Compressed sensing based cone-beam computed tomography reconstruction with a first-order method

Department of Electrical Engineering, Stanford University, Stanford, California 94305, USA.
Medical Physics (Impact Factor: 2.64). 09/2010; 37(9):5113-25. DOI: 10.1118/1.3481510
Source: PubMed

ABSTRACT This article considers the problem of reconstructing cone-beam computed tomography (CBCT) images from a set of undersampled and potentially noisy projection measurements.
The authors cast the reconstruction as a compressed sensing problem based on l1 norm minimization constrained by statistically weighted least-squares of CBCT projection data. For accurate modeling, the noise characteristics of the CBCT projection data are used to determine the relative importance of each projection measurement. To solve the compressed sensing problem, the authors employ a method minimizing total-variation norm, satisfying a prespecified level of measurement consistency using a first-order method developed by Nesterov.
The method converges fast to the optimal solution without excessive memory requirement, thanks to the method of iterative forward and back-projections. The performance of the proposed algorithm is demonstrated through a series of digital and experimental phantom studies. It is found a that high quality CBCT image can be reconstructed from undersampled and potentially noisy projection data by using the proposed method. Both sparse sampling and decreasing x-ray tube current (i.e., noisy projection data) lead to the reduction of radiation dose in CBCT imaging.
It is demonstrated that compressed sensing outperforms the traditional algorithm when dealing with sparse, and potentially noisy, CBCT projection views.

