High-precision noise power spectrum measurements in digital radiography imaging

Accurately and precisely estimating the noise power spectrum (NPS) is important for characterizing the performance of a radiography detector and helpful for improving the performance when developing radiography detectors. In order to produce an accurate estimate, the frequency resolution should be sufficiently high, and for a precise estimate, the sample size for the sample mean should also be large enough. However, there is a trade-off between the frequency resolution and the sample size if the available samples are limited. To improve the precision of the estimate, a radial averaging technique is employed in the IEC standard without sacrificing the frequency resolution or the estimate accuracy. In the radial averaging technique, directional NPS curves of a range are averaged from the two-dimensional NPS, and thus, directional error and poor precision problems occur, especially at low frequencies. This problem also leads to uncertainties in calculating the detective quantum efficiency (DQE). Therefore, the purpose of this study is to develop algorithms that can improve the precisions in estimating NPS to replace the radial averaging technique or to add additional precision.

The horizontal or vertical NPS curve can be estimated using the sample mean of the summation of directional cross periodograms with various distances from the two-dimensional NPS. In practical x-ray imaging, the amplitude response of the cross periodograms decreases rapidly as the distance increases. Hence, a partial summation of the cross periodograms can provide an accurate estimate of the NPS. This partial summation can increase the sample size and thus improve the estimate precision for the entire frequency range without causing directional errors. This paper proposes two estimate algorithms under the notion of the partial use of cross periodograms.

In order to evaluate the precisions from the proposed algorithms, a relative precision, which is defined as the standard deviation of the estimate divided by its average, was employed. The relative precisions were calculated using 100 x-ray images acquired from a general radiography detector. For the detector, we were able to achieve a better precision compared to using the radial averaging technique. For an image of 900 × 900 pixels and the region of interest size 256 in a direction with a half overlap, the conventional approach of the IEC standard yielded an average relative precision of 6.96% with the worst precision of 36.1% at the zero frequency. However, the proposed algorithms could yield an average relative precision of 4.14% with the zero-frequency precision of 5.79%.

Without using the radial averaging technique, the proposed algorithms in this paper could improve the estimate precisions for the entire frequency range under the notion of a partial summation of the cross periodograms. Especially for low frequencies including the zero frequency, the proposed algorithms could achieve a high-precision to estimate the NPS.