Iterative CBCT reconstruction using Hessian penalty

Sun, Tao; Sun, Nanbo; Wang, Jing; Tan, Shan

doi:10.1088/0031-9155/60/5/1965

Cited by 39 publications

(43 citation statements)

References 41 publications

(59 reference statements)

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“…These TV reconstruction images were degraded by the piecewise constant regions and lost their original structures. The Hessian penalty suppresses the staircase effect by introducing the secondorder derivative into the CBCT reconstruction process [21]. However, the Hessian penalty cannot properly preserve the edge of the line-style and the annular objects of the CS phantom ( Fig.…”

Section: Discussionmentioning

confidence: 99%

“…Although the TV penalty in CBCT reconstruction presents advantages in noise suppression and edge preservation [31], it may also lead to the staircase effect. We extended the first-order derivative to a second-order derivative and defined the Hessian penalty in our previous study for CBCT reconstruction [21].…”

Section: Adaptive Structure Reconstructionmentioning

confidence: 99%

“…The Hessian penalty successfully suppresses the staircase effect in CBCT reconstruction, but also reduces image resolution and blurs object edges [21]. In contrast, the TV penalty successfully preserves those edges.…”

Section: Adaptive Structure Reconstructionmentioning

confidence: 99%

“…In a previous study [21], we adopted the Hessian penalty to reduce the staircase effect in PWLS iterative CBCT reconstruction. Unlike TV, Hessian is a second-order penalty [19], which allows for linear smooth intensity transition between neighboring pixels.…”

Section: Introductionmentioning

confidence: 99%

“…The Hessian penalty has a number of favorable properties including convexity, homogeneity, and rotation and translation invariance. It can also suppress the staircase effect of the TV penalty for PWLS CBCT reconstruction [21]. However, like most higher-order penalties, Hessian tends to slightly blur the edges of the reconstructed image.…”

Section: Introductionmentioning

confidence: 99%

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Structure-adaptive CBCT reconstruction using weighted total variation and Hessian penalties

Shi¹,

Sun²,

Sun³

et al. 2016

Biomed. Opt. Express

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Abstract:The exposure of normal tissues to high radiation during cone-beam CT (CBCT) imaging increases the risk of cancer and genetic defects. Statistical iterative algorithms with the total variation (TV) penalty have been widely used for low dose CBCT reconstruction, with state-of-the-art performance in suppressing noise and preserving edges. However, TV is a first-order penalty and sometimes leads to the so-called staircase effect, particularly over regions with smooth intensity transition in the reconstruction images. A second-order penalty known as the Hessian penalty was recently used to replace TV to suppress the staircase effect in CBCT reconstruction at the cost of slightly blurring object edges. In this study, we proposed a new penalty, the TV-H, which combines TV and Hessian penalties for CBCT reconstruction in a structure-adaptive way. The TV-H penalty automatically differentiates the edges, gradual transition and uniform local regions within an image using the voxel gradient, and adaptively weights TV and Hessian according to the local image structures in the reconstruction process. Our proposed penalty retains the benefits of TV, including noise suppression and edge preservation. It also maintains the structures in regions with gradual intensity transition more successfully. A majorization-minimization (MM) approach was designed to optimize the objective energy function constructed with the TV-H penalty. The MM approach employed a quadratic upper bound of the original objective function, and the original optimization problem was changed to a series of quadratic optimization problems, which could be efficiently solved using the Gauss-Seidel update strategy. We tested the reconstruction algorithm on two simulated digital phantoms and two physical phantoms. Our experiments indicated that the TV-H penalty visually and quantitatively outperformed both TV and Hessian penalties.

