Journal ArticleDOI
A new method of magnetic resonance image reconstruction with short acquisition time and truncation artifact reduction
P. Barone,G. Sebastiani +1 more
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A method for the reconstruction of magnetic resonance images that allows for a substantial reduction of the quantity of measured data and, therefore, of the acquisition time is described and the truncation artifact is reduced, improving the image quality.Abstract:
A method for the reconstruction of magnetic resonance images that allows for a substantial reduction of the quantity of measured data and, therefore, of the acquisition time is described. The truncation artifact is also reduced, improving the image quality. The method is based on techniques for getting superresolution in spectral analysis such as autoregressive modeling and Prony's method. Moreover, some new ideas about the autoregressive order selection are introduced. The method is compared to the standard one for reconstructing simulated, phantom, and medical magnetic resonance images. The numerical stability and the computational cost issues of the resulting algorithm are also addressed. >read more
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Journal ArticleDOI
Linear Differential Operators. By C. Lanczos. Pp. 580. 80s. 1961. (Van Nostrand, London)
TL;DR: In this article, the Fourier series for differentiable functions of higher differentiability has been studied and an alternative method of estimation has been proposed for estimating the Gibbs oscillations of the finite Fourier expansion.
Journal ArticleDOI
Low-Rank Modeling of Local $k$ -Space Neighborhoods (LORAKS) for Constrained MRI
TL;DR: A novel and flexible framework for constrained image reconstruction that uses low-rank matrix modeling of local k-space neighborhoods (LORAKS) and enables calibrationless use of phase constraints, while calibration-based support and phase constraints are commonly used in existing methods.
Journal ArticleDOI
Adaptive weights smoothing with applications to image restoration
Jörg Polzehl,Vladimir Spokoiny +1 more
TL;DR: In this article, the authors proposed a nonparametric estimation method based on locally constant smoothing with an adaptive choice of weights for every pair of data points, and demonstrated the performance of the method on some simulated univariate and bivariate examples.
Journal ArticleDOI
On the numerical inversion of the Laplace transform for nuclear magnetic resonance relaxometry
TL;DR: In this article, several different methods, both deterministic and stochastic, were studied to solve the nuclear magnetic resonance relaxometry problem, which is strongly related to finding a non-negative function given a finite number of values of its Laplace transform embedded in noise.
Journal ArticleDOI
MRI Gibbs-ringing artifact reduction by means of machine learning using convolutional neural networks.
Qianqian Zhang,Guohui Ruan,Wei Yang,Yilong Liu,Kaixuan Zhao,Qianjin Feng,Wufan Chen,Ed X. Wu,Yanqiu Feng +8 more
TL;DR: A machine learning approach using convolutional neural network for reducing MRI Gibbs‐ringing artifact is developed and a novel approach to solve the challenge of reducing Gibbs-ringing artifacts is proposed.
References
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Prolate spheroidal wave functions, fourier analysis and uncertainty — II
David Slepian,H. O. Pollak +1 more
TL;DR: In this paper, the authors apply the theory developed in the preceding paper to a number of questions about timelimited and bandlimited signals, and find the signals which do the best job of simultaneous time and frequency concentration.
Digital spectral analysis with applications
TL;DR: In this article, a broad perspective of spectral estimation techniques and their implementation is provided, focusing on spectral estimation of discretespace sequences derived by sampling continuous space signals, including parametric methods, minimum variance method, eigenanalysis-based estimators, multichannel methods, and twodimensional methods.
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