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

Low Dose CT Image Reconstruction Based on Structure Tensor Total Variation Using Accelerated Fast Iterative Shrinkage Thresholding Algorithm

Low dose computed tomography (CT) has drawn much attention in the medical imaging field because of its ability to reduce the radiation dose. Recently, statistical iterative reconstruction (SIR) with total variation (TV) penalty has been developed to low dose CT image reconstruction. Nevertheless, the TV penalty has the drawback of creating blocky effects in the reconstructed images. To overcome the limitations of TV, in this paper we firstly introduce the structure tensor total variation (STV₁) penalty into SIR framework for low dose CT image reconstruction. Then, an accelerated fast iterative shrinkage thresholding algorithm (AFISTA) is developed to minimize the objective function. The proposed AFISTA reconstruction algorithm was evaluated using numerical simulated low dose projection based on two CT images and realistic low dose projection data of a sheep lung CT perfusion. The experimental results demonstrated that our proposed STV₁-based algorithm outperform FBP and TV-based algorithm in terms of removing noise and restraining blocky effects.

Image Regularizations Based on the Sparsity of Corner Points

Many analysis-based regularizations proposed so far employ a common prior information, i.e., edges in an image are sparse. However, in local edge regions and texture regions, this prior may not hold. As a result, the performance of regularizations based on the edge sparsity may be unsatisfactory in such regions for image-related inverse problems. These regularizations tend to smooth out the edges while eliminating the noise. In other words, these regularizations' abilities of preserving edges are limited. In this paper, a new prior that the corner points in a natural image are sparse was proposed to construct regularizations. Intuitively, even in local edge regions and texture regions, the sparsity of corner points may still exist, and hence, the regularizations based on it can achieve better performance than those based on the edge sparsity. As an example, by utilizing the sparsity of corner points, we proposed a new regularization based on Noble's corner measure function. Our experiments demonstrated the excellent performance of the proposed regularization for both image denoising and deblurring problems, especially in local edge regions and texture regions.

Structure tensor total variation for CBCT reconstruction

The total variation (TV) regularization has been widely used in statistically iterative cone-beam computed tomography (CBCT) reconstruction, showing ability to preserve object edges. However, the TV regularization can also produce staircase effect and tend to over-smooth the reconstructed images due to its piecewise constant assumption. In this study, we proposed to use the structure tensor total variation (STV) that penalizes the eigenvalues of the structure tensor for CBCT reconstruction. The STV penalty extends the TV penalty, with many important properties maintained such as convexity and rotation and translation invariance. The STV penalty utilizes gradient information more effectively and has a stronger ability to capture local image structural variation. The objective function was constructed with the penalized weighted least-square (PWLS) strategy and the gradient descent (GD) method was used to optimize the objective function. Besides, we investigated whether the norms involved in the STV penalty affected the reconstruction performance and found that the l1-norm gave the better performance than the l2-norm and l ∞-norm. We also examined performance of the STV penalties constructed using different kernel functions and found that the STV with the Gaussian kernel had the best performance, and the STVs with Uniform, Logistic, and Sigmoid kernels had similar performance to each other. We evaluated our reconstruction method with the STV penalty on computer simulated phantoms and physical phantoms. The results demonstrated that STV led to better reconstruction performance than TV, both visually and quantitatively. For the Catphan 600 physical phantom, the STV1 penalty was 175% and 623% better than the low-dose FDK and the high-dose FDK, and 14% better than the TV penalty at the matched noise level, according to the average contrast-to-noise ratio (CNR); while for the Compressed Sensing simulation phantom, the peak signal to noise ratio (PSNR) of reconstructed results using STV1, STV2, and STV ∞ were 40.67 dB, 38.72 dB, and 37.40 dB, respectively, all being significantly better than 36.84 dB using TV.

Statistical Iterative CBCT Reconstruction Based on Neural Network

Cone-beam computed tomography (CBCT) plays an important role in radiation therapy. Statistical iterative reconstruction (SIR) algorithms with specially designed penalty terms provide good performance for low-dose CBCT imaging. Among others, the total variation (TV) penalty is the current state-of-the-art in removing noises and preserving edges, but one of its well-known limitations is its staircase effect. Recently, various penalty terms with higher order differential operators were proposed to replace the TV penalty to avoid the staircase effect, at the cost of slightly blurring object edges. We developed a novel SIR algorithm using a neural network for CBCT reconstruction. We used a data-driven method to learn the "potential regularization term" rather than design a penalty term manually. This approach converts the problem of designing a penalty term in the traditional statistical iterative framework to designing and training a suitable neural network for CBCT reconstruction. We proposed using transfer learning to overcome the data deficiency problem and an iterative deblurring approach specially designed for the CBCT iterative reconstruction process during which the noise level and resolution of the reconstructed images may change. Through experiments conducted on two physical phantoms, two simulation digital phantoms, and patient data, we demonstrated the excellent performance of the proposed network-based SIR for CBCT reconstruction, both visually and quantitatively. Our proposed method can overcome the staircase effect, preserve both edges and regions with smooth intensity transition, and provide reconstruction results at high resolution and low noise level.

Low-Dose CBCT Reconstruction Using Hessian Schatten Penalties

Cone-beam computed tomography (CBCT) has been widely used in radiation therapy. For accurate patient setup and treatment target localization, it is important to obtain high-quality reconstruction images. The total variation (TV) penalty has shown the state-of-the-art performance in suppressing noise and preserving edges for statistical iterative image reconstruction, but it sometimes leads to the so-called staircase effect. In this paper, we proposed to use a new family of penalties-the Hessian Schatten (HS) penalties-for the CBCT reconstruction. Consisting of the second-order derivatives, the HS penalties are able to reflect the smooth intensity transitions of the underlying image without introducing the staircase effect. We discussed and compared the behaviors of several convex HS penalties with orders 1, 2, and for CBCT reconstruction. We used the majorization-minimization approach with a primal-dual formulation for the corresponding optimization problem. Experiments on two digital phantoms and two physical phantoms demonstrated the proposed penalty family's outstanding performance over TV in suppressing the staircase effect, and the HS penalty with order 1 had the best performance among the HS penalties tested.