Magnetic Particle Imaging System Matrix Research Articles

Using Low-Rank Tensors for the Recovery of MPI System Matrices

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.

Direct Image Reconstruction of Lissajous-Type Magnetic Particle Imaging Data Using Chebyshev-Based Matrix Compression

Image reconstruction in magnetic particle imaging (MPI) is done using an algebraic approach for Lissajous-type measurement sequences. By solving a large linear system of equations, the spatial distribution of magnetic nanoparticles can be determined. Despite the use of iterative solvers that converge rapidly, the size of the MPI system matrix leads to reconstruction times that are typically much longer than the actual data acquisition time. For this reason, matrix compression techniques have been introduced that transform the MPI system matrix into a sparse domain and then utilize this sparsity for accelerated reconstruction. Within this work, we investigate the Chebyshev transformation for matrix compression and show that it can provide better reconstruction results for high compression rates than the commonly applied Cosine transformation. By reducing the number of coefficients per matrix row to one, it is even possible to derive a direct reconstruction method that obviates the usage of iterative solvers.

Symmetries of the 2D magnetic particle imaging system matrix

In magnetic particle imaging (MPI), the relation between the particle distribution and the measurement signal can be described by a linear system of equations. For 1D imaging, it can be shown that the system matrix can be expressed as a product of a convolution matrix and a Chebyshev transformation matrix. For multidimensional imaging, the structure of the MPI system matrix is not yet fully explored as the sampling trajectory complicates the physical model. It has been experimentally found that the MPI system matrix rows have symmetries and look similar to the tensor products of Chebyshev polynomials. In this work we will mathematically prove that the 2D MPI system matrix has symmetries that can be used for matrix compression.

Reconstruction Enhancement by Denoising the Magnetic Particle Imaging System Matrix Using Frequency Domain Filter

Magnetic particle imaging is a new modality, which allows the determination of the spatial distribution of magnetic nanoparticles in-vivo. A standard approach for magnetic particle image reconstruction employs a so-called system matrix. The system matrix is typically acquired by a calibration measurement, whereby the system response at numerous positions in the field-of-view is measured. Due to the measurement process, the system matrix contains noise, which affects the reconstruction of the particle distribution. In this paper, the special structure of the system matrix is exploited for noise reduction by applying frequency domain filters. It is shown that image reconstruction with the denoised system matrix yields an improved resolution and a better signal-to-noise ratio.

Reconstruction of the Magnetic Particle Imaging System Matrix Using Symmetries and Compressed Sensing

Magnetic particle imaging (MPI) is a tomographic imaging technique that allows the determination of the 3D spatial distribution of superparamagnetic iron oxide nanoparticles. Due to the complex dynamic nature of these nanoparticles, a time-consuming calibration measurement has to be performed prior to image reconstruction. During the calibration a small delta sample filled with the particle suspension is measured at all positions in the field of view where the particle distribution will be reconstructed. Recently, it has been shown that the calibration procedure can be significantly shortened by sampling the field of view only at few randomly chosen positions and applying compressed sensing to reconstruct the full MPI system matrix. The purpose of this work is to reduce the number of necessary calibration scans even further. To this end, we take into account symmetries of the MPI system matrix and combine this knowledge with the compressed sensing method. Experiments on 2D MPI data show that the combination of symmetry and compressed sensing allows reducing the number of calibration scans compared to the pure compressed sensing approach by a factor of about three.

Local System Matrix Compression for Efficient Reconstruction in Magnetic Particle Imaging

Magnetic particle imaging (MPI) is a quantitative method for determining the spatial distribution of magnetic nanoparticles, which can be used as tracers for cardiovascular imaging. For reconstructing a spatial map of the particle distribution, the system matrix describing the magnetic particle imaging equation has to be known. Due to the complex dynamic behavior of the magnetic particles, the system matrix is commonly measured in a calibration procedure. In order to speed up the reconstruction process, recently, a matrix compression technique has been proposed that makes use of a basis transformation in order to compress the MPI system matrix. By thresholding the resulting matrix and storing the remaining entries in compressed row storage format, only a fraction of the data has to be processed when reconstructing the particle distribution. In the present work, it is shown that the image quality of the algorithm can be considerably improved by using a local threshold for each matrix row instead of a global threshold for the entire system matrix.

On the formulation of the image reconstruction problem in magnetic particle imaging

In magnetic particle imaging (MPI), the spatial distribution of magnetic nanoparticles is determined by applying various static and dynamic magnetic fields. Due to the complex physical behavior of the nanoparticles, it is challenging to determine the MPI system matrix in practice. Since the first publication on MPI in 2005, different methods that rely on measurements or simulations for the determination of the MPI system matrix have been proposed. Some methods restrict the simulation to an idealized model to speed up data reconstruction by exploiting the structure of an idealized MPI system matrix. Recently, a method that processes the measurement data in x-space rather than frequency space has been proposed. In this work, we compare the different approaches for image reconstruction in MPI and show that the x-space and the frequency space reconstruction techniques are equivalent.