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


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.
    Full-text · Article · Sep 2015 · Physics in Medicine and Biology
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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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    • "Such methods are capable of reconstructing high quality images from a substantially smaller number of views than those needed in FBP [10], thereby permitting the use of a much lower dose scanning protocol than that needed in conventional reconstruction methods. However, conventional CSbased CT reconstructions are computationally expensive and the statistics of CT measurements are not usually incorporated in the problem formulation [11] [12] [13] [14] [15] [16]. "
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    ABSTRACT: In X-ray computed tomography (CT) an important objective is to reduce the radiation dose without significantly degrading the image quality. Compressed sensing (CS) enables the radiation dose to be reduced by producing diagnostic images from a limited number of projections. However, conventional CS-based algorithms are computationally intensive and time-consuming. We propose a new algorithm that accelerates the CS-based reconstruction by using a fast pseudopolar Fourier based Radon transform and rebinning the diverging fan beams to parallel beams. The reconstruction process is analyzed using a maximum-a-posterior approach, which is transformed into a weighted CS problem. The weights involved in the proposed model are calculated based on the statistical characteristics of the reconstruction process, which is formulated in terms of the measurement noise and rebinning interpolation error. Therefore, the proposed method not only accelerates the reconstruction, but also removes the rebinning and interpolation errors. Simulation results are shown for phantoms and a patient. For example, a 512 × 512 Shepp-Logan phantom when reconstructed from 128 rebinned projections using a conventional CS method had 10% error, whereas with the proposed method the reconstruction error was less than 1%. Moreover, computation times of less than 30 sec were obtained using a standard desktop computer without numerical optimization.
    Full-text · Article · May 2015 · Computational and Mathematical Methods in Medicine
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