基于压缩感知的核磁共振成像重建技术研究
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摘要
核磁共振成像作为一种极其重要的医学成像技术，具有对病灶诊断精确、对人体安全性高等优点，但是较长的数据采集时间成为其广泛应用的瓶颈。因此，在保证成像质量的前提下，探索一种新的快速成像方法迫在眉睫。压缩感知作为一种全新的信号采样理论，针对稀疏信号或可压缩信号，可以在采样数量远少于传统采样方式的情况下精确地恢复出原始信号，这就为核磁共振图像的快速获取提供了一种新的思路。因此，本文在深入研究了压缩感知、核磁共振成像的相关理论之后，对基于压缩感知的核磁共振成像重建技术进行了研究，主要工作和创新包括以下几个方面：
（1）针对传统欠采样方式造成的图像混叠伪影问题，研究了几种常用的采样轨迹，考虑到图像的高频部分只包含较少的能量，能量主要集中于低频部分的特点，提出了一种基于变密度的笛卡尔随机采样方式。实验结果表明，该采样方式在基于压缩感知的核磁共振成像中取得了良好的效果，有效地降低了图像的混叠伪影问题。
（2）针对传统二维小波变换不能对核磁共振图像提供最优表示的问题，研究了基于多尺度几何分析的剪切波理论，提出了一种新的基于离散剪切波变换的核磁共振图像稀疏表示方法。实验验证了离散剪切波变换重建的准确性以及稀疏性；与小波变换相比，离散剪切波变换在保留系数为1%，相同采样率的情况下，重建图像的结构化相似度值平均优于小波变换0.06，具有更高的重建精度，更有利于保留图像的边缘和纹理信息。
（3）针对信号重建过程中算法复杂度高、不利于实时处理的问题，提出了一种基于FPGA硬件平台的内点法设计。将计算量最大的线性方程组的求解进行了改进，选用内在并行性高的共轭梯度算法完成主要的运算，进而提出了FPGA实现的总体设计和分模块设计方案，并着重设计了并行度高、计算密集的矩阵-向量乘模块。并行化和流水的协处理器有效的利用了算法内在的并行性和FPGA本身的并行结构，提高了整个系统的处理速度。仿真实验证明，该系统资源耗费少，硬件加速比可达21倍。
（4）针对基于压缩感知理论的核磁共振成像重建算法包含大量的浮点运算，重建所花费的时间要远远大于傅里叶正反变换重建的问题。基于GPU强大的并行处理能力，利用JACKET技术对正交匹配追踪算法进行了并行化设计与实现。实验结果表明，图像大小为10242时，算法移植到GPU平台获得最大的性能加速比，单精度浮点计算和双精度浮点计算分别获得49和24倍的加速。
Magnetic resonance imaging as an extremely important imaging technique in themedical field, has advantages of lesion localization precision and high security for human.But the long data acquisition time become the bottleneck of wide application. It is urgent tofind a fast imaging methods, in the premise of ensuring the quality of imaging. Compressedsensing is a new signal processing method which can abandon the redundant information inthe current information sampling. Under the conditions of sparse or compressible, samplingsignal can accurately reconstruct original signals form a small quantity of measurements.So it improves the speed of sampling. This provides a new way to solve the key issues inmagnetic resonance imaging. Therefore, we apply the compressed sensing to the magneticresonance image reconstruction, in the foundation of the deeper research on many theories.And the major work and innovations in this paper include the following aspects:
(1) In order to solve the image’s aliasing artifacts caused by the traditionalsub-sampling, it is proposed a way named random variable density sampling. Through thecomparison of several commonly used sampling trajectory, we adopt a kind of mode nameda variable density Cartesian random sampling mode, then we instruction this mode. Theresults show that the variable density Cartesian random sampling mode achieved goodresults based on compressed sensing MRI.
(2) In order to solve problems of traditional two-dimensional wavelet transform cannot sparsely represent curves and edges. In this paper, we introduce a geometric imagetransform, the shearlet, to overcome this shortage. after discussing the implementation ofthe, reconstruction accuracy and sparsity of the discrete shearlet transform are analyzed.Experimental results shows that, discrete shearlet transform in the retention coefficient of1%, the value of SSIM is better than wavelet transform on average0.06at the samesampling rate. At the same time, discrete shearlet transform can improve quality ofreconstructed image and preserve more information about texture and edge.
(3) signal reconstruction algorithms based on compressed sensing are high complexity,can not conducive to real-time processing. In view of the above problems, we propose adesign for interior point method that is based on the Field Programmable Gate Array(FPGA)hardware platform. We improvements the primal-dual corrector interior method,make it more suitable for FPGA of parallel processing. The array structure of the conjugategradients algorithm completes the main operations, and the parallel and pipelinecoprocessor effectively take advantage of the inherent parallelism of the algorithm and theparallel structure of FPGA. Thus, it can speedup about21times over the software versionof the same algorithm.