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Available from: Lei Zhu, Aug 22, 2014
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    • "60 (2015) 7437 2006, Sidky and Pan 2008, Sidky et al 2010). Total variation (TV) or l 1 –regularization is an established method for recovery of signals that are sparse in their gradient (Choi et al 2010). These algorithms may also further reduce aliasing artifacts due to under-sampled sinograms (Ramani and Fessler 2012, Sidky et al 2012, Long et al 2013). "
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    ABSTRACT: For PET/CT systems, PET image reconstruction requires corresponding CT images for anatomical localization and attenuation correction. In the case of PET respiratory gating, multiple gated CT scans can offer phase-matched attenuation and motion correction, at the expense of increased radiation dose. We aim to minimize the dose of the CT scan, while preserving adequate image quality for the purpose of PET attenuation correction by introducing sparse view CT data acquisition.We investigated sparse view CT acquisition protocols resulting in ultra-low dose CT scans designed for PET attenuation correction. We analyzed the tradeoffs between the number of views and the integrated tube current per view for a given dose using CT and PET simulations of a 3D NCAT phantom with lesions inserted into liver and lung. We simulated seven CT acquisition protocols with {984, 328, 123, 41, 24, 12, 8} views per rotation at a gantry speed of 0.35 s. One standard dose and four ultra-low dose levels, namely, 0.35 mAs, 0.175 mAs, 0.0875 mAs, and 0.043 75 mAs, were investigated. Both the analytical Feldkamp, Davis and Kress (FDK) algorithm and the Model Based Iterative Reconstruction (MBIR) algorithm were used for CT image reconstruction. We also evaluated the impact of sinogram interpolation to estimate the missing projection measurements due to sparse view data acquisition. For MBIR, we used a penalized weighted least squares (PWLS) cost function with an approximate total-variation (TV) regularizing penalty function. We compared a tube pulsing mode and a continuous exposure mode for sparse view data acquisition. Global PET ensemble root-mean-squares-error (RMSE) and local ensemble lesion activity error were used as quantitative evaluation metrics for PET image quality.With sparse view sampling, it is possible to greatly reduce the CT scan dose when it is primarily used for PET attenuation correction with little or no measureable effect on the PET image. For the four ultra-low dose levels simulated, sparse view protocols with 41 and 24 views best balanced the tradeoff between electronic noise and aliasing artifacts. In terms of lesion activity error and ensemble RMSE of the PET images, these two protocols, when combined with MBIR, are able to provide results that are comparable to the baseline full dose CT scan. View interpolation significantly improves the performance of FDK reconstruction but was not necessary for MBIR. With the more technically feasible continuous exposure data acquisition, the CT images show an increase in azimuthal blur compared to tube pulsing. However, this blurring generally does not have a measureable impact on PET reconstructed images.Our simulations demonstrated that ultra-low-dose CT-based attenuation correction can be achieved at dose levels on the order of 0.044 mAs with little impact on PET image quality. Highly sparse 41- or 24- view ultra-low dose CT scans are feasible for PET attenuation correction, providing the best tradeoff between electronic noise and view aliasing artifacts. The continuous exposure acquisition mode could potentially be implemented in current commercially available scanners, thus enabling sparse view data acquisition without requiring x-ray tubes capable of operating in a pulsing mode.
    Physics in Medicine and Biology 09/2015; 60(19):7437-7460. DOI:10.1088/0031-9155/60/19/7437 · 2.76 Impact Factor
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    • "In recent years, there have been tremendous developments in CT image reconstruction algorithms in terms of both analytical reconstruction (AR) methods and iterative reconstruction (IR) methods, particularly sparsity-regularized model-based IR methods [12] [13] inspired by compressive sensing [14] [15] for a wide range of CT problems [16] [17] [18] [19] [20] [21] [22] [23]. For the purpose of synergizing AR and IR, we investigated a filtration-weighted formulation of data fidelity with sparsity regularization in the setting of 2D fan-beam CT and developed the image reconstruction algorithm based on alternating direction method of multipliers (ADMM) [24] or split Bregman method [25], i.e., so-called fused analytical and iterative reconstruction (AIR) [26] [27]. "
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    ABSTRACT: This work is to develop a general framework, namely filtered iterative reconstruction (FIR) method, to incorporate analytical reconstruction (AR) method into iterative reconstruction (IR) method, for enhanced CT image quality. Specifically, FIR is formulated as a combination of filtered data fidelity and sparsity regularization, and then solved by proximal forward-backward splitting (PFBS) algorithm. As a result, the image reconstruction decouples data fidelity and image regularization with a two-step iterative scheme, during which an AR-projection step updates the filtered data fidelity term, while a denoising solver updates the sparsity regularization term. During the AR-projection step, the image is projected to the data domain to form the data residual, and then reconstructed by certain AR to a residual image which is in turn weighted together with previous image iterate to form next image iterate. Since the eigenvalues of AR-projection operator are close to the unity, PFBS based FIR has a fast convergence. The proposed FIR method is validated in the setting of circular cone-beam CT with AR being FDK and total-variation sparsity regularization, and has improved image quality from both AR and IR. For example, AIR has improved visual assessment and quantitative measurement in terms of both contrast and resolution, and reduced axial and half-fan artifacts.
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    • "For these reasons, much research has been conducted focusing on developing novel CBCT reconstruction algorithms to retrieve high quality CBCT images based on projection data acquired at a low exposure level (mAs per projection) and/or reduced number of projections. Regularization methods have been utilized to maintain image quality and suppress artifacts, such as total variation and its variants (Sidky et al 2006, Song et al 2007, Sidky and Pan 2008, Tang et al 2009, Bian et al 2010, Jia et al 2010, Choi et al 2010, Defrise et al 2011, Ritschl et al 2011, Tian et al 2011), tight frame (Jia et al 2011, Yan et al 2012), soft-thresholding (Yu and Wang 2009, 2010), dictionary-based methods (Xu et al 2012, Lu et al 2012), and prior image-based methods (Chen et al 2008a, Lee et al 2012, Yan et al 2013). Although these novel approaches have demonstrated a great potential to substantially reduce radiation doses to patients, technical difficulties, such as high computational burdens, still prevent them from clinical practice. "
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    ABSTRACT: With the aim of maximally reducing imaging dose while meeting requirements for adaptive radiation therapy (ART), we propose in this paper a new cone beam CT (CBCT) acquisition and reconstruction method that delivers images with a low noise level inside a region of interest (ROI) and a relatively high noise level outside the ROI. The acquired projection images include two groups: densely sampled projections at a low exposure with a large field of view (FOV) and sparsely sampled projections at a high exposure with a small FOV corresponding to the ROI. A new algorithm combining the conventional filtered back-projection algorithm and the tight-frame iterative reconstruction algorithm is also designed to reconstruct the CBCT based on these projection data. We have validated our method on a simulated head-and-neck (HN) patient case, a semi-real experiment conducted on a HN cancer patient under a full-fan scan mode, as well as a Catphan phantom under a half-fan scan mode. Relative root-mean-square errors (RRMSEs) of less than 3% for the entire image and ~1% within the ROI compared to the ground truth have been observed. These numbers demonstrate the ability of our proposed method to reconstruct high-quality images inside the ROI. As for the part outside ROI, although the images are relatively noisy, it can still provide sufficient information for radiation dose calculations in ART. Dose distributions calculated on our CBCT image and on a standard CBCT image are in agreement, with a mean relative difference of 0.082% inside the ROI and 0.038% outside the ROI. Compared with the standard clinical CBCT scheme, an imaging dose reduction of approximately 3-6 times inside the ROI was achieved, as well as an 8 times outside the ROI. Regarding computational efficiency, it takes 1-3 min to reconstruct a CBCT image depending on the number of projections used. These results indicate that the proposed method has the potential for application in ART.
    Physics in Medicine and Biology 10/2014; 59(20):6251-66. DOI:10.1088/0031-9155/59/20/6251 · 2.76 Impact Factor
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