The upper limits of the SNR in radiography and CT with polyenergetic x-rays

Abstract

The aim of the study is to determine the upper limits of the signal-to-noise ratio (SNR) in radiography and computed tomography (CT) with polyenergetic x-ray sources. In x-ray imaging, monoenergetic x-rays provide a higher SNR compared to polyenergetic x-rays. However, the SNR in polyenergetic x-ray imaging can be increased when a photon-counting detector is used and x-rays are optimally weighted according to their energies. For a particular contrast/background combination and at a fixed x-ray entrance skin exposure, the SNR in energy-weighting x-ray imaging depends on tube voltage and can be maximized by selecting the optimal tube voltage. The SNR in energy-weighted x-ray images acquired at this optimal tube voltage is the highest SNR that can be achieved with polyenergetic x-ray sources. The optimal tube voltages and the highest SNR were calculated and compared to the SNR of monoenergetic x-ray imaging. Monoenergetic, energy-weighting polyenergetic and energy-integrating polyenergetic x-ray imagings were simulated at a fixed entrance skin exposure of 20 mR. The tube voltages varied in the range of 30–140 kVp with 10 kV steps. Contrast elements of CaCO3, iodine, adipose and tumor with thicknesses of 280 mg cm−2, 15 mg cm−2, 1 g cm−2 and 1 g cm−2, respectively, inserted in a soft tissue background with 10 cm and 20 cm thicknesses, were used. The energy weighting also improves the contrast-to-noise ratio (CNR) in CT when monoenergetic CT projections are optimally weighted prior to CT reconstruction (projection-based weighting). Alternatively, monoenergetic CT images are reconstructed, optimally weighted and composed to yield a final CT image (image-based weighting). Both projection-based and image-based weighting methods improve the CNR in CT. An analytical approach was used to determine which of these two weighting methods provides the upper limit of the CNR in CT. The energy-weighting method was generalized and expanded as a weighting method applicable in areas other than x-ray and CT. An optimal x-ray tube voltage providing the highest SNR in energy-weighting x-ray imaging was determined for each contrast/background combination. Depending on the imaging task, the highest SNR with energy-weighted polyenergetic x-rays was close to the SNR provided by monoenergetic x-rays. In CT, projection-based weighting provided higher CNR than image-based weighting, thus determining an upper limit of the CNR in CT. The weighting approach can be applied to imaging methods with contrast mechanisms other than x-ray interaction. A unique, task-dependent tube voltage exists in photon-counting x-ray and CT that provides the highest SNR with polyenergetic x-rays. The highest SNR achieved in photon-counting energy-weighted x-ray and CT can approach the SNR of monoenergetic x-ray and CT imaging, depending on the imaging task.