Low-dose computed tomography reconstruction regularized by structural group sparsity joined with gradient prior

Highlights

• The proposed reconstruction model is designed mainly for low-dose X-ray computed tomography without the aid of previously scanned CT image database.

• The proposed reconstruction can avoid the drawback of gradient prior based method in image domain.

• Both structural group sparsity and gradient prior sparsity are jointed as a novel regularization for low-dose X-ray computed tomography.

• The proposed reconstruction model is solved following alternating direction method of multipliers (ADMM) framework.

• The performance of the proposed method is superior than gradient prior based method and the existing iterative reconstruction methods in terms of preserving the edge structure and suppressing the noise and artifacts.

Abstract

Low-dose computed tomography (LdCT) imaging can greatly reduce the radiation dose imposed to patient, however it leads to the low signal-to-noise ratio (SNR) measured projection data. Using conventional analytical reconstruction method (e.g., filtered back-projection method), the reconstruction results usually suffer from serious noise in LdCT. To obtain high-quality CT images, iterative reconstruction method combined with prior knowledge of the object is of great importance. In this work, both structural group sparsity and gradient prior sparsity are jointed as a novel regularization constraint in the proposed CT reconstruction model. To solve the optimization-based CT reconstruction problem, original problem was transformed into a series of sub-problems based on alternating direction method of multipliers framework. The merit of the proposed joint regularization method is that global and local sparsity are both utilized. To valid the performance of proposed reconstruction algorithm, we did simulated experiments with different noise levels and real data studies. The qualitative and quantitative analyses show that the proposed reconstruction algorithm has better performance than other iterative reconstruction algorithms. What's more, compared to the existing iterative reconstruction methods, the proposed reconstruction algorithm can well reconstructed important structure features and effectively suppress the noise and artifacts.

Introduction

Nowadays, X-ray computed tomography (CT) has been widely used as one of the best effective imaging diagnosis tools. Since excessive radiation dose delivered to patient might induce high risk of cancer and gene mutation [1,2], the reduction of radiation dose has arisen worldwide concerns. Therefore, the investigation of low-dose computed tomography (LdCT) imaging technique is active in medical field.

To reduce the radiation dose, there are many approaches which can be mainly divided into two categories: one is to change the scanning protocol by lowering the tube voltage and/or tube current [3,4], the other is to down-sample the measured data for CT reconstruction (such as interior CT [5], [6], [7], limited-angle CT [8], [9], [10], [11], [12] and sparse-view CT [13], [14], [15], [16]). However, the radiation dose reduction using the first category will make the measured CT data contaminated by serious noise. The quality of CT image reconstructed by standard filtered back-projection (FBP) method [17] is seriously degraded by the noise-contaminated CT data. As for the second category to reduce the radiation dose, the measured CT data will be truncated for CT reconstruction, which will lead to ill-posed inverse problem. Especially when the measured CT data is incomplete for CT reconstruction, the reconstruction images by FBP method will present terrible stripe artifacts with serious noise and/or limited-angle artifacts. Thus, to maintain clinically acceptable image quality for LdCT is desirable in practical applications. Some existing works have shown that when the radiation dose is significant reduced as in LdCT, iterative reconstruction techniques can provide similar image quality compared with the reconstruction by FBP with normal dose [18], [19], [20], [21], [22].

