Fast compressed sensing-based CBCT reconstruction using Barzilai-Borwein formulation for application to on-line IGRT

Authors

  • Park Justin C.,

    1. Center for Advanced Radiotherapy Technologies and Department of Radiation Medicine and Applied Sciences, University of California San Diego, La Jolla, California 92093 and Department of Electrical and Computer Engineering, University of California San Diego, La Jolla, California 92093
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  • Song Bongyong,

    1. Center for Advanced Radiotherapy Technologies and Department of Radiation Medicine and Applied Sciences, University of California San Diego, La Jolla, California 92093
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    • Electronic mail: bosong@ucsd.edu; Telephone: +1-858-720-1085; Fax: +1-858-822-5568.

  • Kim Jin Sung,

    1. Department of Radiation Oncology, Samsung Medical Center, Seoul, South Korea
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  • Park Sung Ho,

    1. Department of Radiation Oncology, Asan Medical Center, College of Medicine, University of Ulsan, Seoul, South Korea
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  • Kim Ho Kyung,

    1. School of Mechanical Engineering, Pusan National University, Busan, South Korea
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  • Liu Zhaowei,

    1. Department of Electrical and Computer Engineering, University of California San Diego, La Jolla, California 92093
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  • Suh Tae Suk,

    1. Department of Biomedical Engineering, Catholic University of Korea, Seoul, South Korea
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  • Song William Y.

    1. Center for Advanced Radiotherapy Technologies and Department of Radiation Medicine and Applied Sciences, University of California San Diego, La Jolla, California 92093
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    • Electronic mail: wysong@ucsd.edu; Telephone: +1-858-246-0886; Fax: +1-858-822-5568.


Abstract

Purpose:

Compressed sensing theory has enabled an accurate, low-dose cone-beam computed tomography (CBCT) reconstruction using a minimal number of noisy projections. However, the reconstruction time remains a significant challenge for practical implementation in the clinic. In this work, we propose a novel gradient projection algorithm, based on the Gradient-Projection-Barzilai-Borwein formulation (GP-BB), that handles the total variation (TV)-norm regularization-based least squares problem for the CBCT reconstruction in a highly efficient manner, with speed acceptable for routine use in the clinic.

Methods:

CBCT is reconstructed by minimizing an energy function consisting of a data fidelity term and a TV-norm regularization term. Both terms are simultaneously minimized by calculating the gradient projection of the energy function with the step size determined using an approximate Hessian calculation at each iteration, based on the Barzilai-Borwein formulation. To speed up the process, a multiresolution optimization is used. In addition, the entire algorithm was designed to run with a single graphics processing unit (GPU) card. To evaluate the performance, the Shepp-Logan numerical phantom, the CatPhan 600 physical phantom, and a clinically-treated head-and-neck patient were acquired from the TrueBeam™ system (Varian Medical Systems, Palo Alto, CA). For each scan, in total, 364 projections were acquired in a 200° rotation. The imager has 1024 × 768 pixels with 0.388 × 0.388-mm resolution. This was down-sampled to 512 × 384 pixels with 0.776 × 0.776-mm resolution for reconstruction. Evenly spaced angles were subsampled and used for varying the number of projections for the image reconstruction. To assess the performance of our GP-BB algorithm, we have implemented and compared with three compressed sensing-type algorithms, the two of which are popular and published (forward–backward splitting techniques), and the other one with a basic line-search technique. In addition, the conventional Feldkamp-Davis-Kress (FDK) reconstruction of the clinical patient data is compared as well.

Results:

In comparison with the other compressed sensing-type algorithms, our algorithm showed convergence in ≤30 iterations whereas other published algorithms need at least 50 iterations in order to reconstruct the Shepp-Logan phantom image. With the CatPhan phantom, the GP-BB algorithm achieved a clinically-reasonable image with 40 projections in 12 iterations, in less than 12.6 s. This is at least an order of magnitude faster in reconstruction time compared with the most recent reports utilizing GPU technology given the same input projections. For the head-and-neck clinical scan, clinically-reasonable images were obtained from 120 projections in 34–78 s converging in 12–30 iterations. In this reconstruction range (i.e., 120 projections) the image quality is visually similar to or better than the conventional FDK reconstructed images using 364 projections. This represents a dose reduction of nearly 67% (120/364 projections) while maintaining a reasonable speed in clinical implementation.

Conclusions:

In this paper, we proposed a novel, fast, low-dose CBCT reconstruction algorithm using the Barzilai-Borwein step-size calculation. A clinically viable head-and-neck image can be obtained within ∼34–78 s while simultaneously cutting the dose by approximately 67%. This makes our GP-BB algorithm potentially useful in an on-line image-guided radiation therapy (IGRT).

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