Low-dose CT Imaging Via Variational Regularizations

Computed tomography (CT) has been widely applied in clinical diagnosis and treatment with high temporal, spatial and contrast resolution. However, the excessive x-ray radiation exposure during clinical examinations has been reported to be linked to increased lifetime risk of cancers in patients. This fact has become a major concern for clinical application of CT scans. Therefore, it is highly desirable to reduce x-ray radiation dose while maintaining clinically acceptable image quality.To reduce the radiation dose in CT examinations, various techniques have been ex-tensively investigated, including advanced image reconstruction methods and optimal scan protocols. A simple way to reduce the x-ray dose is to lower milliampere-seconds (mAs) levels in CT data acquisition protocols. Nonetheless, this approach will result in an insufficient number of x-ray photons detected at the detector and hence elevate the quantum noise level on the sinogram. As a consequence, the quality of the CT images reconstructed from a conventional filtered backprojection (FBP) algorithm will be de-graded by the noise-contaminated sinogram data. Another way to reduce imaging dose is to decrease the number of x-ray projections acquired by operating the x-ray generator in a high-frequency pulsed model with hardware modification. Yet, this will cause se-rious streaking artifacts in the reconstructed CT images, as the filtered back-projection (FBP) algorithms require that the number of projections should satisfy the Shannon sampling theorem. As a result, the diagnostic quality of the CT images could be de-graded if inadequate methods are applied during the image reconstruction operations. To address these problems, various image processing and reconstruction methods with capability for noise suppression and recovery of missing data have been reported.To our knowledge, three classes of strategies have been widely discussed for low-dose x-ray CT imaging:1) investigate sophisticated linear and nonlinear noise filtering techniques for low-dose CT image; 2) restore the ideal line integrals sinogram data (i.e., projection after log-transformation) from acquired noisy projection data and re-construct the CT image from the estimated ideal sinogram with FBP algorithm; and 3) model the noise properties of the measurements and impose adequate regularization in statistical iterative reconstruction (SIR). Among them, the SIR methods, which take into account the statistical noise properties of the measurement and accommodate the imaging geometry, have shown great potential to reduce the quantum noise and artifacts as comparison with the FBP reconstruction method.Generally, the SIR methods can be derived from the maximum a posteriori (MAP) estimator given the observed data or measurement, which usually consist of two terms in the associative objective function. Specifically, the first term, named as the datafi-delity term, models the statistical measurement; and the second term, named as the image prior or regularization term, penalizes the solution. A major drawback of the SIR methods is the computational burden associated with the multiple re-projection and back-projection operation cycles through the image domain. However, with the de-velopment of fast computers and dedicated hardware, the modified SIR methods will be used recently in advanced CT equipments. Compressive sensing (CS) theory has now become popular, and has been instrumental for x-ray CT image reconstruction from incomplete and noisy projection. CS theory allows a sparse signal to be accurately reconstructed from samples far less than what is required by the Shannon/Nyquist sam-pling theorem. The key for the success of CS is the sparsity of a signal under study. Although an object is not sparse in general, often times a sparsifying transform can be used to convert it into a domain in which the signal has a sparse representation. One common sparsifying transform is the discrete gradient transform (DGT) whose coef-ficients can be summed up to form the so-called total variation (TV). Inspired by CS theory, various TV minimization algorithms were suggested to solve the sparse-view CT imaging problems. For example, the TV-based image reconstruction results usually suffers from the staircase and patchy artifacts due to the piecewise constant assumption.In order to mitigate abovementioned drawback in x-ray CT imaging, we did fol-lowing work in this paper:1. Statistical iterative reconstruction (SIR) for x-ray computed tomography (CT) un-der the penalized weighted least-squares criteria can yield significant gains over conventional analytical reconstruction from the noisy measurement. However, due to the multiple reprojection and back-projection operation cycles through the image domain, most exiting algorithms related to the SIR unavoidably suf-fer from heavy computation load and slow convergence rate, especially when an edge-preserving or sparsity-based penalty or regularization is incorporated. In this work, to mitigate this drawback of the general algorithms related to the SIR, we propose an adaptive nonmonotone alternating direction algorithm in the framework of augmented Lagrangian multiplier method, which is termed as "ALM-ANAD". The algorithm