# Resolving Gas Bubbles Ascending in Liquid Metal from Low-SNR Neutron Radiography Images
## 2 Image and Bubble Characterization
### Image Properties  
The acquired images are 16-bit 1-channel TIFTs with a 1024 \(\times\) 1024 pixel resolution (2 \(\times\) 2 average-binned \(2048\times 2048\) frames) with a 0.11-0.12 mm pixel size (0.12 mm for the reference experiments). Short exposure times (10 ms) result in strong Poisson (multiplicative) noise from neutrons and converted photons, and salt-and-pepper noise of varying density is present due to overexposed (gamma ray noise) or \"dead\" camera pixels. The neutron beam flux over the FOV is non-uniform with a fall-off near the edges of the acquired images.  
Figure 1a is an example of an acquired raw image. Here gas flow rate was 120 sccm (standard cubic centimeters per minute) and static vertical magnetic field of 125 mT was applied to the bubble chain region. Typically one can see the following captured in a full FOV image: the liquid gallium volume within the glass container (delimited by the interior orange lines and the light blue line), the container walls (orange lines), the free surface of liquid metal (the light blue line), the surrounding air (regions outside the walls and above the metal free surface) and the neutron flux shielding (borated polyethylene, the red line) for the magnetic field system. However, not all of the FOV is of interest--Figure 1b shows the FOV cropped to the liquid metal volume in false color after pre-processing (Section 3.2). Note also the bubble regions highlighted in Figure 1a,b--these are the objects of interest that must be segmented and their properties such as centroids, projection areas, tilt angles, aspect ratios, etc. measured. Note that the same color scheme and normalized luminance scale as in Figure 1b are used in all further figures unless stated otherwise.  
Figures 2 and 3 illustrate the image processing challenge with examples of image noise and neutron flux transmission signal for bubbles after pre-processing (Section 3.2). Figure 2 shows a typical luminance distribution about a bubble region: here, moving averages (window width in the scan direction equal to one pixel) over (a) horizontal and (b) vertical image patches are shown, since plots over any given single pixel line would be unintelligible. Estimates from a control set of bubble regions for different frames indicate many of the images have \(\text{SNR}=\langle S_{\text{b}}^{2}\rangle/\sigma_{\text{n}}^{2}\sim\) 1.5-1.6 (\(S_{\text{b}}\) is the bubble signal intensity, \(\sigma_{\text{n}}\) is the noise standard deviation), and there are cases with SNR as low as \(\sim\)1.2. Similar plots for (a) horizontal and (b) vertical patches for the entire width/length of the cropped FOV are shown in Figure 3.  
Figure 1: (**a**) Original captured FOV after outlier removal and luminance normalization with marked container walls (orange dashed lines), the mean gallium free surface level (light blue), the neutron flux shielding (red, borated polyethylene) and bubble locations within the FOV (white). Note the scale bar in the bottom-left corner. (**b**) FOV in false color (color bar on the right) after cropping to the container walls and the metal free surface, dark current and flat field corrections, and normalization.  
Figure 2: Bubble neighborhood analysis: width mean of luminance (gray) over the length of (**a**) horizontal and (**b**) vertical patches roughly fitted to the bubble region within the FOV. Normalized luminance versus pixel coordinates is shown in both cases. Note the pixel-to-\(mm\) scale bar in (**b**). Bubble neighborhood patches shown in (**a,b**) are not to scale and are normalized as in Figure 1. Scan directions are indicated by the dashed blue arrows and the red curve is the total variation filtered (Gaussian, regularization parameter equal to 1 [58]) gray curve.  
While visible in (a), it is especially evident in (b) that despite the compensation for neutron flux non-uniformity over the FOV, the background \"mean\" is still not uniform /flat. One also has rather densely packed noise peaks with luminance values comparable to the values associated with the bubbles.