Recently, deep learning(DL) methods have been proposed for the low-dose computed tomography(LdCT) enhancement, and obtain good trade-off between computational efficiency and image quality. Most of them need large number of pre-collected ground-truth high-dose sinograms with less noise, and train the network in a supervised end-to-end manner. This may bring major limitations on these methods because the number of such low-dose high-dose training sinogram pairs would affect the network's capability and sometimes the ground-truth sinograms are hard to be obtained in large scale. Since large number of low-dose ones are relatively easy to obtain, it should be critical to make these sources play roles in network training in an unsupervised learning manner. To address this issue, we propose an unsupervised DL method for LdCT enhancement that incorporates unlabeled LdCT sinograms directly into the network training. The proposed method effectively considers the structure characteristics and noise distribution in the measured LdCT sinogram, and then learns the proper gradient of the LdCT sinogram in a pure unsupervised manner. Similar to the labeled ground-truth, the gradient information in an unlabeled LdCT sinogram can be used for sufficient network training. The experiments on the patient data show effectiveness of the proposed method.
The penalized weighted least-square (PWLS) method is the representative work on the first class. One typical PWLS method was proposed by @cite_19 , who modeled accurate noise distribution and imposed a proper regularization to reduce sinogram noise. Moreover, @cite_4 proposed a method taking full use of both the statistical properties of projection data and prior structure knowledge under sinogram domain for CT denoising and reached the state-of-the-art in this kind of methods. Comparatively, MBIR methods can offer the potential to reconstruct CT image with better bias-variance performance by using prior information of CT image domain. Some works explored different prior information in recovery model, such as total variation(TV) and its variants @cite_18 @cite_24 @cite_5 , dictionary learning @cite_22 and nonlocal means @cite_13 .
@cite_18 @cite_4 @cite_22 @cite_24 @cite_19 @cite_5 @cite_13
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Statistical image reconstruction using penalized weighted least-squares (PWLS) criteria can improve image-quality in X-ray computed tomography (CT). However, the huge dynamic range of the statistical weights leads to a highly shift-variant inverse problem making it difficult to precondition and accelerate existing iterative algorithms that attack the statistical model directly. We propose to alleviate the problem by using a variable-splitting scheme that separates the shift-variant and ("nearly") invariant components of the statistical data model and also decouples the regularization term. This leads to an equivalent constrained problem that we tackle using the classical method-of-multipliers framework with alternating minimization. The specific form of our splitting yields an alternating direction method of multipliers (ADMM) algorithm with an inner-step involving a "nearly" shift-invariant linear system that is suitable for FFT-based preconditioning using cone-type filters. The proposed method can efficiently handle a variety of convex regularization criteria including smooth edge-preserving regularizers and non- smooth sparsity-promoting ones based on the l1-norm and total variation. Numerical experiments with synthetic and real in vivo human data illustrate that cone-filter preconditioners accelerate the proposed ADMM resulting in fast convergence of ADMM compared to conventional (nonlinear conjugate gradient, ordered subsets) and state-of-the-art (MFISTA, split-Bregman) algorithms that are applicable for CT. Computed tomography (CT) image recovery from low-mAs acquisitions without adequate treatment is always severely degraded due to a number of physical factors. In this paper, we formulate the low-dose CT sinogram preprocessing as a standard maximum a posteriori (MAP) estimation, which takes full consideration of the statistical properties of the two intrinsic noise sources in low-dose CT, i.e., the X-ray photon statistics and the electronic noise background. In addition, instead of using a general image prior as found in the traditional sinogram recovery models, we design a new prior formulation to more rationally encode the piecewise-linear configurations underlying a sinogram than previously used ones, like the TV prior term. As compared with the previous methods, especially the MAP-based ones, both the likelihood loss and prior regularization terms in the proposed model are ameliorated in a more accurate manner and better comply with the statistical essence of the generation mechanism of a practical sinogram. We further construct an efficient alternating direction method of multipliers algorithm to solve the proposed MAP framework. Experiments on simulated and real low-dose CT data demonstrate the superiority of the proposed method according to both visual inspection and comprehensive quantitative performance evaluation. Most of existing image denoising methods assume the corrupted noise to be additive white Gaussian noise (AWGN). However, the realistic noise in real-world noisy images is much more complex than AWGN, and is hard to be modeled by simple analytical distributions. As a result, many state-of-the-art denoising methods in literature become much less effective when applied to real-world noisy images captured by CCD or CMOS cameras. In this paper, we develop a trilateral weighted sparse coding (TWSC) scheme for robust real-world image denoising. Specifically, we introduce three weight matrices into the data and regularization terms of the sparse coding framework to characterize the statistics of realistic noise and image priors. TWSC can be reformulated as a linear equality-constrained problem and can be solved by the alternating direction method of multipliers. The existence and uniqueness of the solution and convergence of the proposed algorithm are analyzed. Extensive experiments demonstrate that the proposed TWSC scheme outperforms state-of-the-art denoising methods on removing realistic noise. Most of existing image denoising methods assume the corrupted noise to be additive white Gaussian noise (AWGN). However, the realistic noise in real-world noisy images is much more complex than AWGN, and is hard to be modelled by simple analytical distributions. As a result, many state-of-the-art denoising methods in literature become much less effective when applied to real-world noisy images captured by CCD or CMOS cameras. In this paper, we develop a trilateral weighted sparse coding (TWSC) scheme for robust real-world image denoising. Specifically, we introduce three weight matrices into the data and regularisation terms of the sparse coding framework to characterise the statistics of realistic noise and image priors. TWSC can be reformulated as a linear equality-constrained problem and can be solved by the alternating direction method of multipliers. The existence and uniqueness of the solution and convergence of the proposed algorithm are analysed. Extensive experiments demonstrate that the proposed TWSC scheme outperforms state-of-the-art denoising methods on removing realistic noise.