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Section: Discussionmentioning

confidence: 99%

Section: Adaptive Structure Reconstructionmentioning

confidence: 99%

Section: Adaptive Structure Reconstructionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Structure-adaptive CBCT reconstruction using weighted total variation and Hessian penalties

Shi¹,

Sun²,

Sun³

et al. 2016

Biomed. Opt. Express

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Regularization strategies in statistical image reconstruction of low‐dose x‐ray CT: A review

et al. 2018

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Statistical image reconstruction (SIR) methods have shown potential to substantially improve the image quality of low-dose x-ray computed tomography (CT) as compared to the conventional filtered back-projection (FBP) method. According to the maximum a posteriori (MAP) estimation, the SIR methods are typically formulated by an objective function consisting of two terms: (a) a data-fidelity term that models imaging geometry and physical detection processes in projection data acquisition, and (b) a regularization term that reflects prior knowledge or expectations of the characteristics of the to-be-reconstructed image. SIR desires accurate system modeling of data acquisition, while the regularization term also has a strong influence on the quality of reconstructed images. A variety of regularization strategies have been proposed for SIR in the past decades, based on different assumptions, models, and prior knowledge. In this paper, we review the conceptual and mathematical bases of these regularization strategies and briefly illustrate their efficacies in SIR of low-dose CT.

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Learning low‐dose CT degradation from unpaired data with flow‐based model

Liang

Deng

et al. 2022

Medical Physics

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Background There has been growing interest in low‐dose computed tomography (LDCT) for reducing the X‐ray radiation to patients. However, LDCT always suffers from complex noise in reconstructed images. Although deep learning‐based methods have shown their strong performance in LDCT denoising, most of them require a large number of paired training data of normal‐dose CT (NDCT) images and LDCT images, which are hard to acquire in the clinic. Lack of paired training data significantly undermines the practicability of supervised deep learning‐based methods. To alleviate this problem, unsupervised or weakly supervised deep learning‐based methods are required. Purpose We aimed to propose a method that achieves LDCT denoising without training pairs. Specifically, we first trained a neural network in a weakly supervised manner to simulate LDCT images from NDCT images. Then, simulated training pairs could be used for supervised deep denoising networks. Methods We proposed a weakly supervised method to learn the degradation of LDCT from unpaired LDCT and NDCT images. Concretely, LDCT and normal‐dose images were fed into one shared flow‐based model and projected to the latent space. Then, the degradation between low‐dose and normal‐dose images was modeled in the latent space. Finally, the model was trained by minimizing the negative log‐likelihood loss with no requirement of paired training data. After training, an NDCT image can be input to the trained flow‐based model to generate the corresponding LDCT image. The simulated image pairs of NDCT and LDCT can be further used to train supervised denoising neural networks for test. Results Our method achieved much better performance on LDCT image simulation compared with the most widely used image‐to‐image translation method, CycleGAN, according to the radial noise power spectrum. The simulated image pairs could be used for any supervised LDCT denoising neural networks. We validated the effectiveness of our generated image pairs on a classic convolutional neural network, REDCNN, and a novel transformer‐based model, TransCT. Our method achieved mean peak signal‐to‐noise ratio (PSNR) of 24.43dB, mean structural similarity (SSIM) of 0.785 on an abdomen CT dataset, mean PSNR of 33.88dB, mean SSIM of 0.797 on a chest CT dataset, which outperformed several traditional CT denoising methods, the same network trained by CycleGAN‐generated data, and a novel transfer learning method. Besides, our method was on par with the supervised networks in terms of visual effects. Conclusion We proposed a flow‐based method to learn LDCT degradation from only unpaired training data. It achieved impressive performance on LDCT synthesis. Next, we could train neural networks with the generated paired data for LDCT denoising. The denoising results are better than traditional and weakly supervised methods, comparable to supervised deep learning methods.

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Iterative CBCT reconstruction using Hessian penalty

Cited by 39 publications

References 41 publications

Structure-adaptive CBCT reconstruction using weighted total variation and Hessian penalties

Structure-adaptive CBCT reconstruction using weighted total variation and Hessian penalties

Regularization strategies in statistical image reconstruction of low‐dose x‐ray CT: A review

Learning low‐dose CT degradation from unpaired data with flow‐based model

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