| In this work, a method to perform simultaneous scatter and attenuation correction for PET is developed within the context of statistical image reconstruction methods. The principles are demonstrated using both numerical simulations of artificially constructed scatter distributions and Monte Carlo studies of phantoms, showing the viability of this method in practice. In addition, a new transmission scan protocol is defined which is necessary to collect the required data in order to perform the corrections. The method has several distinct advantages over traditional filtered back-projection techniques. These include treating scatter and attenuation simultaneously so that a correction can be made during image reconstruction, leading to a one-step method; guaranteed non-negativity of the reconstructed pixel intensity values; predictable noise propagation; and improved counting performance by 65% resulting in an increased signal-to-noise ratio (on the order of 28%), achieved using non-windowed acquisition. Noise Equivalent Count rate analysis indicates that for a nominal clinical activity concentration of 37 kBq/cc (1 muCi/cc), a three-fold improvement in scanner performance can be realized for a standard acquisition window, compared to an uncorrected image and a five-fold improvement is achievable using an extended acquisition window. |
