# Resolving Gas Bubbles Ascending in Liquid Metal from Low-SNR Neutron Radiography Images
## 5 Experimental Validation
### Error Analysis  
With the images from the reference experiments processed and the error metrics calculated, one can now assess the performance of the developed code more strictly than in Section 4.3. Starting with the imaging for a static reference body, the results are presented in Figures 24-26. One can see in the \(S_{\Delta}\) histograms (Figure 24) that the global filter error distribution peaks and means are shifted towards higher \(S_{\Delta}\) values going from neutron flux transmission along the shorter (a) to longer (b) axis, and value dispersion is also increased with considerably more instances of \(S_{\Delta}>10\%\). When the body is moved 1 cm away from the scintillator (c), the global filter peak is shifted further towards higher values but the dispersion does not change significantly. The maximum values (not shown) are higher as well with respect to (b). Similar tendencies can be observed for the local filter errors, but the overall error values are considerably decreased and distribution peaks are shifted back to lower \(S_{\Delta}\) values. The \(S_{\Delta}\) dispersion and maximum values are also diminished across the board. Thus, while not radical, the improvements due to local filtering are still very clear. Figure 24: Static reference body: smooth normalized \(S_{\Delta}\) histograms for neutron flux transmission along the (**a**) smaller (20 mm) axis, (**b**) larger (30 mm) axis and (**c**) larger axis with an extra 1 cm distance between the scintillator and the body (0 mm by default). Note the color legends in the upper right corners of (**a**–**c**) indicating results for the global and local filters. Here \(\rho\) is the normalized event density. Histogram bins were determined using the Scott method and 2-order interpolation was applied to bin density values. Figure 25: Static reference body: smooth normalized \(\delta S\) histograms for neutron flux transmission along the (**a**) smaller axis, (**b**) larger axis and (**c**) larger axis with an extra 1 cm distance between the scintillator and the body. The \(\delta S\) distributions shown in Figure 25 are different in that there are many more instances of \(\delta S<5\%\). Note that, while in (a) where there are relatively less \(\delta S<5\%\) values than in (b,c) for the global filter, the local filter improves the results significantly--dispersion is minimized and the distribution mean is shifted below \(\delta S=2\%\). This is in contrast to what is seen in (b,c): in (b), the \(\delta S\) peak is shifted towards larger values by the local filter, and in (c) it stays at roughly the same position. However, again, the local filter drastically minimized \(\delta S\) dispersion and maxima. The reason why one observes relatively less \(\delta S<5\%\) values in (b,c) than in (a) is that the local filter performance depends on how well the first three stages of the global filter improve SNR and CNR. That is to say, most of the instances with \(\delta S\gtrsim 7\%\) are converted to values about the peaks of the local filter error distribution because the local filter in most cases cannot achieve improvement to below than \(\delta S\lesssim 3\%\). Therefore it stands to reason that less such values are seen in (c) than in (b). As with \(S_{\Delta}\) (Figure 24), one can see that the local filter performs progressively worse from (a) to (c), as expected. In the static body case one would expect \(\delta x\approx\delta y\), which is indeed the case, since there is no bias due to motion blur. Figure 26 therefore shows the norm of the position error vector. Notice that here the local filter improves the error distributions only sightly, reducing the relative amount of higher \(\|\delta x,\delta y\|\) values in all cases. It is important to point out that \(\delta r\) distributions conform to \(\delta S\) plots and the \(\delta r\) metric values are lower by a factor of 2, while \(\delta c\) is negligible across the board. The error values seen in Figures 24-26 are within acceptable ranges.