Theoretical Investigation on an Unmatched Backprojector for Iterative Reconstruction in Emission Computed Tomography

초록

Several studies show better performance using unmatched projector/backprojector pairs for iterative image reconstruction. The validity of an unmatched pair can be provided if all eigenvalues of the multiplication of a backprojector and a projector are positive. However, the verification of this condition requires heavy computation in practice. In this paper, we show that if the backprojector represents the adjoint transform of the linear transform defined by a given projector, then the projector/backprojector pair is valid. We claim that selection of a valid unmatched backprojector can be much more easily performed by finding a problem-specific inner product than by computing the backprojector directly from the projector using positivity condition on eigenvalues. To support our claim: we show how we select problem-specific; inner products and compute corresponding unmatched backprojectors in parallel hole SPECT (single photon emission computed tomography) with distance-dependent detector blurring. We provide simulation results using unmatched projector/backprojector pairs in ML-EM (maximum likelihood-expectation maximization) and ART (algebraic reconstruction technique) iterations.

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