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A Learnt Half-Quadratic Splitting-Based Algorithm for Fast and High-Quality Industrial Cone-beam CT Reconstruction

Aniket Pramanik, Singanallur V. Venkatakrishnan, Obaidullah Rahman, Amirkoushyar Ziabari

TL;DR

Industrial XCTs require high-quality reconstructions from sparse-view data, but traditional MBIR is computationally prohibitive. The authors propose a learned half-quadratic splitting (HQS) algorithm that uses a CNN as a proximal operator and a conjugate-gradient data-consistency step, enabling memory-efficient, iterative CBCT reconstruction with $\min_x \|A x - b\|_2^2 + \lambda Q(x)$ objective. The method updates $z_{n+1}$ via $z_{n+1} = D_{\theta_{n+1}}(x_n)$ and $x_{n+1}$ via $x_{n+1} = (A^T A + \beta I)^{-1}(A^T b + \beta z_{n+1})$, with a fixed CG budget and a tunable $\beta$. On the public Walnuts dataset, the approach with unshared CNN weights achieves higher PSNR/SSIM than MBIR and U-Net, generalizes to unseen imaging conditions, and substantially reduces runtime compared with MBIR, highlighting its practical impact for large-scale industrial CBCT reconstruction.

Abstract

Industrial X-ray cone-beam CT (XCT) scanners are widely used for scientific imaging and non-destructive characterization. Industrial CBCT scanners use large detectors containing millions of pixels and the subsequent 3D reconstructions can be of the order of billions of voxels. In order to obtain high-quality reconstruction when using typical analytic algorithms, the scan involves collecting a large number of projections/views which results in large measurement times - limiting the utility of the technique. Model-based iterative reconstruction (MBIR) algorithms can produce high-quality reconstructions from fast sparse-view CT scans, but are computationally expensive and hence are avoided in practice. Single-step deep-learning (DL) based methods have demonstrated that it is possible to obtain fast and high-quality reconstructions from sparse-view data but they do not generalize well to out-of-distribution scenarios. In this work, we propose a half-quadratic splitting-based algorithm that uses convolutional neural networks (CNN) in order to obtain high-quality reconstructions from large sparse-view cone-beam CT (CBCT) measurements while overcoming the challenges with typical approaches. The algorithm alternates between the application of a CNN and a conjugate gradient (CG) step enforcing data-consistency (DC). The proposed method outperforms other methods on the publicly available Walnuts data-set.

A Learnt Half-Quadratic Splitting-Based Algorithm for Fast and High-Quality Industrial Cone-beam CT Reconstruction

TL;DR

Industrial XCTs require high-quality reconstructions from sparse-view data, but traditional MBIR is computationally prohibitive. The authors propose a learned half-quadratic splitting (HQS) algorithm that uses a CNN as a proximal operator and a conjugate-gradient data-consistency step, enabling memory-efficient, iterative CBCT reconstruction with objective. The method updates via and via , with a fixed CG budget and a tunable . On the public Walnuts dataset, the approach with unshared CNN weights achieves higher PSNR/SSIM than MBIR and U-Net, generalizes to unseen imaging conditions, and substantially reduces runtime compared with MBIR, highlighting its practical impact for large-scale industrial CBCT reconstruction.

Abstract

Industrial X-ray cone-beam CT (XCT) scanners are widely used for scientific imaging and non-destructive characterization. Industrial CBCT scanners use large detectors containing millions of pixels and the subsequent 3D reconstructions can be of the order of billions of voxels. In order to obtain high-quality reconstruction when using typical analytic algorithms, the scan involves collecting a large number of projections/views which results in large measurement times - limiting the utility of the technique. Model-based iterative reconstruction (MBIR) algorithms can produce high-quality reconstructions from fast sparse-view CT scans, but are computationally expensive and hence are avoided in practice. Single-step deep-learning (DL) based methods have demonstrated that it is possible to obtain fast and high-quality reconstructions from sparse-view data but they do not generalize well to out-of-distribution scenarios. In this work, we propose a half-quadratic splitting-based algorithm that uses convolutional neural networks (CNN) in order to obtain high-quality reconstructions from large sparse-view cone-beam CT (CBCT) measurements while overcoming the challenges with typical approaches. The algorithm alternates between the application of a CNN and a conjugate gradient (CG) step enforcing data-consistency (DC). The proposed method outperforms other methods on the publicly available Walnuts data-set.
Paper Structure (7 sections, 6 equations, 5 figures, 1 table, 1 algorithm)

This paper contains 7 sections, 6 equations, 5 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Theory
  3. Memory Efficient Training and Implementation
  4. Experiments and Results
  5. Data-set, CNN Architecture and Methods for Comparisons
  6. Performance and Run-time Comparisons
  7. Conclusion

Figures (5)

  • Figure 1: The Cone-beam CT geometry. A cone-beam source of X-rays is incident on an object and the resulting transmitted signal is captured by a detector. The object is rotated and scanned at different angles (views).
  • Figure 2: Iterative rule of the proposed algorithm and its network architecture. $\text{\bf{D}}$ represents a artifact suppression CNN and the block in orange represent a data-consistency block that ensures a good fit to the measurements.
  • Figure 3: Performance comparisons on Walnut Data. Walnut1 is the training data and the rest are testing data. Proposed-S-75 is the shared weights version of the algorithm applied on 75 views - a subsampling factor of 16 compared to the original measurements. PSNR in dB and SSIM values are reported for the zoomed patches. The proposed method with unshared weights preserves edges and details better compared to rest of the methods.
  • Figure 4: Performance comparison of the two versions of the proposed method, shared vs unshared CNN weights. Each row displays results from three iterations. Proposed-S-75-$K$itr stands for the shared weights version on 75 views at $K^{\rm th}$ iteration while Proposed is the unshared one. Proposed-S is missing details due to excessive smoothing while the edges get sharper with more iterations for unshared weights. PSNR in dB and SSIM values are reported for the zoomed patches.
  • Figure 5: Performance comparison of U-Net and the proposed method with unshared weights on out-of-distribution data as characterized by a different sparse-view measurement scenario. PSNR in dB and SSIM are reported for the zoomed patches. The results are shown on data from different sub-sampling scenario (50 views) which the networks have not been trained with. The proposed method shows significantly improved performance both visually and also in terms of performance metrics.