Making X-ray imaging faster!

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X-ray computed tomography is a versatile technique for 3D structure characterization, and the pursuit of a faster yet reliable scan is never ended. A lot of methods, such as the maximum likelihood expectation maximization (MLEM) and maximum-a-posteriori (MAP), have been proposed and developed to improve the speed, but most of they are mainly for the "step-scan" mode. At synchrotron facilities such as the FXI beamline at Brookhaven National Laboratory, data is normally collected in the high-speed "fly-scan" mode,  which inevitably results in a blurred image using traditional reconstruction algorithms. Figure 1 illustrates how a "fly-scan" mode can introduce artifacts due to the nature of rotation. MLEM and MAP+TV methods can be employed on top of the FBP reconstruction algorithm, however, their performance is still limited (see Figure 3).

Figure 1. Blurring effects in fly-scan. (a) schematics of a fly-scan data collection. The blue shadow  illustrates the area that is exposed to x-ray under single exposure. In the line profile, the red part manifests the blurring effects compared to the blur curve obtained in the regular step-scan. (b)  simulated reconstruction of a grid pattern with blurring angle. (c) enlarged view of area enclosed by the blur  rectangular in (b).

In this work, we are trying to push the fly-scan imaging speed limit further, down to sub-10 second, by using the machine learning (ML) method.  We chose the filtered-back-projection (FBP) method that reconstructs the sinogram to get a “blurred tomogram”, acknowledging that the obtained tomogram consists of both blurring artifacts and noise artifacts. The blurred tomogram is then fed into our neural network model, which is composed of three residual-in-residual dense block (RRDB) modules as the backbone and other layers (see Fig. 2b). The RRDB follows the same architecture as stated in the literature, and three modules achieves a good  balance between the numerical accuracy and computation speed.  The pixel-wise difference between the ML outputs and ground truth is back propagated to update the ML model.  We have prepared four types of images with different geometries, feature sizes, and feature types as a general representation of a vast variety of samples that we commonly encountered in the experiments.

Figure 2. Machine learning for tomography reconstruction. (a) workflow. Blurred sinogram is calculated from the synthetic ground truth image (GT image) using Eq. (5). (b) Scheme of RRDB network containing four sequentially connected RRDB models. (c) scheme of individual RRDB model (as outlined by the black rectangle in figure b) containing three dense blocks. 

We compare the reconstruction results using different reconstruction algorithms: FBP, MLEM, MAP+TV, and ML. From figure 3, the construction using FBP gives a noisy reconstruction, originating from the limited projections number and the Poisson noise in the sinogram.  Reconstruction from MLEM displays strong blurring and noise at the image edge.   The noise level in MAP+TV method is largely suppressed, and boundaries are sharply preserved compared to the reconstruction from FBP and MLEM.  However, we also note that MAP+TV generates additional artifacts. The reconstruction tends to form straight edges at particle boundaries; the round shape ball-like particles turn into facet ones. The ML results give the closest-to-grand-truth reconstruction. Compared to MAP+TV, ML does not have straight-boundary artifacts and preserves even sharper boundaries for small features than MAP+TV (see the arrows in Figure 3i and 3j). The improved reconstruction quality is also measured by the increased PSNR and SSIM (refer to Table 1 in the original article).

Figure 3. Evaluation of different reconstruction methods. (a) ground truth. (b) Reconstruction using FBP, with PSNR = 11.69 and SSIM = 0.38. (c) Reconstruction using MLEM, with PSNR = 17.77 and SSIM  = 0.60. (d) Reconstruction using TV regularized MAP, with PSNR = 21.70 and SSIM = 0.77. (e) Reconstruction using machine learning (ML) method, with PSNR = 25.02 and SSIM = 0.88. Enlarged views inside the dashed square are shown in (f-j), respectively. Note: the dashed lines in (i) illustrate the straight  boundary of the original curved particle reconstructed using the MAP+TV method. The arrows in (i) and (j) compare the reconstruction of a small feature (empty hole) using MAP and ML.

Even though the speedup is not in the magnitude of order's level (currently a typical fly-scan cost is around 1 min), considering the fact that FXI and other similar TXM facilities are supporting worldwide researchers, an even small improvement can save a huge amount of total experiment time!

If you are interested, check out our paper for more details and discuss it here!

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