1. Introduction In Positron Emission Tomography (PET), each line of response (LOR) has a different sensitivity due to the scanner's geometry and the detector's properties. In order to achieve artifact-free and good quality images, these non-uniformities must be corrected using normalization correction factors (NCFs). A widely used normalization method is the component-based normalization (CBN), where the number of parameters to estimate is dramatically reduced by modeling the efficiency of each LOR as a product of multiple factors. In the CBN, the components can be separated into time-invariant, time- variant and acquisition-dependent components. The crystal efficiencies are the main time-variant factors and are updated by a regular normalization scan. However, the effective crystal efficiencies can change between normalization scans for many reasons, including, for example, variations in temperature. Therefore, it would be advantageous to be able to estimate the effective crystal efficiencies directly for each unique emission scan. Self-Normalization of 3D PET Data by Estimating Scan-Dependent Effective Crystal Efficiencies Martin A Belzunce and Andrew J Reader King's College London, Division of Imaging Sciences, St Thomas Hospital, London, UK crystal interference geometric factors crystal efficiencies dead-time axial factors Crystal Set Projected Noisy Sinogram Purpose To estimate scan-dependent effective crystal efficiencies directly from the emission data using a component-based normalization (CBN). This method enables the reconstruction of good quality images without the need for an independent, separate, normalization scan. It involves using time-invariant normalization factors. Component-Based Normalization Methods N C : complete normalization factors N TI : time-invariant components (geometric, crystal interference, axial factors) N TV : time-variant components (crystal efficiencies) N AQ : acquisition-dependent components (dead-time) Normalization Factor in Bin i: Component Classification: Scan-Dependent Crystal Efficiencies Complete Forward Model in EM reconstruction: Time-Invariant Forward Model: Reconstruction q: projected image using the complete forward model q TI : projected image using the a forward model with only time-invariant factors f c : image reconstructed with complete normalization factors f artifact : image reconstructed with time-invariant normalization factors X: x-ray transform that projects image into a sinogram Rate of two noisy matrices We could estimate time variant normalization factors with: b: emission sinogram The NTV depends only on the crystal efficiencies. If we work on crystal space, the number of parameters to estimate is reduced in 4 orders of magnitude and a variance reduction is achieved. Self-Normalization Algorithm 1. The time-variant NFs (N TV ) are generated from the current crystal efficiencies estimate x k. 2. The complete NFs are generated with N C = N TV · N TI. 3. The measured emission fully 3D sinogram B is reconstructed into image f k using N C. 4. f k is projected into a sinogram P k and multiplied by N C. 5. C[] is applied to the projected and to the input sinograms. 6. The ratio between C[B] and C[P ◦ N C ] is computed and then normalized to get a multiplicative correction factor for the current crystal efficiencies. Sinogram to Crystal Operator Fan-sum algorithm to get the crystal efficiency of one crystal from the N TV sinogram: We use both detectors in a sinogram bin to reduce uncertainty. The operator in matrix notation: Crystal to Sinogram Operator Each sinogram bin represents a unique combination of two crystal elements (span 1 and without polar mashing). Efficiency of a sinogram bin: Matrix Operator: D 1 : matrix with as many rows as bins and columns as crystal element. It has a 1 for each row to identify detector 1. D 2 : idem for detector 2. : Hadamard Product (Element by Element) : Matrix Multiplication OP-OSEM reconstruction with Project reconstructed image Transform to crystal- space Ratio with emission sinogram in crystal space Iter 1Iter 2Xtal in Norm Conclusions Dfdsf