Scatter-induced non-linear signal compression and SDNR loss in triple-energy photon-counting iodine imaging

Triple-energy x-ray imaging with photon-counting detectors (PCDs) enables material decomposition, but energy-dependent scatter introduces bin-specific distortions that propagate nonlinearly through triple-energy subtraction and degrade image quality. The purpose of this work is to quantify how bin-dependent scatter alters triple-energy iodine signal formation and to determine its impact on signal-difference-to-noise ratio (SDNR). Analytical expressions for iodine signal difference, noise, and SDNR were derived incorporating energy-bin-specific scatter fractions (SF) and their nonlinear coupling with iodine areal density. Measurements were performed using a CdTe-based PCD and an image-quality phantom, with scatter varied via field of view (FOV) and quantified using the air-gap method. SDNR was evaluated over iodine areal densities of 33-140 mg/cm², SF values of ~0.2-0.8, tube voltages of 60-100 kV, and phantom thicknesses of 10-20 cm. A physics-informed empirical model was fit to the data. Simulations including charge sharing and beam hardening were used to support interpretation. Scatter fractions differed across energy bins, with the lowest-energy bin exhibiting the highest SF. Increasing scatter introduced curvature in energy-bin iodine signals as a function of areal density. When combined through triple-energy subtraction, these unequal responses produced pronounced signal compression in the triple-energy image. The model accurately predicted energy-bin and combined signal differences (R{{}^2} > 0.92) but showed reduced agreement for SDNR (R{{}^2} = 0.82-0.94), reflecting additional coupling between signal, noise, and scatter in the triple-energy combination. SDNR degradation exceeded that expected from first-order scatter scaling: for 52 mg/cm² iodine, SDNR decreased by ~20% at SF ≈ 0.2 and ~70% at SF ≈ 0.8. Simulations reproduced both linear contrast loss and the additional nonlinear compression observed experimentally. Bin-dependent scatter induces nonlinear signal compression in triple-energy imaging that directly amplifies SDNR loss with increasing iodine thickness. Because this behavior arises from the structure of triple-energy subtraction, first-order scatter scaling systematically underestimates performance degradation.