(4) Sparse MRI image reconstruction algorithm contains a large number of floatingpoint arithmetic based on Compressed Sensing theory. It can be more time-consuming thantraditional inverse Fourier reconstruction. To solve this problem, the existing sparse MRIreconstruction algorithm is made practical by parallelizing it under the framework ofNVIDIA CUDA using GPU. The experimental results show that, based on the GPU, thisplatform provides very fast iterative reconstruction. Reconstruction of10242MRI canobtain speedups of24and49in the double precision floating point calculation and sigleprecision floating point calculation.
（1）针对传统欠采样方式造成的图像混叠伪影问题，研究了几种常用的采样轨迹，考虑到图像的高频部分只包含较少的能量，能量主要集中于低频部分的特点，提出了一种基于变密度的笛卡尔随机采样方式。实验结果表明，该采样方式在基于压缩感知的核磁共振成像中取得了良好的效果，有效地降低了图像的混叠伪影问题。
（2）针对传统二维小波变换不能对核磁共振图像提供最优表示的问题，研究了基于多尺度几何分析的剪切波理论，提出了一种新的基于离散剪切波变换的核磁共振图像稀疏表示方法。实验验证了离散剪切波变换重建的准确性以及稀疏性；与小波变换相比，离散剪切波变换在保留系数为1%，相同采样率的情况下，重建图像的结构化相似度值平均优于小波变换0.06，具有更高的重建精度，更有利于保留图像的边缘和纹理信息。
（3）针对信号重建过程中算法复杂度高、不利于实时处理的问题，提出了一种基于FPGA硬件平台的内点法设计。将计算量最大的线性方程组的求解进行了改进，选用内在并行性高的共轭梯度算法完成主要的运算，进而提出了FPGA实现的总体设计和分模块设计方案，并着重设计了并行度高、计算密集的矩阵-向量乘模块。并行化和流水的协处理器有效的利用了算法内在的并行性和FPGA本身的并行结构，提高了整个系统的处理速度。仿真实验证明，该系统资源耗费少，硬件加速比可达21倍。
（4）针对基于压缩感知理论的核磁共振成像重建算法包含大量的浮点运算，重建所花费的时间要远远大于傅里叶正反变换重建的问题。基于GPU强大的并行处理能力，利用JACKET技术对正交匹配追踪算法进行了并行化设计与实现。实验结果表明，图像大小为10242时，算法移植到GPU平台获得最大的性能加速比，单精度浮点计算和双精度浮点计算分别获得49和24倍的加速。
Magnetic resonance imaging as an extremely important imaging technique in themedical field, has advantages of lesion localization precision and high security for human.But the long data acquisition time become the bottleneck of wide application. It is urgent tofind a fast imaging methods, in the premise of ensuring the quality of imaging. Compressedsensing is a new signal processing method which can abandon the redundant information inthe current information sampling. Under the conditions of sparse or compressible, samplingsignal can accurately reconstruct original signals form a small quantity of measurements.So it improves the speed of sampling. This provides a new way to solve the key issues inmagnetic resonance imaging. Therefore, we apply the compressed sensing to the magneticresonance image reconstruction, in the foundation of the deeper research on many theories.And the major work and innovations in this paper include the following aspects:
(1) In order to solve the image’s aliasing artifacts caused by the traditionalsub-sampling, it is proposed a way named random variable density sampling. Through thecomparison of several commonly used sampling trajectory, we adopt a kind of mode nameda variable density Cartesian random sampling mode, then we instruction this mode. Theresults show that the variable density Cartesian random sampling mode achieved goodresults based on compressed sensing MRI.
(2) In order to solve problems of traditional two-dimensional wavelet transform cannot sparsely represent curves and edges. In this paper, we introduce a geometric imagetransform, the shearlet, to overcome this shortage. after discussing the implementation ofthe, reconstruction accuracy and sparsity of the discrete shearlet transform are analyzed.Experimental results shows that, discrete shearlet transform in the retention coefficient of1%, the value of SSIM is better than wavelet transform on average0.06at the samesampling rate. At the same time, discrete shearlet transform can improve quality ofreconstructed image and preserve more information about texture and edge.
(3) signal reconstruction algorithms based on compressed sensing are high complexity,can not conducive to real-time processing. In view of the above problems, we propose adesign for interior point method that is based on the Field Programmable Gate Array(FPGA)hardware platform. We improvements the primal-dual corrector interior method,make it more suitable for FPGA of parallel processing. The array structure of the conjugategradients algorithm completes the main operations, and the parallel and pipelinecoprocessor effectively take advantage of the inherent parallelism of the algorithm and theparallel structure of FPGA. Thus, it can speedup about21times over the software versionof the same algorithm.
(4) Sparse MRI image reconstruction algorithm contains a large number of floatingpoint arithmetic based on Compressed Sensing theory. It can be more time-consuming thantraditional inverse Fourier reconstruction. To solve this problem, the existing sparse MRIreconstruction algorithm is made practical by parallelizing it under the framework ofNVIDIA CUDA using GPU. The experimental results show that, based on the GPU, thisplatform provides very fast iterative reconstruction. Reconstruction of10242MRI canobtain speedups of24and49in the double precision floating point calculation and sigleprecision floating point calculation.
引文
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