GPU Based Parallel Framework for the Estimation of Receiver Coil Sensitivities in SENSE Reconstruction
Afaq Ashfaq1, Muhammad Adil Khalil1, Hassan Shahzad2, Sohaib Ayyaz1, and Hammad Omer1

1Electrical Engineering, COMSATS University Islamabad, Islamabad, Pakistan, 2National Centre for Physics, Islamabad, Pakistan


The estimation of receiver coil sensitivity information is important for SENSE (Sensitivity Encoding) reconstruction. Inaccurate sensitivity profiles degrade the reconstructed image quality. However, the methods to estimate the receiver coils sensitivity information are computationally intensive. This work proposes a parallel framework (for GPU implementation) for a recently proposed method of sensitivity estimation (which uses Eigen value decomposition of the multi coil low resolution images). The results show that the proposed method provides a 3.5x speed in our experiments while maintaining the reconstructed image quality.


Sensitivity Encoding (SENSE)1 reconstructs MR image by using the receiver coil sensitivity information and undersampled data acquired from multiple receiver coils. Estimation of receiver coils sensitivities plays a vital role in SENSE reconstruction and any inaccuracies in their estimation will result in faulty image reconstruction1. To estimate receiver coil sensitivity information, Eigen-value method was recently proposed in literature by Uecker. M2. This is an efficient and stable method to estimate the receiver coil sensitivity information2 with a benefit that it does not require any pre-scan image. However, the method is computationally intensive which results in delay to estimate the maps. This work proposes a parallel framework for this method to accelerate sensitivity maps estimation using Graphics Processing Unit (GPUs).


Eigen-value method for receiver coil sensitivity estimation is shown in Figure 1. It uses a series of eigenvalue decompositions in k-space and provides receiver coil sensitivities which appear corresponding to the main eigenvector. The input to the algorithm, shown in Figure 1, is the low resolution multi coil images. The processes shown with grey blocks in Figure 1 are the ones which have been identified to be highly intensive in terms of computation times. However, they contain inherit parallelism, which can be exploited using Graphics Processing Units (GPUs). After analyzing the parallelism in these processes, CUDA kernels were designed for all the processes (grey blocks in Figure 1) to exploit their inherent parallelism on GPU. These kernels include “Fast 3D Matrix Augmentation” of Eigen values and Eigen vectors, efficient data processing from GPU memories and the synchronization of the GPU kernels to avoid race conditions. The synchronization of all the parallel processes also helped to remove the chance of corrupted output. The most computationally intensive task is the computation of Singular Value Decomposition (SVD)3, for which we used the Jacobi SVD algorithm proposed by S.A. Qazi7.

Once the receiver coils sensitivity information is obtained using the proposed architecture, image reconstruction is performed with SENSE using the sensitivity maps estimated by the proposed framework (on GPU) and the conventional Eigen Value method on Central Processing Unit (CPU).

To test the proposed method, a fully-sampled human brain data was acquired using 1.5T scanner with eight-channel receiver coils2 having dimensions 200 × 200. The GPU used for this research is NVIDIA’s GeForce GTX 1060 having 6GB memory and 1280 cores with a clock speed of 1.7MHz. While the CPU used is Intel’s Core i-7 having 16GB RAM with 3.6GHZ clock speed.

Results and Discussions

Figure 2 shows the receiver coil sensitivity estimates obtained using the conventional implementation of Eigen-value method on CPU (Figure 2a) and the sensitivity maps using the proposed method (Figure 2b). The difference between the sensitivity maps estimations of both the methods is shown in Figure 2c.

The difference images in Figure 2(c) show that there is no difference between the receiver coil sensitivity maps obtained using the proposed method and the conventional implementation on CPU. Figure 3 shows the reconstructed images obtained from both (conventional and proposed) the methods at different acceleration factors (2 and 4). Visually there is no difference between both the images, which is also confirmed using artifact power at different acceleration factors. Both methods (conventional and proposed) provide same artifact power at a given acceleration factor; which is 0.0053 and 0.0067 at acceleration factor 2 and 4 respectively.

Figure 4 shows the computation time comparison of the proposed method and the conventional Eigen-value method. The conventional method takes 6240 milliseconds while the proposed method takes only 1621 milliseconds to get the reconstructed images. The results show that the proposed framework of Eigen-value method on GPU significantly reduces the computation time for sensitivity map estimation, thus making SENSE reconstruction more proficient.


A parallel framework of Eigen-value method of sensitivity map estimation on GPU is proposed and the results compared with the respective conventional implementation. The results demonstrate that the proposed method reduces the computation time (by a factor of 3.5x in our experiments) with no effect on the reconstructed image quality.


No acknowledgement found.


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[5] Nvidia Corp. CuSolver: CUDA toolkit documentation. [https://docs.nvidia.com/cuda/cusolver/index.html]. Accessed [Jan 2018].

[6] NVIDIA Corp. [Website] https://developer.nvidia.com/cuda-downloads. Accessed [2018].

[7] Sohaib.A.Qazi, Abeera S, Saima N, Hammad O. Singular Value Decomposition Using Jacobi Algorithm in pMRI and CS. Appl Magn Reson (2017) 48:461–471.


Flow chart of Eigen-value method with initialization parameters and outputs. Whereas the highlighted parts are implemented on GPU.

Images show the magnitude component of the receiver coil sensitivity maps estimated (a) using conventional approach on CPU,(b) by the proposed method on GPU and (c) the difference images

Reconstruction results of 1.5T human head data set using conventional method and the proposed method at Acceleration Factor (AF) 2 and 4.

Computation time comparison of proposed method (on GPU) with the conventional Eigen-value method (on GPU) along with Jacobi SVD on CPU (Conventional) and GPU (Proposed).

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)