Song Bongyong, Park Justin C, Song William Y
Department of Radiation Medicine and Applied Sciences, University of California San Diego, La Jolla, CA 92093, USA.
Phys Med Biol. 2014 Nov 7;59(21):6565-82. doi: 10.1088/0031-9155/59/21/6565. Epub 2014 Oct 16.
The Barzilai-Borwein (BB) 2-point step size gradient method is receiving attention for accelerating Total Variation (TV) based CBCT reconstructions. In order to become truly viable for clinical applications, however, its convergence property needs to be properly addressed. We propose a novel fast converging gradient projection BB method that requires 'at most one function evaluation' in each iterative step. This Selective Function Evaluation method, referred to as GPBB-SFE in this paper, exhibits the desired convergence property when it is combined with a 'smoothed TV' or any other differentiable prior. This way, the proposed GPBB-SFE algorithm offers fast and guaranteed convergence to the desired 3DCBCT image with minimal computational complexity. We first applied this algorithm to a Shepp-Logan numerical phantom. We then applied to a CatPhan 600 physical phantom (The Phantom Laboratory, Salem, NY) and a clinically-treated head-and-neck patient, both acquired from the TrueBeam™ system (Varian Medical Systems, Palo Alto, CA). Furthermore, we accelerated the reconstruction by implementing the algorithm on NVIDIA GTX 480 GPU card. We first compared GPBB-SFE with three recently proposed BB-based CBCT reconstruction methods available in the literature using Shepp-Logan numerical phantom with 40 projections. It is found that GPBB-SFE shows either faster convergence speed/time or superior convergence property compared to existing BB-based algorithms. With the CatPhan 600 physical phantom, the GPBB-SFE algorithm requires only 3 function evaluations in 30 iterations and reconstructs the standard, 364-projection FDK reconstruction quality image using only 60 projections. We then applied the algorithm to a clinically-treated head-and-neck patient. It was observed that the GPBB-SFE algorithm requires only 18 function evaluations in 30 iterations. Compared with the FDK algorithm with 364 projections, the GPBB-SFE algorithm produces visibly equivalent quality CBCT image for the head-and-neck patient with only 180 projections, in 131.7 s, further supporting its clinical applicability.
巴齐莱-博温（BB）两点步长梯度法因能加速基于全变差（TV）的锥形束CT（CBCT）重建而受到关注。然而，为了在临床应用中真正可行，需要妥善解决其收敛性问题。我们提出了一种新颖的快速收敛梯度投影BB方法，该方法在每个迭代步骤中“最多只需一次函数求值”。这种选择性函数求值方法，在本文中称为GPBB-SFE，当与“平滑TV”或任何其他可微先验相结合时，表现出所需的收敛特性。通过这种方式，所提出的GPBB-SFE算法以最小的计算复杂度快速且有保证地收敛到所需的三维CBCT图像。我们首先将该算法应用于Shepp-Logan数字模型。然后将其应用于CatPhan 600物理模型（幻影实验室，纽约州塞勒姆）以及一名临床治疗的头颈患者，两者均采集自TrueBeam™系统（瓦里安医疗系统公司，加利福尼亚州帕洛阿尔托）。此外，我们通过在NVIDIA GTX 480 GPU卡上实现该算法来加速重建。我们首先使用具有40个投影的Shepp-Logan数字模型，将GPBB-SFE与文献中最近提出的三种基于BB的CBCT重建方法进行比较。结果发现，与现有的基于BB的算法相比，GPBB-SFE显示出更快的收敛速度/时间或更优的收敛特性。对于CatPhan 600物理模型，GPBB-SFE算法在30次迭代中仅需3次函数求值，并仅使用60个投影重建出标准的、具有364个投影的FDK重建质量图像。然后我们将该算法应用于一名临床治疗的头颈患者。观察到GPBB-SFE算法在30次迭代中仅需18次函数求值。与具有364个投影的FDK算法相比，GPBB-SFE算法仅使用180个投影，在131.7秒内为头颈患者生成了质量明显相当的CBCT图像，进一步支持了其临床适用性。
