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: 3.01). 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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    • "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 · 2.92 Impact Factor
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    • "We review here only sparsity-promoting and wavelet-based approaches. Total variation regularization has been used in [17] [57] [43] [61] [62] [44] [49] [63] [28] [65] [19] [5] [4] [33] [30] [67], level set methods in [76] [21] [58] [42] [75] [40], various sparsity-promoting methods in [9] [8] [77] [78] [12] [32] [46], and multiresolution-sparsity methods in [59] [54] [64] [73] [39] [23]. "
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    ABSTRACT: A wavelet-based sparsity-promoting reconstruction method is studied in the context of tomography with severely limited projection data. Such imaging problems are ill-posed inverse problems, or very sensitive to measurement and modeling errors. The reconstruction method is based on minimizing a sum of a data discrepancy term based on an 2 -norm and another term containing an 1 -norm of a wavelet coefficient vector. Depending on the viewpoint, the method can be considered (i) as finding the Bayesian maximum a posteriori (MAP) estimate using a Besov-space B 1 11 (T 2) prior, or (ii) as deterministic regularization with a Besov-norm penalty. The minimization is performed using a tailored primal-dual path following interior-point method, which is applicable to problems larger in scale than commercially available general-purpose optimization package algorithms. The choice of "regularization parameter" is done by a novel technique called the S-curve method, which can be used to incorporate a priori information on the sparsity of the unknown target to the recon-struction process. Numerical results are presented, focusing on uniformly sampled sparse-angle data. Both simulated and measured data are considered, and noise-robust and edge-preserving multireso-lution reconstructions are achieved. In sparse-angle cases with simulated data the proposed method offers a significant improvement in reconstruction quality (measured in relative square norm error) over filtered back-projection (FBP) and Tikhonov regularization.
    SIAM Journal on Scientific Computing 05/2013; 35(3):644-665. DOI:10.1137/120876277 · 1.94 Impact Factor
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    • "The ROI RMSE error at N views = 64 is 5.46×10 −4 for constrained TV-minimization, while the equivalent RMSE for the Tikhonov result is only achieved at N views ≈ 240, a factor of nearly 4 times as many views. This would seem to indicate a degree of stability towards inconsistent data of constrained TV-minimization, which could perhaps explain the successful exploitation of gradient magnitude sparsity on actual CT scanner data [2], [3], [5], [7], [8], [9], [10], [48]. "
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    ABSTRACT: Iterative image reconstruction with sparsity-exploiting methods, such as total variation (TV) minimization, investigated in compressive sensing claim potentially large reductions in sampling requirements. Quantifying this claim for computed tomography (CT) is nontrivial, because both full sampling in the discrete-to-discrete imaging model and the reduction in sampling admitted by sparsity-exploiting methods are ill-defined. The present article proposes definitions of full sampling by introducing four sufficient-sampling conditions (SSCs). The SSCs are based on the condition number of the system matrix of a linear imaging model and address invertibility and stability. In the example application of breast CT, the SSCs are used as reference points of full sampling for quantifying the undersampling admitted by reconstruction through TV-minimization. In numerical simulations, factors affecting admissible undersampling are studied. Differences between few-view and few-detector bin reconstruction as well as a relation between object sparsity and admitted undersampling are quantified.
    IEEE Transactions on Medical Imaging 02/2013; 32(2):460-473. DOI:10.1109/TMI.2012.2230185 · 3.80 Impact Factor
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