image "blockiness" because B-splines yield a spatially continuous representation. We used trilinear B-splines to reconstruct images for a ^99mTc-sestamibi cardiac SPECT/CT patient study. Attenuation and depth-dependent point response were modeled. Spline coefficients were estimated by minimizing a least-squares criterion by direct matrix inversion. Images were reconstructed with use of (1) more-spatially-compact splines, (2) less-spatially-compact splines, and (3) a multiresolution basis composed of more-compact splines in the heart volume and less-compact splines elsewhere. Image noise was reduced with use of less-compact or multiresolution splines, and the multiresolution basis also yielded good myocardial resolution. Encouraged by these results, we are using multiresolution B-splines to analyze dynamic SPECT data from rest/stress cardiac patient studies.