SVD investigation of modeling scatter in multiple energy windows for improved SPECT images

In this work singular value decomposition (SVD) techniques are used to investigate how the use of low energy photons and multiple energy windows affects the noise properties of SPECT reconstructions. We have previously shown that, when modeling scatter in the projector of iterative reconstruction algorithms, simultaneous reconstruction from multiple energy window data can result in very different noise characteristics. Further, the properties depend upon the width and number of energy windows used. To investigate this further, we have generated photon transport matrices for an elliptical phantom and a number of energy window schemes. Transfer matrices were also generated for the cases of perfect scatter rejection, and ideal scatter subtraction. These matrices were decomposed using SVD, and the signal and noise power spectra were computed using the projection eigenvector basis. Results indicate very different noise properties for the various energy window combinations. The perfect scatter rejection case resulted in the lowest noise power; and modeling scatter in a 20% window performed slightly better than the scatter subtraction case. When including lower energies, forming a contiguous series of seven small energy windows outperformed a single large energy window, but neither method achieved a lower noise power than the standard 20% window. Finally, one combination of windows is presented which utilizes low energy scattered photons and achieves a lower noise power than the standard 20% energy window.