Data distributions in magnetic resonance images: a review.

[1]  H. Nyquist.  Thermal Agitation of Electric Charge in Conductors , 1928 .

[2]  D. A. Wilbur.  Thermal Agitation of Electricity in Conductors. , 1932 .

[3]  S. Rice.  Mathematical analysis of random noise , 1944 .

[4]  H. Cramér.  Mathematical Methods of Statistics (PMS-9), Volume 9 , 1946 .

[5]  E. Bedrosian.  A Product Theorem for Hilbert Transforms , 1963 .

[6]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[7]  B. P. Lathi.  An introduction to random signals Communication theory , 1968 .

[8]  Franklin A. Graybill,et al.  Introduction to The theory , 1974 .

[9]  Franklin A. Graybill,et al.  Introduction to the Theory of Statistics, 3rd ed. , 1974 .

[10]  W. Edelstein,et al.  A signal-to-noise calibration procedure for NMR imaging systems. , 1984, Medical physics.

[11]  John G. Proakis,et al.  Probability, random variables and stochastic processes , 1985, IEEE Trans. Acoust. Speech Signal Process..

[12]  R. Henkelman.  Measurement of signal intensities in the presence of noise in MR images. , 1985, Medical physics.

[13]  R. Henkelman.  Erratum: Measurement of signal intensities in the presence of noise in MR images [Med. Phys. 12, 232 (1985)] , 1986 .

[14]  J. Koenig,et al.  Calculation of T1, T2, and proton spin density images in nuclear magnetic resonance imaging , 1989 .

[15]  Alex L. MacKay,et al.  Quantitative interpretation of NMR relaxation data , 1989 .

[16]  P. Roemer,et al.  Noise correlations in data simultaneously acquired from multiple surface coil arrays , 1990, Magnetic resonance in medicine.

[17]  P. Roemer,et al.  The NMR phased array , 1990, Magnetic resonance in medicine.

[18]  J. Pauly,et al.  A homogeneity correction method for magnetic resonance imaging with time-varying gradients. , 1991, IEEE transactions on medical imaging.

[19]  M. Bronskill,et al.  Investigation of analysis techniques for complicated NMR relaxation data , 1991 .

[20]  G. Glover,et al.  Encoding strategies for three‐direction phase‐contrast MR imaging of flow , 1991, Journal of magnetic resonance imaging : JMRI.

[21]  M. Harpen.  Noise correlations exist for independent RF coils , 1992, Magnetic resonance in medicine.

[22]  James L. Massey,et al.  Proper complex random processes with applications to information theory , 1993, IEEE Trans. Inf. Theory.

[23]  J. Hogg.  Magnetic resonance imaging. , 1994, Journal of the Royal Naval Medical Service.

[24]  Bernard C. Picinbono,et al.  On circularity , 1994, IEEE Trans. Signal Process..

[25]  H. Gudbjartsson,et al.  The rician distribution of noisy mri data , 1995, Magnetic resonance in medicine.

[26]  Adriaan van den Bos,et al.  The multivariate complex normal distribution-a generalization , 1995, IEEE Trans. Inf. Theory.

[27]  Sailes K. Sengijpta.  Fundamentals of Statistical Signal Processing: Estimation Theory , 1995 .

[28]  J. Boire,et al.  T2 maximum likelihood estimation from multiple spin‐echo magnitude images , 1996, Magnetic resonance in medicine.

[29]  A. Macovski.  Noise in MRI , 1996, Magnetic resonance in medicine.

[30]  M. T. Vlaardingerbroek,et al.  Magnetic Resonance Imaging: Theory and Practice , 1996 .

[31]  Bonny,et al.  Optimal Measurement of Magnitude and Phase from MR Data , 1996, Journal of magnetic resonance. Series B.

[32]  A. H. Andersen,et al.  Analysis of noise in phase contrast MR imaging. , 1996, Medical physics.

[33]  M. Donahue,et al.  Artifacts in magnetic resonance imaging from metals , 1996 .

[34]  E. McVeigh,et al.  Signal‐to‐noise measurements in magnitude images from NMR phased arrays , 1997 .

[35]  J Sijbers,et al.  Estimation of the noise in magnitude MR images. , 1998, Magnetic resonance imaging.

