Fast binary CT using Fourier null space regularization (FNSR)

Abstract

X-ray CT is increasingly being adopted in manufacturing as a non destructive inspection tool. Traditionally, industrial workflows follow a two step procedure of reconstruction followed by segmentation. Such workflows suffer from two main problems: (1) the reconstruction typically requires thousands of projections leading to increased data acquisition times. (2) The application of the segmentation process a posteriori is dependent on the quality of the original reconstruction and often does not preserve data fidelity. We present a fast iterative x-ray CT method which simultaneously reconstructs and segments an image from a limited number of projections called Fourier null space regularization (FNSR). The novelty of the approach is in the explicit updating of the image null space with values derived from a regularized image from the previous iteration, thus compensating for any missing projections and effectively regularizing the reconstruction. The speed of the method is achieved by directly applying the Fourier Slice Theorem where the non-uniform fast Fourier transform (NUFFT) is used to compute the frequency spectrum of the projections at their positions in the image k-space. At each iteration a segmented image is computed which is used to populate the null values of the image k-space effectively steering the reconstruction towards a binary solution. The effectiveness of the method to generate accurate reconstructions is demonstrated and benchmarked against other iterative reconstruction techniques using a series of numerical examples. Finally, FNSR is validated using industrial x-ray CT data where accurate reconstructions were achieved with 18 or more projections, a significant reduction from the 5000 needed by filtered back projection.

CT image reconstruction via industrial CT fast scanning

“…Figure 3 demonstrates that our present method exhibits significantly improved edge contours, as shown in the region of interest (ROI) of figure 3(e) and figure 3(j). In terms of quantitative evaluation metrics, our algorithm achieves a superior SSIM score, outperforming the Fast Null Space Reconstruction (FNSR) [25] algorithm by 0.0175. In addition, our method achieves a higher PSNR score, outperforming FNSR by 1.656.…”