Non-Equispaced System Matrix Acquisition for Magnetic Particle Imaging Based on Lissajous Node Points

Kaethner, Christian; Erb, Wolfgang; Ahlborg, Mandy; Szwargulski, Patryk; Knopp, Tobias; Buzug, Thorsten M.

doi:10.1109/tmi.2016.2580458

Cited by 32 publications

(25 citation statements)

References 32 publications

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“…In our upcoming tests, we will use the points LS (n) 2 , with n 1 , n 2 relatively prime and n 1 + n 2 odd as underlying interpolation nodes. These node sets were already used in [10,14,23] for applications in MPI. The number of points is given by #LS (n) 2 = 2n 1 n 2 + n 1 + n 2 , see [12,14].…”

Section: Lissajous Interpolation Nodesmentioning

confidence: 99%

“…Commonly used trajectories in MPI are Lissajous curves [25]. To reduce the amount of calibration measurements, it is shown in [23] that the reconstruction can be restricted to particular sampling points along the Lissajous curves, i.e., the Lissajous nodes LS (n) 2 introduced in (4.2). By using a polynomial interpolation method on the Lissajous nodes [12] the entire density of the magnetic particles can then be restored.…”

Section: Applications In Magnetic Particlementioning

confidence: 99%

See 1 more Smart Citation

Shape-Driven Interpolation With Discontinuous Kernels: Error Analysis, Edge Extraction, and Applications in Magnetic Particle Imaging

Marchi¹,

Erb²,

Marchetti³

et al. 2020

SIAM J. Sci. Comput.

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Accurate interpolation and approximation techniques for functions with discontinuities are key tools in many applications as, for instance, medical imaging. In this paper, we study an RBF type method for scattered data interpolation that incorporates discontinuities via a variable scaling function. For the construction of the discontinuous basis of kernel functions, information on the edges of the interpolated function is necessary. We characterize the native space spanned by these kernel functions and study error bounds in terms of the fill distance of the node set. To extract the location of the discontinuities, we use a segmentation method based on a classification algorithm from machine learning. The conducted numerical experiments confirm the theoretically derived convergence rates in case that the discontinuities are a priori known. Further, an application to interpolation in magnetic particle imaging shows that the presented method is very promising.

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Section: Lissajous Interpolation Nodesmentioning

confidence: 99%

Section: Applications In Magnetic Particlementioning

confidence: 99%

Shape-Driven Interpolation With Discontinuous Kernels: Error Analysis, Edge Extraction, and Applications in Magnetic Particle Imaging

Marchi¹,

Erb²,

Marchetti³

et al. 2020

SIAM J. Sci. Comput.

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“…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 ]. The SM is the discretized representation of the system function (SF), which describes the mapping of the spatial concentration distribution and the induced voltage signal, including magnetic field characteristics and complex particle characteristics [ 34 ].…”

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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“…Nevertheless, to our knowledge, its usage in image processing has been mainly limited to particular cases, such as Magnetic Particle Imaging that is strictly related to Lissajous curves generating the Padua points ( see e.g. [21,18,14]).…”

Section: Introductionmentioning

confidence: 99%

Lagrange-Chebyshev Interpolation for image resizing

Ramella¹,

Themistoclakis²

2021

Preprint

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Image resizing is a basic tool in image processing and in literature we have many methods, based on different approaches, which are often specialized in only upscaling or downscaling. In this paper, independently of the (reduced or enhanced) size we aim to get, we approach the problem at a continuous scale where the underlying continuous image is globally approximated by the tensor product Lagrange polynomial interpolating at a suitable grid of first kind Chebyshev zeros. This is a well-known approximation tool that is widely used in many applicative fields, due to the optimal behavior of the related Lebesgue constants. Here we show how Lagrange-Chebyshev interpolation can be fruitfully applied also for resizing an arbitrary digital image in both downscaling and upscaling. The performance of the proposed method has been tested in terms of the standard SSIM and PSNR metrics. The results indicate that, in upscaling, it is almost comparable with the classical Bicubic resizing method with slightly better metrics, but in downscaling a much higher performance has been observed in comparison with Bicubic and other recent methods too. Moreover, in downscaling cases with an odd scale factor, we give an estimate of the mean squared error produced by our method and prove it is theoretically null (hence PSNR equals to infinite and SSIM equals to one) in absence of noise or initial artifacts on the input image.

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Non-Equispaced System Matrix Acquisition for Magnetic Particle Imaging Based on Lissajous Node Points

Cited by 32 publications

References 32 publications

Shape-Driven Interpolation With Discontinuous Kernels: Error Analysis, Edge Extraction, and Applications in Magnetic Particle Imaging

Shape-Driven Interpolation With Discontinuous Kernels: Error Analysis, Edge Extraction, and Applications in Magnetic Particle Imaging

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

Lagrange-Chebyshev Interpolation for image resizing

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