Cine Cone Beam CT Reconstruction Using Low-Rank Matrix Factorization: Algorithm and a Proof-of-Principle Study

Cai, Jian-Feng; Jia, Xun; Gao, Hao; Jiang, Steve B; Shen, Zuowei; Zhao, Hongkai

doi:10.1109/tmi.2014.2319055

Cited by 126 publications

(102 citation statements)

References 38 publications

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“…A recent application of low-rank decomposition to take the advantage of lung anatomy spatial–temporal coherence has been demonstrated for 4D cone beam CT reconstruction of digital phantoms (29, 30). To the authors’ best knowledge, this is the first study in the radiation therapy context, where the lung tumor tracking is of particular interest and long duration of dynamic MR images is performed.…”

Section: Discussionmentioning

confidence: 99%

Accelerating Dynamic Magnetic Resonance Imaging (MRI) for Lung Tumor Tracking Based on Low-Rank Decomposition in the Spatial–Temporal Domain: A Feasibility Study Based on Simulation and Preliminary Prospective Undersampled MRI

Sarma

Rapacchi

et al. 2014

International Journal of Radiation Oncology*Biology*Physics

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Purpose To evaluate a low-rank decomposition method to reconstruct down-sampled k-space data for the purpose of tumor tracking. Methods and Materials Seven retrospective lung cancer patients were included in the simulation study. The fully-sampled k-space data were first generated from existing 2-dimensional dynamic MR images and then down-sampled by 5 × −20 × before reconstruction using a Cartesian undersampling mask. Two methods, a low-rank decomposition method using combined dynamic MR images (k-t SLR based on sparsity and low-rank penalties) and a total variation (TV) method using individual dynamic MR frames, were used to reconstruct images. The tumor trajectories were derived on the basis of autosegmentation of the resultant images. To further test its feasibility, k-t SLR was used to reconstruct prospective data of a healthy subject. An undersampled balanced steady-state free precession sequence with the same undersampling mask was used to acquire the imaging data. Results In the simulation study, higher imaging fidelity and low noise levels were achieved with the k-t SLR compared with TV. At 10 × undersampling, the k-t SLR method resulted in an average normalized mean square error <0.05, as opposed to 0.23 by using the TV reconstruction on individual frames. Less than 6% showed tracking errors >1 mm with 10 × down-sampling using k-t SLR, as opposed to 17% using TV. In the prospective study, k-t SLR substantially reduced reconstruction artifacts and retained anatomic details. Conclusions Magnetic resonance reconstruction using k-t SLR on highly undersampled dynamic MR imaging data results in high image quality useful for tumor tracking. The k-t SLR was superior to TV by better exploiting the intrinsic anatomic coherence of the same patient. The feasibility of k-t SLR was demonstrated by prospective imaging acquisition and reconstruction.

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Section: Discussionmentioning

confidence: 99%

Accelerating Dynamic Magnetic Resonance Imaging (MRI) for Lung Tumor Tracking Based on Low-Rank Decomposition in the Spatial–Temporal Domain: A Feasibility Study Based on Simulation and Preliminary Prospective Undersampled MRI

Sarma

Rapacchi

et al. 2014

International Journal of Radiation Oncology*Biology*Physics

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“…In the result section, we compare TICMR with FBP and the following TV based material reconstruction

Z^{*} = arg min_{Z} \frac{1}{2} {false‖ A Z B - P false‖}_{W}^{2} + λ {false| \nabla Z false|}_{1} .

normals . normalt . Z C = D, L \leq Z \leq U .

Note that in terms of the regularization in (17), the alternative strategies can be used, such as tensor framelet transform (as a natural high-order generalization of isotropic TV) [3], [11], [29]–[31], and low-rank models [7], [10], [15], [32], [33]. …”

Section: Methodsmentioning

confidence: 99%

TICMR: Total Image Constrained Material Reconstruction via Nonlocal Total Variation Regularization for Spectral CT

