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Self-normalization of 3D PET data by estimating scan-dependent effective crystal efficiencies

Normalization of the lines of response (LORs) or sinogram bins is necessary to avoid artifacts in fully 3D PET imaging. Component-based normalization (CBN) is an effective strategy to generate normalization factors (NFs) from short time scans of known emission sources. In the CBN, the NFs can be factorized into time-invariant and time-variant components. The effective crystal efficiencies are the main time-variant component, and a frequent normalization scan is needed to update their values. Therefore, it would be advantageous to be able to estimate unique effective crystal efficiencies to account for this time-variant component. In this work, we present a self-normalization algorithm to estimate the crystal efficiencies directly from any emission acquisition. The algorithm is based on the principle that if the true image were known, the mismatch between its projections, corrected for the time-invariant NFs, and the acquired data could be used to estimate the effective crystal efficiencies. We show that the algorithm successfully estimates the effective crystal efficiencies for simulated sinograms with different levels of Poisson noise and for different distributions of crystals efficiencies. This algorithm permits the reconstruction of good quality images without the need for an independent, separate, normalization scan. A key advantage of the method is the estimation of relatively few parameters (~ 104) compared to the number of NFs for 3D data (~ 108).