In this work, we will focus the first category for LdCT. To deal with the problems mentioned above, many scholars have made great efforts in this field. As analytic reconstruction methods (such as FBP) present poor performance for LdCT imaging, classical iterative reconstruction (IR) methods (such as Algebraic Reconstruction Technique [23], ART and Simultaneous Algebraic Reconstruction Technique [24], SART) combined with prior regularization constraint proved to be effective. Total variation (TV) [25] known as one of the famous prior regularization constraints has been widely used for CT reconstruction with under-sampled projection data [9,26]. Since the limitation of TV regularization lies in the assumption that the reconstruction image is piecewise constant [25], the reconstructed image by TV may loss some tiny details and texture features. Therefore, to improve the image quality, its variants for LdCT have been proposed [27], [28], [29], [30], [31], [32], [33], [34]. Tian etal [27] designed an edge-preserving TV norm as regularization term which is prefer to smoothing the non-edge part of the object and giving low weight to penalize the pixels at the edges. Liu etal [28] designed a local image-intensity gradient dependent weight for TV minimization which considers the anisotropic edge property among neighboring image voxels. Yang etal [29] generalized the piecewise constant assumption of TV minimization to piecewise polynomial, and then introduced high-order TV minimization for interior problem. Ritschl etal [30] proposed an improved method to optimize the parameter adaption within the framework of [26]. This improvement makes their algorithm converge to the lowest possible value of object function and meanwhile hold a low value of the sparsity constraint. As the good performance of total generalized variation (TGV) [31] regularization which utilizes higher order derivatives of the image to be reconstructed, Niu etal [32] presented a penalized weighted least-squares (PWLS) scheme based on TGV and showed the superiority of their method in accuracy and resolution properties. Analogously, to penalize the higher-order derivatives of the image to be reconstructed, Zeng etal [33,34] utilized structure tensor total variation (STV) regularization to eliminate the patchy artifacts usually appeared in TV regularization for multienergy CT and Cerebral perfusion CT. Niu etal [35] considered the low-rank and sparse matrix characteristic of a series of enhanced sequential perfusion X-ray CT images, and then proposed a low-dose PCT image restoration model to reduce the radiation exposure. Since the measured projection data is degraded with serious noise, some sinogram filtering methods are feasible to estimate noise-free sinogram for CT reconstruction [36], [37], [38]. Zhang etal [38] proposed a low-dose CT scheme which includes removing isolated data in sinogram domain and exploited segmentation-based adaptive filtering technique. Lee etal [39] demonstrated that sinogram-affirmed iterative reconstruction enables ultra-low-dose CT with very low radiation doses. Wang etal [40] analyzed the noise property of CT sinogram data in Radon space with different mAs levels which is helpful to improve CT image quality for screening applications. Some other scholars considered incorporating non-local means image filtering [41,42]. Ma etal [41] maked full use of the redundancy information from previous normal-dose scan by which the non-local weights are calculated. Instead of replacing previous normal-dose scan, Bian etal [42] used the FBP image reconstructed from the sinogram restored by PWLS algorithm in the Karhunen-Loéve domain. The presented algorithm makes full use of the advantages of the restored sinogram and non-local means image filtering algorithm and shows superiority in terms of noise reduction and image resolution. Considering both the X-ray photon statistics and the electronic noise background, Xie etal [43] formulated a robust sinogram preprocessing based on noise-generating mechanism. In order to evaluate the effect on the radiation exposure and image quality, Cianci etal [44] adopted a scheme which combined automatic tube current modulation and sinogram-affirmed iterative reconstruction technique in ultra-low dose CT colonography. Compared with low-dose CT colonography, their works showed that the radiation dose in ultra-low dose CT colonography can be reduced up to 63% and there is no relevant image quality deterioration. Considering the similarity of spectral CT images, a reconstruction method combined image gradient l₀-norm constraint and tensor dictionary learning (TDL) for spectral CT was proposed [45], whose method emphasizes the spatial sparsity which can overcome the drawback of TDL on edge preserving. Considering the good property of relative total variation (RTV), Gong etal [46] proposed RTV-based method for CT reconstruction, the structural information of the target very well, however, details are easy to be lost. With the aid of previous high-dose reconstructions of the same object, templates technology can also play an important role in CT reconstruction, which can compensate for the low-dose artefacts [47].

In recent years, machine learning technology has been extensively studied. As an important branch of machine learning, deep learning (DL) [48] technique especially convolutional neural network (CNN) based method demonstrates superior performance in the field of image processing such as image classification, image detection, image segmentation and image restoration. Due to the good performance of DL-based method in these areas, some scholars have extended it to medical imaging domain such as LdCT for high precision CT reconstruction [49], [50], [51], [52], [53], [54], [55]. The success of these DL-based method for LdCT benefits from a large number of data training samples which is significantly important for deep learning. It is well known that DL-based methods usually require high computational power and storage capacity which depend on computer hardware devices, such as Graphics Processing Unit (GPU) etc. However, this requires the upgrading of existing computer hardware which would require additional funding. Due to the inconsistent storage standards of most CT manufacturers’ original CT data and the confidentiality of patients’ CT data, it is difficult to meet the training sample size required for DL-based CT reconstruction methods, which limits the promotion of DL technology. In addition, DL-based methods are sensitive to hyperparameters which need a long time (usually measured in hours or days) to be chosen.

Since iterative reconstruction method is more flexible and advantageous than analytic method, in this paper, we will study iterative reconstruction algorithm for LdCT without the help of huge CT image database. As discussed above, although the gradient-based sparsity in image domain denoted as TV is one of the popular prior information for CT reconstruction, there is some shortcomings presented in TV-based results. In this study, inspired with the structural group sparse representation (SGSR) proposed for natural image restoration [56], we present a hybrid regularization constraint for LdCT reconstruction problem. The presented CT reconstruction method can overcome the shortcomings of TV-based reconstruction method since both the structural group sparsity and gradient sparsity (SGSaGS) are simultaneously enforced as the regularization constraint in image domain. To effectively solve the proposed unconstrained optimization problem, we utilize the alternating direction method of multipliers (ADMM) and then transformed the original optimization problem into a series of sub-problems. Both the simulated phantom study and real CT data study performed to qualitatively and quantitatively evaluate the proposed LdCT reconstruction. The results show that the proposed algorithm has the potential to spectral computed tomography.

The remainder of this paper is organized as follows. In Section 2, the CT imaging model, gradient sparsity-based CT reconstruction model and brief review of structural group sparse (SGS) representation modeling are respectively presented, and then the proposed CT reconstruction model is described in detail. In Section 3, our experimental results of LdCT image reconstruction are provided. Finally, discussion and conclusion are given in Section 4.