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Constrained reconstruction: A superresolution, optimal signal‐to‐noise alternative to the Fourier transform in magnetic resonance imaging
Author(s) -
Haacke E. Mark,
Liang ZhiPei,
Izen Steven H.
Publication year - 1989
Publication title -
medical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.473
H-Index - 180
eISSN - 2473-4209
pISSN - 0094-2405
DOI - 10.1118/1.596427
Subject(s) - ringing , ringing artifacts , iterative reconstruction , singular value decomposition , fourier transform , algorithm , synthetic data , gibbs phenomenon , computer science , image restoration , gaussian noise , image processing , mathematics , artificial intelligence , computer vision , filter (signal processing) , mathematical analysis , image (mathematics)
Many problems in physics involve imaging objects with high spatial frequency content in a limited amount of time. The limitation of available experimental data leads to the infamous problem of diffraction limited data which manifests itself by causing ringing in the image. This ringing is due to the interference phenomena in optics and is known as the Gibbs phenomenon in engineering. Present tehniques to cope with this problem include filtering and regularization schemes based on minimum norm or maximum entropy constraints. In this paper, a new technique based on object modeling and estimation is developed to achieve superresolution reconstruction from partial Fourier transform data. The nonlinear parameters of the object model are obtained using the singular value decomposition (SVD)‐based all‐pole model framework, and the linear parameters are determined using a standard least squares estimation method. This technique is capable, in principle, of unlimited resolution and is robust with respect to Gaussian white noise perturbation to the measured data and with respect to systematic modeling errors. Reconstruction results from simulated data and real magnetic resonance data are presented to illustrate the performance of the proposed method.