Cascaded systems analysis of noise reduction algorithms in dual-energy imaging

An important aspect of dual-energy (DE) x-ray image decomposition is the incorporation of noise reduction techniques to mitigate the amplification of quantum noise. This article extends cascaded systems analysis of imaging performance to DE imaging systems incorporating linear noise reduction algorithms. A general analytical formulation of linear DE decomposition is derived, with weighted log subtraction and several previously reported noise reduction algorithms emerging as special cases. The DE image noise-power spectrum (NPS) and modulation transfer function (MTF) demonstrate that noise reduction algorithms impart significant, nontrivial effects on the spatial-frequency-dependent transfer characteristics which do not cancel out of the noise-equivalent quanta (NEQ). Theoretical predictions were validated in comparison to the measured NPS and MTF. The resulting NEQ was integrated with spatial-frequency-dependent task functions to yield the detectability index, d', for evaluation of DE imaging performance using different decomposition algorithms. For a 3 mm lung nodule detection task, the detectability index varied from d' < 1 (i.e., nodule barely visible) in the absence of noise reduction to d' > 2.5 (i.e., nodule clearly visible) for "anti-correlated noise reduction" (ACNR) or "simple-smoothing of the high-energy image" (SSH) algorithms applied to soft-tissue or bone-only decompositions, respectively. Optimal dose allocation (A*, the fraction of total dose delivered in the low-energy projection) was also found to depend on the choice of noise reduction technique. At fixed total dose, multi-function optimization suggested a significant increase in optimal dose allocation from A* = 0.32 for conventional log subtraction to A* = 0.79 for ACNR and SSH in soft-tissue and bone-only decompositions, respectively. Cascaded systems analysis extended to the general formulation of DE image decomposition provided an objective means of investigating DE imaging performance across a broad range of acquisition and decomposition algorithms in a manner that accounts for the spatial-frequency-dependent imaging task.