Application of Implicit Regularization Learning Network Based on Noise Generation and Imaging Mechanisms in Low-Dose CT Reconstruction

Low-Dose Computed Tomography (LDCT) has become an important tool in modern medical imaging, aiming to reduce radiation risks while maintaining image quality. However, reducing the X-ray dose often leads to data corruption and poor back-projection (FBP) reconstruction, thereby affecting image quality. Researchers have been continuously developing advanced algorithms to obtain high-quality images while reducing noise and artifacts. This report will detail a new research achievement aimed at achieving high-performance LDCT reconstruction.

Background Introduction

In X-ray CT imaging, reducing radiation dose has always been an objective, achieved by lowering X-ray tube current and/or voltage, sparse view, and limiting angle scans. However, these imaging protocols may lead to data corruption and unstable reconstruction, resulting in poor image quality when using classical FBP algorithms. As such, developing new high-quality reconstruction algorithms, especially for LDCT, is an urgent need.

Traditional methods can be divided into three categories: projection-based correction methods, image-based recovery methods, and iterative reconstruction algorithms. Projection-based correction methods combine the statistical characteristics of measured noise and prior knowledge to denoise, and then use FBP to reconstruct the projection data obtained. Image-based recovery methods utilize prior information in the image domain to handle artifacts and noise in the reconstructed image. Iterative reconstruction algorithms combine statistical characteristics of measured noise and prior information of CT images to construct an objective function, and high-quality CT images are obtained through optimization iterations. However, selecting appropriate regularization and hyperparameters is challenging, and iterative algorithms are often computationally expensive due to repeated forward and backward projections, which limits their clinical application.

In recent years, CT reconstruction technology has increasingly focused on deep learning (DL) methods, especially data-driven and model-driven deep learning strategies. These strategies learn a nonlinear mapping from noisy measurements or images to target images using paired training data. Despite encouraging results in terms of computational cost and application, the output may lack data consistency and require large amounts of clinical training data.

Research Origin

This research, titled “Noise-Generating and Imaging Mechanism Inspired Implicit Regularization Learning Network for Low Dose CT Reconstruction,” is published in the IEEE Transactions on Medical Imaging, Volume 43, Issue 5, in May 2024. The authors include Xing Li, Kaili Jing, Yan Yang, Yongbo Wang, Jianhua Ma, Hairong Zheng, and Zongben Xu, from institutions including Xi’an Jiaotong University, University of Ottawa, Southern Medical University, Shenzhen Institutes of Advanced Technology, and other research institutes.

Research Method

This paper proposes a new LDCT reconstruction model based on global noise generation and imaging mechanisms, taking into account the statistical properties of inherent LDCT noise and prior information in both the image and sinogram domains. The model is solved using an optimization algorithm based on proximal gradient techniques, with the following specific steps:

Model Construction

1. Defining the Generation Model:

   • Projection data ( s ) usually contains noise; we set the generation model as: [ s = t + \epsilon ]
   • Where ( t ) represents the ray quantum detected, following a Poisson distribution; ( \epsilon ) is electronic noise, following a Gaussian distribution.

2. Transforming the Optimization Problem:

   • According to the Maximum A Posteriori (MAP) estimation theory, we find the noise-free clean projection data ( y ). Then add the data fidelity constraint of the reconstructed CT image ( x ) and sufficient regularization in the sinogram and image domains, the optimization problem is formalized as: [ \min{t,y,x} \sum{i=1}^n \left((s_i - t_i )^2 / 2\sigma^2 - t_i \ln I_0 + t_i y_i + \ln t_i ! + I_0 e^{-y_i}\right) + \lambda_1 g_1(y) + \lambda_2 g_2(x) + |Ax - y|_2^2 / 2 ]

Model Optimization

Alternate updates of data in the projection domain, sinogram domain, and image domain are employed, with specific steps as follows:

1. Updating Projection Data ( t ):

   • Solve the problem with compound Poisson distribution parameters, using Newton’s method to update projection data through continuous variable relaxation.

2. Updating Sinogram Data ( y ):

   • According to the approximate second-order derivative to minimize the objective function, calculate the update formula for ( y ): [ y^{(n)} = \textrm{prox}_{\lambda_1 \eta_2}(y^{(n-1)} - \eta_2 \nabla f(y^{(n-1)})) ]

3. Updating CT Image ( x ):

   • Similarly, using the second-order derivative to minimize the objective function, calculate the update formula for ( x ): [ x^{(n)} = \textrm{prox}_{\lambda_2 \eta_3}(x^{(n-1)} - \eta_3 \nabla f(x^{(n-1)})) ]

Network Structure

We extended the algorithm into a deep network by unfolding each iteration step, constructing a network architecture called NGIM-IRL. This network includes the following three modules:

1. T-Net: Solves the sub-problem of updating projection data.
2. Y-Net: Solves the problem of sinogram data recovery.
3. X-Net: Solves the problem of CT image recovery.

This network structure implicitly learns the corresponding regularization operators in the sinogram and image domains through two deep neural networks, enhancing the interpretability and effectiveness of the reconstruction process.

Research Results

This method demonstrates superior performance on multiple datasets.

Data Sets and Experimental Setup

Experiments were conducted using the Whole-body CT Scan Images dataset from Mayo Clinic and the Lodopab-CT dataset, simulating low-dose images at various degradation levels.

Experimental Results

Experimental results under different dose levels show that, compared to traditional and other deep learning-based methods, NGIM-IRL performs excellently in terms of Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index (SSIM), and Root Mean Squared Error (RMSE). Specific performance details are as follows:

1. Low-Dose CT Grand Challenge Dataset: At three dose levels, this method consistently exhibited the best image quality and lowest artifact levels.
2. Lodopab-CT Dataset: The method significantly outperformed other comparison methods in quantitative metrics, demonstrating its good adaptability and robustness in LDCT reconstruction tasks.

Network Training and Execution Efficiency

Compared to other iterative deep learning methods, NGIM-IRL has a shorter training time and faster execution time, which is particularly important in clinical applications.

Research Significance

1. Scientific Significance: This research proposes a new model based on noise generation and imaging mechanisms, improving the theory and practice of LDCT reconstruction, bridging the gap between traditional methods and purely machine learning-based methods.
2. Application Value: The method shows significant advantages in reducing computational costs and improving image quality, with important clinical application potential.

The NGIM-IRL method proposed in this paper not only surpasses existing methods in multiple quantitative metrics but also demonstrates significant advantages in actual image quality and execution efficiency, providing a new solution and research direction for the field of LDCT reconstruction. Going forward, the research team will continue to explore the possibility of extending this method to photon-counting CT and spectral CT to further enhance its clinical application value.