effectively combines an alternating direction technique with an adaptive nonmonotone line search to minimize the augmented Lagrangian function at each iteration. To evaluate the present ALM-ANAD algo-rithm, both qualitative and quantitative studies were conducted by using digital XCAT phantom and patient data. Experimental results show that the present ALM-ANAD algorithm can achieve noticeable gains over the classical nonlin-ear conjugate gradient algorithm and state-of-the-art split Bregman algorithm in terms of noise reduction, contrast-to-noise ratio, convergence rate, and universal quality index metrics.2. Sparse-view CT reconstruction algorithms via total variation (TV) optimize the data iteratively on the basis of a noise-and artifact-reducing model, resulting in significant radiation dose reduction while maintaining image quality. However, the piecewise constant assumption of TV minimization often leads to the appear-ance of noticeable patchy artifacts in reconstructed images. To obviate this draw-back, we present a penalized weighted least-squares (PWLS) scheme to retain the image quality by incorporating the new concept of total generalized variation (TGV) regularization. We refer to the proposed scheme as "PWLS-TGV" for simplicity. Specifically, TGV regularization utilizes higher order derivatives of the objective image, and the weighted least-squares term considers datadependent variance estimation, which fully contribute to improving the image quality with sparse-view projection measurement. Subsequently, an alternating optimization algorithm was adopted to minimize the associative objective function. To evalu-ate the PWLS-TGV method, both qualitative and quantitative studies were con-ducted by using digital and physical phantoms. Experimental results show that the present PWLS-TGV method can achieve images with several noticeable gains over the original TV-based method in terms of accuracy and resolution properties.3. In x-ray computed tomography (CT) image reconstruction, accurate modeling of the statistical properties of the measured data (i.e., both the transmission data and the sinogram data after linearity calibration) is essential to achieve high qual-ity diagnostic image. By current x-ray CT systems, the acquired transmission data can be described by a compound Poisson distribution upon an electronic noise background. However, such a statistical distribution is numerically in-tractable for CT image reconstruction. To obviate this drawback, in this work we develop an iterative CT image reconstruction method by alpha-divergence constrained total generalized variation (TGV) minimization. The CT image is reconstructed by minimizing the energy consisting of the TGV regularization and the alpha-divergence fidelity term posed by the x-ray projections. We re-fer to the proposed scheme as "AD-TGV". Specifically, the alpha-divergence is utilized to measure the discrepancy between the measured and estimated data in the presented AD-TGV model. The TGV regularization is proposed to eliminate the staircase and patchy artifacts which is often observed in total variation (TV) regularization. Subsequently, proximal forward-backward splitting algorithm, a popular alogorithm with theoretically justified fast convergence rate, was adopted to minimize the associative objective function. To evaluate the presented AD-TGV method, both qualitative and quantitative studies were conducted by using digital and physical phantoms. Experimental results show that the present AD-TGV method can achieve images with several noticeable gains over the TV-based method in terms of accuracy and resolution properties.4. Cerebral perfusion x-ray computed tomography (PCT) is an important functional imaging modality for evaluating cerebrovascular diseases and has been widely used in clinics over the past decades. However, due to the protocol of PCT imaging with repeated dynamic sequential scans, the associative radiation dose unavoidably increases as compared with that used in conventional CT examina-tions. Minimizing the radiation exposure in PCT examination is a major task in the CT field. In this paper, considering the rich similarity redundancy infor-mation among enhanced sequential PCT images, we propose a low-dose PCT image restoration model by incorporating the low-rank and sparse matrix charac-teristic of sequential PCT images. Specifically, the sequential PCT images were first stacked into a matrix (i.e., low-rank matrix), and then a non-convex spec-tral norm/regularization and a spatio-temporal total variation norm/regularization were then built on the low-rank matrix to describe the low rank and sparsity of the sequential PCT images, respectively. Subsequently, an improved split Breg-man method was adopted to minimize the associative objective function. Both qualitative and quantitative studies were conducted using the digital phantom and clinical cerebral PCT datasets to evaluate the present method. Experimental re-sults show that the present method can achieve images with several noticeable ad-vantages over the existing methods in terms of several evaluation metrics. More importantly, the present method can produce more accurate kinetic enhanced de-tails and diagnostic hemodynamic parameter maps than the existing methods.