@article{1e0c7238296047eb9b484d4ff4c1e5c5,
title = "Cascaded systems analysis of noise reduction algorithms in dual-energy imaging",
abstract = "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.",
keywords = "Cascaded systems analysis, DQE, Dual-energy imaging, Flat-panel detector, Imaging performance, Imaging task, MTF, NEQ, NPS, Noise reduction",
author = "Samuel Richard and Siewerdsen, {Jeffrey H.}",
note = "Funding Information: 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. TABLE I. Summary of low- and high-energy convolution filters for four DE decomposition algorithms (SLS, SSH, ACNR, and GLNR), shown to be special cases of the general form in Eq. (1) . Algorithm h L ( x , y ) h H ( x , y ) H L ( u , v ) H H ( u , v ) SLS − w δ ( x , y ) δ ( x , y ) − w 1 SSH − w δ ( x , y ) h L P F ( x , y ) − w H LPF ( u , v ) ACNR w n w c h HPF ( x , y ) − w δ ( x , y ) δ ( x , y ) − w n h HPF ( x , y ) w n w c H HPF ( u , v ) − w 1 − w n H HPF ( u , v ) GLNR w L h L , HPF ( x , y ) − w h L , LPF ( x , y ) h H , LPF ( x , y ) − w H h H , HPF ( x , y ) w L H L , HPF ( u , v ) − w H L , L P F ( u , v ) H H , LPF ( u , v ) − w H H H , HPF ( u , v ) TABLE II. Summary of DE image decomposition parameters. Decomposition parameters Soft-issue image Bone-only image w 0.27 0.60 w c 0.60 0.27 d LPF 0.90 0.15 w n 0.90 0.90 d HPF 0.50 0.30 FIG. 1. Photograph of the experimental DE imaging bench, showing (1) the x-ray tube, (2) an anthropomorphic chest phantom, and (3) the flat-panel detector. FIG. 2. Example DE images of an anthropomorphic chest phantom produced by various noise reduction algorithms. Each image is zoomed-in about a region of the right lung to illustrate subtle differences in spatial resolution and noise, (a,b) Low- and high-energy projections. (c,e,g) Soft-tissue images decomposed using SLS, SSH, and ACNR algorithms, respectively. (d,f,h) Bone-only images decomposed using SLS, SSH, and ACNR algorithms, respectively. DE image decomposition parameters associated with each case are summarized in Table II . FIG. 3. Measured (data points) and theoretical (straight lines) NNPS for (a) “soft-tissue” and (b) “bone-only” flat-field images formed using the three decomposition algorithms. SSH and ACNR are seen to reduce noise significantly compared to SLS. Theoretical calculations using cascaded systems analysis show excellent agreement with measurements. FIG. 4. Flood-field images depicting quantum mottle under different DE image decomposition algorithms corresponding to the NPS plots shown in Fig. 3 . The algorithms are seen to dramatically affect the magnitude and spatial-frequency content of the noise. FIG. 5. Measured and theoretical MTF associated with DE images formed using various noise reduction algorithms. The dashed line is the MTF of the detector as determined from ESF measurements using an angled Pb edge. For the SSH and ACNR algorithms, the MTF depends on the signal differences presenting in low- and high-energy images. (a,b) The MTF for SSH in soft-tissue and bone-only images. (c,d) The MTF for ACNR in soft-tissue and bone-only images. The data points with error bars are measurements, and the solid lines are theoretical calculations. FIG. 6. Calculations of the DE MTF for various decomposition algorithms. (a) MTF for the soft-tissue image, for which the structure of interest is HDPE ( k rel = 1.7 ) . (b) MTF for the bone-only image, for which the structure of interest is a Teflon sphere ( k rel = 2.4 ) . FIG. 7. NEQ calculated from the NNPS and MTF of Figs. 3 and 6 , respectively, (a) NEQ of the soft-tissue image, taking HDPE (similar to a solid pulmonary nodule) as the material of interest in the decomposition, (b) NEQ of the bone-only image, taking Teflon (similar to cortical bone) as the material of interest in the decomposition. FIG. 8. Detectability index computed as a function of dose allocation for the detection of: (a) a 3 mm HDPE sphere in a soft-tissue image and (b) a 3 mm Teflon sphere in a bone-only image. FIG. 9. Soft-tissue DE images of a 3 mm HDPE sphere at various dose allocation and decomposition algorithms corresponding to the calculations of Fig. 8(a) . The detectability index (soft-tissue sphere detection task) computed using Eq. (18) is superimposed. Qualitative agreement is observed between the trends in d ′ and conspicuity of the sphere. FIG. 10. Bone-only DE images of a 3 mm Teflon sphere at various dose allocation and decomposition algorithms corresponding to the calculations of Fig. 8(b) . The detectability index (bony sphere detection task) computed using Eq. (18) is superimposed. Qualitative agreement is observed between the trends in d ′ and conspicuity of the sphere. FIG. 11. DE images decomposed using GLNR decomposition for soft-tissue and bone-only image compared to optimal SLS, SSH, and ACNR images. Top row: soft-tissue images of a polyethylene sphere. Bottom row: bone-only images of a Teflon sphere. ",
year = "2008",
doi = "10.1118/1.2826556",
language = "English (US)",
volume = "35",
pages = "586--601",
journal = "Medical physics",
issn = "0094-2405",
publisher = "AAPM - American Association of Physicists in Medicine",
number = "2",
}