CoS-MRXI - Compressed sensing for magnetorelaxometry imaging of magnetic nanoparticles

磁性纳米粒子提供了大量有前途的生物医学应用，特别是在癌症治疗中。为了这些应用的安全性和效率，需要关于颗粒分布的定量知识。直到今天，临床上还没有成像技术可用于颗粒的定量体内检测。非均匀激发场磁弛豫成像（MRXI）能够定量检测磁性纳米颗粒在体内的分布。最近，这种技术的潜力已在实验测量中得到证实。在这些实验中，连续激活以规则阵列定位的激励线圈，并在每个步骤中测量颗粒的磁弛豫。通过求解逆问题，从这些测量中重建颗粒的分布。虽然成像结果是有希望的，但相对于单个线圈的连续激活，需要较长的测量时间，并且需要记录大量的数据。在本项目中，压缩传感的方法将被调整和扩展到磁性纳米颗粒的磁弛豫成像的应用。我们的目标是为现有系统开发适当的激励序列，以及激励线圈和传感器设置的设计方法。这些发展将最终导致成像技术的实质性进步，包括空间分辨率的实质性增强以及线圈数量和测量时间的显著减少。从理论的角度来看，我们预计只有部分给定的传感矩阵的压缩传感范例的理解得到了改善，在其他生物医学成像应用产生实际影响。为了实现本课题的研究目标，本文将研究MRXI压缩感知的数学背景，并将基于稀疏性的重构算法应用于MRXI环境。此外，压缩传感方法将研究双线性和三线性优化问题的解决方案。为了将生物粒子分布的先验知识结合到重建算法中，将研究这些分布的性质并建立相应的模型。我们将通过优化权重向量和检查相应的恢复条件，为现有的实验MRXI设置开发基于压缩传感的激励方案。一个特别新颖的方面是，自然稀疏约束将用于系统的设计变量以及。这些方法以后将扩展到励磁线圈和传感器系统的设计。最后，将在模拟研究中彻底调查的发展，并在实验体模测量验证。

Magnetic nanoparticles offer a large variety of promising biomedical applications, particularly in cancer therapy. For the safety and efficiency of these applications, quantitative knowledge about the distribution of the particles is required. Until today, no imaging technology is clinically available for the quantitative in-vivo detection of the particles. Magnetorelaxometry imaging (MRXI) with inhomogeneous excitation fields is able to quantitatively detect distributions of magnetic nanoparticles in vivo. Recently, the potential of this technique has been demonstrated in experimental measurements. In these experiments, excitation coils, positioned in regular arrays, were consecutively activated and the magnetic relaxation of the particles was measured in each step. By solving an inverse problem, the distribution of the particles was reconstructed from these measurements. While the imaging results were promising, a long measurement time was required with respect to the consecutive activation of single coils Furthermore, large amounts of data needed to be recorded.In this project, the methods of compressed sensing will be adapted and expanded to the application of magnetorelaxometry imaging of magnetic nanoparticles. We aim at developing appropriate excitation sequences for existing systems as well as design approaches for excitation coils and sensor setups. These developments will finally lead to a substantial advancement in the imaging technology including a substantial enhancement in spatial resolution and a considerable reduction of the number of coils and the measurement times. From a theoretical point of view, we expect an improved understanding of compressed sensing paradigms for only partly given sensing matrices, yielding practical impact in other biomedical imaging applications. Furthermore, quantitative reconstruction algorithms should be developed by compressed sensing paradigms.To achieve the project objectives, the mathematical background of compressed sensing for MRXI will be worked out and sparsity-based reconstruction algorithms will be adapted the MRXI setting. Furthermore, compressed sensing methods will be investigated for the solution of bilinear and trilinear optimization problems. In order to incorporate prior knowledge about the biological particle distribution in the reconstruction algorithms, the properties of these distributions will be studied and a respective model will be set up. We will develop compressed sensing based excitation schemes for existing experimental MRXI setups by optimizing the weight vectors and checking the respective recovery conditions. A particularly novel aspect is that natural sparsity constraints will be used for the design variables of the system as well. These approaches will later be extended to the design of excitation coils and sensor systems. Finally, the developments will be thoroughly investigated in simulation studies and validated in experimental phantom measurements.