Model-based reconstruction for magnetic particle imaging in 2D and 3D

März, Thomas; Weinmann, Andreas

doi:10.3934/ipi.2016033

Cited by 27 publications

(31 citation statements)

References 44 publications

(80 reference statements)

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“…A first step towards a theoretical understanding of this problem, while excluding the temporal dependence, can be found in [39]. A one-dimensional problem setup considering the time-dependency of the measurements was analyzed in [11] for one particular trigonometric excitation.…”

Section: Appendix Iii: Magnetic Particle Imaging (Mpi)mentioning

confidence: 99%

Regularization by Architecture: A Deep Prior Approach for Inverse Problems

et al. 2019

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The present paper studies the so called deep image prior (DIP) technique in the context of inverse problems. DIP networks have been introduced recently for applications in image processing, [50], also first experimental results for applying DIP to inverse problems have been reported [51]. This paper aims at discussing different interpretations of DIP and to obtain analytic results for specific network designs and linear operators. The main contribution is to introduce the idea of viewing these approaches as the optimization of Tiknonov functionals rather than optimizing networks. Besides theoretical results, we present numerical verifications for an academic example (integration operator) as well as for the inverse problem of magnetic particle imaging (MPI). The reconstructions obtained by deep prior networks are compared with state of the art methods.

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Section: Appendix Iii: Magnetic Particle Imaging (Mpi)mentioning

confidence: 99%

Regularization by Architecture: A Deep Prior Approach for Inverse Problems

et al. 2019

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“…MPI is a new biomedical imaging modality that images the distribution of SPIONs. Some researchers adopt mathematical models to describe the physical process, like the equilibrium model [ 25 ] or its variations, the x-space approach [ 3 , 26 , 27 , 28 ], Chebyshev polynomials [ 29 ], and analytic inversion formulas [ 30 , 31 ]. The state-of-the-art reconstruction techniques adopt the experimentally calibrated forward operators, called the SM-based image reconstruction [ 32 , 33 ].…”

Section: The Theory Of Sm-based Mpimentioning

confidence: 99%

“…The average NRMSE of all frequency components is around 10%. In 2017, Marz performed mathematical modeling on the reconstruction of two-dimensional and three-dimensional MPI and obtained a reconstruction formula different from one-dimensional [ 30 ]. In the same year, Knopp described the basic principles of MPI imaging, including signal generation, spatial coding, and signal detection [ 37 ].…”

Section: The Theory Of Sm-based Mpimentioning

confidence: 99%

The Reconstruction of Magnetic Particle Imaging: Current Approaches Based on the System Matrix

et al. 2021

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Magnetic particle imaging (MPI) is a novel non-invasive molecular imaging technology that images the distribution of superparamagnetic iron oxide nanoparticles (SPIONs). It is not affected by imaging depth, with high sensitivity, high resolution, and no radiation. The MPI reconstruction with high precision and high quality is of enormous practical importance, and many studies have been conducted to improve the reconstruction accuracy and quality. MPI reconstruction based on the system matrix (SM) is an important part of MPI reconstruction. In this review, the principle of MPI, current construction methods of SM and the theory of SM-based MPI are discussed. For SM-based approaches, MPI reconstruction mainly has the following problems: the reconstruction problem is an inverse and ill-posed problem, the complex background signals seriously affect the reconstruction results, the field of view cannot cover the entire object, and the available 3D datasets are of relatively large volume. In this review, we compared and grouped different studies on the above issues, including SM-based MPI reconstruction based on the state-of-the-art Tikhonov regularization, SM-based MPI reconstruction based on the improved methods, SM-based MPI reconstruction methods to subtract the background signal, SM-based MPI reconstruction approaches to expand the spatial coverage, and matrix transformations to accelerate SM-based MPI reconstruction. In addition, the current phantoms and performance indicators used for SM-based reconstruction are listed. Finally, certain research suggestions for MPI reconstruction are proposed, expecting that this review will provide a certain reference for researchers in MPI reconstruction and will promote the future applications of MPI in clinical medicine.

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“…The mathematical study on the MPI model is fairly scarce. The only work on FFP trajectories that we are aware of is the work [31]. In a 1D setup with FFP trajectories moving along a line for the equilibrium model, the authors [31] showed that in the limit of large particle diameters, the integral kernel is a Diracdelta function, and thus the imaging problem is well-posed.…”

Section: Introductionmentioning

confidence: 99%

“…The only work on FFP trajectories that we are aware of is the work [31]. In a 1D setup with FFP trajectories moving along a line for the equilibrium model, the authors [31] showed that in the limit of large particle diameters, the integral kernel is a Diracdelta function, and thus the imaging problem is well-posed. Further, they analyzed a related problem which is independent of the FFP trajectory used, under the assumption that each spatial point is scanned multiple times with nonparallel trajectories.…”

Section: Introductionmentioning

confidence: 99%

On the degree of ill-posedness of multi-dimensional magnetic particle imaging

Kluth

Jin

2018

Inverse Problems

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Magnetic particle imaging is an imaging modality of relatively recent origin, and it exploits the nonlinear magnetization response for reconstructing the concentration of nanoparticles. Since first invented in 2005, it has received much interest in the literature. In this work, we study one prototypical mathematical model in multi-dimension, i.e., the equilibrium model, which formulates the problem as a linear Fredholm integral equation of the first kind. We analyze the degree of ill-posedness of the associated linear integral operator by means of the singular value decay estimate for Sobolev smooth bivariate functions, and discuss the influence of various experimental parameters on the decay rate. In particular, applied magnetic fields with a field free point and a field free line are distinguished. The study is complemented with extensive numerical experiments. Keywords: magnetic particle imaging; degree of ill-posedness; equilibrium model; singular value decay; Sobolev smooth bivariate functions.

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Model-based reconstruction for magnetic particle imaging in 2D and 3D

Cited by 27 publications

References 44 publications

Regularization by Architecture: A Deep Prior Approach for Inverse Problems

Regularization by Architecture: A Deep Prior Approach for Inverse Problems

The Reconstruction of Magnetic Particle Imaging: Current Approaches Based on the System Matrix

On the degree of ill-posedness of multi-dimensional magnetic particle imaging

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