In Magnetic Particle Imaging (MPI), the system matrix plays an important role, as it encodes the relationship between particle concentration and the measured signal. Its acquisition requires a time-consuming calibration scan, whereas its size leads to a high memory-demand. Both of these aspects can be limiting factors in practice. In order to reduce measurement time, compressed sensing exploits the knowledge that the MPI system matrix has a sparse representation in a suitably chosen domain. In this work we demonstrate that the rows of the system matrix allow a representation as low-rank tensors. We show that such an approximation leads to a denoising of the system matrix while introducing only a negligible bias. As an application, we develop a new matrix recovery method exploiting aforementioned low rank property in addition to sparsity in the DCT domain. Experiments show that the proposed matrix recovery method yields system matrices with reduced error when compared to a standard compressed sensing recovery.

中文翻译：

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使用低秩张量恢复 MPI 系统矩阵

在磁粒子成像 (MPI) 中，系统矩阵起着重要作用，因为它编码了粒子浓度与测量信号之间的关系。其获取需要耗时的校准扫描，而其大小导致内存需求高。这两个方面在实践中都可能是限制因素。In order to reduce measurement time, compressed sensing exploits the knowledge that the MPI system matrix has a sparse representation in a suitably chosen domain. 在这项工作中，我们证明了系统矩阵的行允许表示为低秩张量。我们表明，这种近似导致系统矩阵去噪，同时仅引入可忽略不计的偏差。作为应用程序，我们开发了一种新的矩阵恢复方法，除了 DCT 域中的稀疏性之外，还利用上述低秩属性。实验表明，与标准压缩感知恢复相比，所提出的矩阵恢复方法产生的系统矩阵具有减少的误差。