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 imagingsystems 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, , for evaluation of DE imaging performance using different decomposition algorithms. For a lung nodule detection task, the detectability index varied from (i.e., nodule barely visible) in the absence of noise reduction to (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 (, 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 for conventional log subtraction to 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.
The authors extend their thanks to Richard Van Metter, Ph.D. and John Yorkston, Ph.D. (Carestream Health Inc., Rochester, NY), Narinder S. Paul, M.D. (University Health Network, Toronto ON), and Michael J. Daly, M.Sc. (Ontario Cancer Institute, Toronto ON) for stimulating discussions regarding this work. The clinical imaging prototype used for phantom imaging was constructed in research collaboration with Carestream Health Inc. Thanks also to Amar C. Dhanantwari, Ph.D., and Dinsie Williams, M.Sc. (Ontario Cancer Institute, Princess Margaret Hospital) and Nicholas A. Shkumat (Department of Medical Biophysics, University of Toronto) for assistance with the clinical system. The enthusiastic support of Christopher J. Paige, Ph.D., and Patrice Bret, M.D. (University Health Network) is gratefully acknowledged. This research was supported by the National Institutes of Health (R01-CA112163-01), the University of Toronto New Staff Award (No. 72022001), a Cunningham Fellowship Award, and a University of Toronto Open Scholarship Award.
II. THEORETICAL METHODS
II.A. Generalization of linear dual-energy decomposition algorithms
II.A.1. Standard log subtraction (SLS)
II.A.2. Simple smoothing of the high-energy image (SSH)
II.A.3. Anti-correlated noise reduction (ACNR)
II.A.4. A general linear noise reduction algorithm (GLNR)
II.B. Cascaded systems analysis
II.B.1. The projection image NPS and MTF
II.B.2. The DE image NPS
II.B.3. The DE imageMTF
II.B.4. The DE noise-equivalent quanta (NEQ)
II.C. Imaging task and detectability index
II.D. Optimization of DE image dose allocation
III. EXPERIMENTAL METHODS
III.A. Experimental setup
III.A.1. DE imagingsystems
III.A.2. DE image acquisition
III.A.3. DE image decomposition
III.B. Measurement of the DE image NPS
III.C. Measurement of the DE imageMTF
III.D. Performance evaluation in phantom images
IV.A. The DE image NPS
IV.B. The DE imageMTF
IV.C. The DE image NEQ
IV.D. Detectability index and optimal dose allocation
V.A. Optimization in the presence of multiple tasks
V.B. Optimal DE image acquisition and decomposition
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