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

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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.