Liu

Ding

Molloi

et al. 2016

IEEE Trans. Med. Imaging

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This work develops a material reconstruction method for spectral CT, namely Total Image Constrained Material Reconstruction (TICMR), to maximize the utility of projection data in terms of both spectral information and high signal-to-noise ratio (SNR). This is motivated by the following fact: when viewed as a spectrally-integrated measurement, the projection data can be used to reconstruct a total image without spectral information, which however has a relatively high SNR; when viewed as a spectrally-resolved measurement, the projection data can be utilized to reconstruct the material composition, which however has a relatively low SNR. The material reconstruction synergizes material decomposition and image reconstruction, i.e., the direct reconstruction of material compositions instead of a two-step procedure that first reconstructs images and then decomposes images. For material reconstruction with high SNR, we propose TICMR with nonlocal total variation (NLTV) regularization. That is, first we reconstruct a total image using spectrally-integrated measurement without spectral binning, and build the NLTV weights from this image that characterize nonlocal image features; then the NLTV weights are incorporated into a NLTV-based iterative material reconstruction scheme using spectrally-binned projection data, so that these weights serve as a high-SNR reference to regularize material reconstruction. Note that the nonlocal property of NLTV is essential for material reconstruction, since material compositions may have significant local intensity variations although their structural information is often similar. In terms of solution algorithm, TICMR is formulated as an iterative reconstruction method with the NLTV regularization, in which the nonlocal divergence is utilized based on the adjoint relationship. The alternating direction method of multipliers is developed to solve this sparsity optimization problem. The proposed TICMR method was validated using both simulated and experimental data. In comparison with FBP and total-variation-based iterative method, TICMR had improved image quality, e.g., contrast-to-noise ratio and spatial resolution.

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“…Though it is a non-convex problem, it can perform well when the number of measurements is large [37], [38]. …”

Section: Theorymentioning

confidence: 99%

“…The nuclear norm is widely used to enforce rank minimization [35], [36]. To enforce the rank-one constraint, we adopt the method of power factorization which performs well with good initials [37], [38]. …”

Section: Introductionmentioning

confidence: 99%

Sinogram Blurring Matrix Estimation From Point Sources Measurements With Rank-One Approximation for Fully 3-D PET

Gong

Zhou

Tohme

et al. 2017

IEEE Trans. Med. Imaging

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An accurate system matrix is essential in PET for reconstructing high quality images. To reduce storage size and image reconstruction time, we factor the system matrix into a product of a geometry projection matrix and a sinogram blurring matrix. The geometric projection matrix is computed analytically and the sinogram blurring matrix is estimated from point source measurements. Previously we have estimated a two dimensional (2D) blurring matrix for a preclinical PET scanner. The 2D blurring matrix only considers blurring effects within a transaxial sinogram and does not compensate for inter-sinogram blurring effects. For PET scanners with a long axial field of view (FOV), inter-sinogram blurring can be a major problem influencing the image quality in the axial direction. Hence estimation of a four dimensional (4D) blurring matrix is desirable to further improve the image quality. Four dimensional blurring matrix estimation is an ill-conditioned problem due to the large number of unknowns. Here we propose a rank-one approximation for each blurring kernel image formed by a row vector of the sinogram blurring matrix to improve the stability of the 4D blurring matrix estimation. The proposed method is applied to simulated data as well as real data obtained from an Inveon microPET scanner. The results show that the newly estimated 4D blurring matrix can improve the image quality over those obtained with a 2D blurring matrix and requires less point source scans to achieve similar image quality compared with an unconstrained 4D blurring matrix estimation.

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Cine Cone Beam CT Reconstruction Using Low-Rank Matrix Factorization: Algorithm and a Proof-of-Principle Study

Cited by 126 publications

References 38 publications

Accelerating Dynamic Magnetic Resonance Imaging (MRI) for Lung Tumor Tracking Based on Low-Rank Decomposition in the Spatial–Temporal Domain: A Feasibility Study Based on Simulation and Preliminary Prospective Undersampled MRI

Accelerating Dynamic Magnetic Resonance Imaging (MRI) for Lung Tumor Tracking Based on Low-Rank Decomposition in the Spatial–Temporal Domain: A Feasibility Study Based on Simulation and Preliminary Prospective Undersampled MRI

TICMR: Total Image Constrained Material Reconstruction via Nonlocal Total Variation Regularization for Spectral CT

Sinogram Blurring Matrix Estimation From Point Sources Measurements With Rank-One Approximation for Fully 3-D PET

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