6 June 2000 Multiresolution constrained least-squares algorithm for direct estimation of time activity curves from dynamic ECT projection data
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We present an algorithm which is able to reconstruct dynamic emission computed tomography (ECT) image series directly from inconsistent projection data that have been obtained using a rotating camera. By finding a reduced dimension time-activity curve (TAC) basis with which all physiologically feasible TAC's in an image may be accurately approximated, we are able to recast this large non-linear problem as one of constrained linear least squares (CLLSQ) and to reduce parameter vector dimension by a factor of 20. Implicit is the assumption that each pixel may be modeled using a single compartment model, as is typical in 99mTc teboroxime wash-in wash-out studies; and that the blood input function is known. A disadvantage of the change of basis is that TAC non-negativity is no longer ensured. As a consequence, non-negativity constraints must appear in the CLLSQ formulation. A warm-start multiresolution approach is proposed, whereby the problem is initially solved at a resolution below that finally desired. At the next iteration, the number of reconstructed pixels is increased and the solution of the lower resolution problem is then used to warm-start the estimation of the higher resolution kinetic parameters. We demonstrate the algorithm by applying it to dynamic myocardial slice phantom projection data at resolutions of 16 X 16 and 32 X 32 pixels. We find that the warm-start method employed leads to computational savings of between 2 and 4 times when compared to cold start execution times. A 20% RMS error in the reconstructed TAC's is achieved for a total number of detected sinogram counts of 1 X 105 for the 16 X 16 problem and at 1 X 106 counts for the 32 X 32 grid. These errors are 1.5 - 2 times greater than those obtained in conventional (consistent projection) SPECT imaging at similar count levels.
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Jonathan S. Maltz, Jonathan S. Maltz, } "Multiresolution constrained least-squares algorithm for direct estimation of time activity curves from dynamic ECT projection data", Proc. SPIE 3979, Medical Imaging 2000: Image Processing, (6 June 2000); doi: 10.1117/12.387719; https://doi.org/10.1117/12.387719

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