Purpose: Cone-beam CT (CBCT) plays an important role in image guided radiation therapy (IGRT). However, the large radiation dose from serial CBCT scans in most IGRT procedures raises a clinical concern, especially for pediatric patients who are essentially excluded from receiving IGRT for this reason. The goal of this work is to develop a fast GPU-based algorithm to reconstruct CBCT from undersampled and noisy projection data so as to lower the imaging dose. Methods: The CBCT is reconstructed by minimizing an energy functional consisting of a data fidelity term and a total variation regularization term. We developed a GPU-friendly version of the forward-backward splitting algorithm to solve this model. A multi-grid technique is also employed. Results: It is found that 20~40 x-ray projections are sufficient to reconstruct images with satisfactory quality for IGRT. The reconstruction time ranges from 77 to 130 sec on a NVIDIA Tesla C1060 GPU card, depending on the number of projections used, which is estimated about 100 times faster than similar iterative reconstruction approaches. Moreover, phantom studies indicate that our algorithm enables the CBCT to be reconstructed under a scanning protocol with as low as 0.1 mAs/projection. Comparing with currently widely used full-fan head and neck scanning protocol of ~360 projections with 0.4 mAs/projection, it is estimated that an overall 36~72 times dose reduction has been achieved in our fast CBCT reconstruction algorithm. Conclusions: This work indicates that the developed GPU-based CBCT reconstruction algorithm is capable of lowering imaging dose considerably. The high computation efficiency in this algorithm makes the iterative CBCT reconstruction approach applicable in real clinical environments.
Deep Dive into GPU-based Fast Cone Beam CT Reconstruction from Undersampled and Noisy Projection Data via Total Variation.
Purpose: Cone-beam CT (CBCT) plays an important role in image guided radiation therapy (IGRT). However, the large radiation dose from serial CBCT scans in most IGRT procedures raises a clinical concern, especially for pediatric patients who are essentially excluded from receiving IGRT for this reason. The goal of this work is to develop a fast GPU-based algorithm to reconstruct CBCT from undersampled and noisy projection data so as to lower the imaging dose. Methods: The CBCT is reconstructed by minimizing an energy functional consisting of a data fidelity term and a total variation regularization term. We developed a GPU-friendly version of the forward-backward splitting algorithm to solve this model. A multi-grid technique is also employed. Results: It is found that 20~40 x-ray projections are sufficient to reconstruct images with satisfactory quality for IGRT. The reconstruction time ranges from 77 to 130 sec on a NVIDIA Tesla C1060 GPU card, depending on the number of projections u
Cone Beam Computed Tomography (CBCT) has been broadly used in image guided radiation therapy (IGRT) to acquire the updated patient's geometry for precise targeting before each treatment fraction. The repeated use of CBCT during a treatment course raises a clinical concern of excessive x-ray dose. This concern has prohibited the use of IGRT for pediatric patients, resulting in compromised treatment outcome.
Imaging dose in CBCT can be reduced by reducing number of x-ray projections and/or mAs level (tube current and pulse duration). These approaches cannot be used with conventional FDK-type algorithms 1 , that are currently clinical standards, because the images reconstructed from under-sampled and/or noisy projection data are highly degraded and thus clinically unacceptable. Recently, a burst of research in compressed sensing [2][3] has demonstrated the feasibility of recovering signals from incomplete measurements through optimization methods, providing us new perspectives of solving the CBCT reconstruction problem 4 . Among various methods of this type, Total Variation (TV) method 5 has presented its tremendous power in CT reconstruction problems in both fan-beam 6 and cone-beam 7 geometries. This approach has also been extensively applied into many other imaging applications [8][9][10] and its efficacy has been enhanced by combining with other techniques, such as incorporating prior information 11 . Despite the great power of the TV-based methods, the computation is very time-consuming owing to the lack of efficient algorithms to handle the large data set encountered in CBCT reconstruction problems. It usually takes several hours or even longer for current TV-based reconstruction approaches to produce a decent CBCT image. This fact prevents them from practical applications in real clinical environments.
Recently, general-purpose computing on graphics processing unit (GPU) has offered us a promising prospect of performing computationally intensive tasks in medical imaging and therapy applications [12][13][14][15][16][17] . By developing new algorithms with mathematical structures suitable for GPU parallelization, we can take advantage of the massive computing power of GPU to dramatically improve the efficiency of the TV-based CBCT reconstruction, as will be seen in the rest of this letter.
Let us consider a patient volumetric image represented by a function , , , , ,
. An operator projects onto an x-ray imager plane in a cone beam geometry at an angle . Denote the observed projection image at an angle by , . A CBCT reconstruction problem is formulated as to retrieve the volumetric image based on the observed functions . In this letter, we aim at reconstructing the CBCT image by minimizing an energy functional:
where and ∑ . Here is the volume in which the CBCT image is reconstructed. is the number of projections and is the projection area on each x-ray imager. … denotes function -norm. The data fidelity term ensures the consistency between the reconstructed image and the observations . The other one, , known as TV semi-norm, has been shown to be extremely powerful 5 to remove artifacts and noise from while preserving its sharp edges.
0 is introduced to adjust the relative weights between these two energy terms. It controls the smoothness of the reconstructed images and is chosen manually for best image quality.
In order to perform the minimization task, we employed an innovative forwardbackward splitting algorithm [18][19] :
Repeat the following steps until convergence in Step 1, apart from some constants, where • denotes a matrix transpose. This approach causes a memory conflict problem when implemented on GPU, which severely limits the exploitation of GPU’s massive parallel computing power. To resolve this issue, a GPUfriendly way of evaluating the functional variation / has been developed as following:
where , is the coordinate on the imager plane at which a ray line connecting the xray source and the point , , intersects the imager.
is the source to imager distance.
, , and , are the distances from the source to the point , , and from the source to the point , on the imager, respectively. For GPU implementation, we first perform the forward x-ray projection operation and compute , , for all , and . Then each thread on GPU can independently evaluate the functional variation at a , , coordinate. Given the vast parallelization ability of GPU, extremely high efficiency in Step 1 can be achieved. Other steps in (A1) can also benefit from GPU implementations considerably. For example, for the purpose of evaluating , we simply have each GPU thread compute this term at an , , coordinate and then a summation over the coordinate is performed. Moreover, we employed the well developed multi-grid method 20 to achieve further efficiency boost.
We first tested our reconstruction algorithm on a digital NCAT phantom 21 . The phantom was generated at thorax region with a size of 512 512 70 voxels. The x-ray
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