【作者】 张鹏；

【导师】 刘杰；

【作者基本信息】 北京交通大学 ， 计算机科学与技术， 2023， 博士

【摘要】 磁纳米粒子成像(Magnetic Particle Imaging,MPI)是一种前沿的医学影像技术。该技术能够基于超顺磁铁纳米粒子(Super Paramagnetic Iron Oxide Nanoparticles,SPIONs)的非线性磁化响应特性实现在体无创成像。相较于其他成像模态,MPI具有高成像灵敏度、高成像分辨率和不受成像深度限制等优势,临床应用前景广阔。成像算法是MPI技术的关键环节之一,其性能直接影响MPI的成像速度和质量。系统矩阵成像算法是目前MPI领域应用最为广泛的一种成像算法,具有较好的成像质量。该算法通过系统矩阵构建SPIONs信号与其空间分布间的映射关系,并利用迭代算法实现MPI图像重建。然而,随着MPI技术的发展,系统矩阵的规模也逐渐增长。由于系统矩阵规模的膨胀,系统矩阵成像算法的计算复杂度随之增加,系统矩阵中的噪声也更加复杂。该问题导致了系统矩阵成像算法的成像速度和质量的降低,限制了三维实时MPI成像、大视野MPI成像等关键MPI技术的发展。本研究针对目前磁纳米粒子成像技术中存在的系统矩阵规模较大且存在冗余和噪声的问题,着力研究系统矩阵压缩算法的改进策略。本研究分别从系统矩阵的频率维度和空间维度展开,通过对系统矩阵的不同维度进行压缩,减少重建数据中的冗余和噪声,降低重建算法的计算复杂度,进而实现MPI成像速度和质量的提升。本文的主要研究内容包括以下三个方面:(1)针对MPI系统矩阵频率压缩问题,引入了能量谱密度特征作为一种新的MPI频率压缩特征,构建了一种基于信号的信噪比特征和能量谱密度特征的双特征频率压缩算法。本研究首先对噪声信号和SPIONs响应信号的能量分布特点进行了分析,基于MPI信号的频谱能量特点引入了能量谱密度特征作为MPI频率筛选的依据。同时,考虑到不同种类的MPI噪声在频谱分布上的区别,提出了一种两步压缩策略。该策略首先通过信噪比特征去除高背景噪声和畸变噪声的频点,再通过能量谱密度特征去除高随机噪声的频点。最后,本研究将双特征频率压缩方法与Kaczmarz重建算法结合,在MPI的仿真数据集和开源实测数据集上进行了算法验证。实验结果表明,所提出的压缩方法能够在不损失关键信息,保证重建效果的前提下,减少75%以上的重建时间。(2)针对MPI系统矩阵噪声降低成像质量的问题,提出了一种基于数据残差特征,能够动态选取重建数据的迭代算法。本研究通过迭代残差与数据噪声的关系,提出了基于残差特征动态筛选迭代数据的压缩策略。通过将该策略与Kaczmarz方法结合,本研究构建了具有高抗噪能力的动态残差Kaczmarz算法,并通过仿真数据和开源实测数据对算法性能进行了测试。实验结果表明,动态残差Kaczmarz方法在不同噪声水平下均能实现高质量重建,成像效果显著优于对比算法。此外,动态残差Kaczmarz方法还可以与多种正则模型进行结合,进一步提升算法的抗噪能力。在应用非负融合LASSO模型的情况下,动态残差Kaczmarz方法能够在信噪比为5 d B的测量信号上实现高质量重建,显著优于其他对比算法。(3)针对MPI系统矩阵空间维度压缩的问题,提出了一种能够对系统矩阵空间维度进行自适应重构的压缩算法。本研究通过引入可行域的概念,实现了系统矩阵空间维度的压缩,有效降低了重建的计算复杂度。针对如何选取可行域这一核心问题,本研究提出了基于共轭梯度法向残差方法的自适应可行域构建策略,并通过三维形态学操作和聚类算法对可行域进行了优化。本研究将该策略与Kaczmarz方法进行结合,构建了自适应可行域Kaczmarz方法。在MPI的仿真数据集上,该方法能够将成像速度提高到Kaczmarz算法的两倍以上。最后,本研究基于激发荧光断层成像技术中的重建问题与MPI重建问题的相似性,对本算法的临床效果进行了探索。实验结果表明,自适应可行域Kaczmarz算法可以对颈动脉粥样硬化斑块进行快速精确定位,临床应用前景广阔。更多还原

【Abstract】 Magnetic Particle Imaging(MPI)is an advanced molecular imaging technology,which images Super Paramagnetic Iron Oxide Nanoparticles(SPIONS)based on the nonlinear magnetization response of particles.Compared to other molecular imaging modalities,MPI has shown advantages in imaging sensitivity,spatial resolution,and imaging depth.These advantages make MPI an extremely promising imaging modality for biomedical applications.The reconstruction method is one of the important parts of MPI technology,which directly influences the imaging speed and quality of MPI.Currently,the system matrixbased reconstruction method is widely used in MPI.The system matrix represents the linear relationship between the measurement signal and the particle concentration.By using the system matrix,the inverse problem of MPI can be transformed into a convex optimization problem.However,with the development of MPI technology,the scale of the system matrix and the noise level are increasing.This problem decreases the efficiency of reconstruction and limits the development of 3D-real-time MPI technology and large-view MPI technology.In this thesis,we develop the system matrix compression method to address this problem.Introducing several new features and developing new compression methods,the system matrix was compressed both in the frequency dimension and calibration dimension.The proposed method can accelerate the reconstruction and improve the imaging quality by using a smaller amount of data but with more importance.The main contributions of this research include three aspects:(1)This work introduces the energy spectral density feature to compress the system matrix and proposes the dual-feature frequency component compression method.Based on the characteristics of the measurement signal,we analyze the relationship between the random noise and the energy of the particle signal.The energy spectral density feature is validated to be capable of evaluating the distribution of noise.Besides,we propose the dual-feature frequency component method and apply the step-wise compression algorithm based on the characteristics of different types of noise.Compared to the previous compression method,the proposed method can achieve similar or better reconstruction quality by using 25% or less reconstruction time.Simulations and experiments validate that the proposed method can efficiently improve the efficiency of MPI technology.(2)This work proposes a new iteration method to improve the noise-reducing capability of the compression algorithm for MPI.We analyze the relationship between the iteration residual and the noise signal and validate the residual feature can be used to compress the system matrix while iteration.Based on this assumption,we propose the dynamic residual Kaczmarz(DRK)method,which has high noise-reducing capabilities.Simulations and experiment results validate that the similarity structure(SSIM)indicator can be improved five times by the proposed method than the traditional Kaczmarz method in 5 d B noise level.Further,the noise-reducing capabilities of the DRK method can be improved by combining it with regularization models.The dynamic residual Kaczmarz method with non-negative fused LASSO regularization(DRK-NFL)can acquire more than 0.7 SSIM indicators in a 5 dB noise level.(3)This work introduces the permissible region strategy to reduce the calibration point dimension of the system matrix to accelerate the MPI reconstruction.We validate that the inverse problem of reconstruction can be solved more efficiently and accurately when the calibration point dimension is compressed.Based on this assumption,we propose the Adaptive Permissible Region(APR)algorithm,which can adaptively generate the permissible region with the morphological operations and clustering algorithms.In simulations and experiments of MPI reconstruction,the proposed APR method is combined with the Kaczmarz method and achieves better reconstruction results while accelerating the reconstruction more than twice that of the original algorithm.Besides,the proposed APR method is applied to detect carotid atherosclerotic plaques in pre-clinical experiments and performs well.更多还原