[36]  Jan Sijbers,et al.  Maximum-likelihood estimation of Rician distribution parameters , 1998, IEEE Transactions on Medical Imaging.

[37]  Jan Sijbers,et al.  Maximum-likelihood signal estimation in phase contrast magnitude MR images , 1998, Medical Imaging.

[38]  O. Karlsen,et al.  Parameter estimation from Rician‐distributed data sets using a maximum likelihood estimator: Application to t1 and perfusion measurements , 1999, Magnetic resonance in medicine.

[39]  Jan Sijbers,et al.  Parameter estimation from magnitude MR images , 1999, Int. J. Imaging Syst. Technol..

[40]  P. Lauterbur,et al.  Principles of magnetic resonance imaging : a signal processing perspective , 1999 .

[41]  P. Boesiger,et al.  SENSE: Sensitivity encoding for fast MRI , 1999, Magnetic resonance in medicine.

[42]  V. Kuperman.  Signal-to-Noise Ratio in MRI , 2000 .

[43]  Vadim Kuperman,et al.  Magnetic Resonance Imaging: Physical Principles and Applications , 2000 .

[44]  Steven Kay,et al.  Fundamentals Of Statistical Signal Processing , 2001 .

[45]  M. Simon.  Probability distributions involving Gaussian random variables : a handbook for engineers and scientists , 2002 .

[46]  Paul C. Lauterbur,et al.  Principles of magnetic resonance imaging : a signal processing perspective , 1999 .

[47]  William H. Press,et al.  Numerical recipes in C , 2002 .

[48]  Robin M Heidemann,et al.  SMASH, SENSE, PILS, GRAPPA: How to Choose the Optimal Method , 2004, Topics in magnetic resonance imaging : TMRI.

[49]  J. Sijbers,et al.  Maximum likelihood estimation of signal amplitude and noise variance from MR data , 2004, Magnetic resonance in medicine.

[50]  J. Reichenbach,et al.  Magnetic susceptibility-weighted MR phase imaging of the human brain. , 2005, AJNR. American journal of neuroradiology.

[51]  R. Mohiaddin,et al.  Applications of phase-contrast flow and velocity imaging in cardiovascular MRI , 2005, European Radiology.

[52]  Wesley E. Snyder,et al.  Magnetic Resonance Image restoration , 2005, Journal of Mathematical Imaging and Vision.

[53]  J. Gieseke,et al.  Blood flow quantification in adults by phase-contrast MRI combined with SENSE--a validation study. , 2005, Journal of cardiovascular magnetic resonance : official journal of the Society for Cardiovascular Magnetic Resonance.

[54]  J. Sijbers,et al.  Estimation of Signal and Noise Parameters from MR Data , 2005 .

[55]  J. Sijbers,et al.  Automatic estimation of the noise variance from the histogram of a magnetic resonance image , 2007, Physics in medicine and biology.

[56]  A. Bos.  Parameter Estimation for Scientists and Engineers , 2007 .

[57]  D. Donoho,et al.  Sparse MRI: The application of compressed sensing for rapid MR imaging , 2007, Magnetic resonance in medicine.

[58]  S. Schoenberg,et al.  Influence of multichannel combination, parallel imaging and other reconstruction techniques on MRI noise characteristics. , 2008, Magnetic resonance imaging.

[59]  Carl-Fredrik Westin,et al.  Noise and Signal Estimation in Magnitude MRI and Rician Distributed Images: A LMMSE Approach , 2008, IEEE Transactions on Image Processing.

[60]  M. Lustig,et al.  Compressed Sensing MRI , 2008, IEEE Signal Processing Magazine.

[61]  Pooi Yuen Kam,et al.  Exact phase noise model and its application to linear minimum variance estimation of frequency and phase of a noisy sinusoid , 2008, 2008 IEEE 19th International Symposium on Personal, Indoor and Mobile Radio Communications.

[62]  T. Hohage,et al.  Image reconstruction by regularized nonlinear inversion—Joint estimation of coil sensitivities and image content , 2008, Magnetic resonance in medicine.

[63]  Jesper L. R. Andersson,et al.  Maximum a posteriori estimation of diffusion tensor parameters using a Rician noise model: Why, how and but , 2008, NeuroImage.

[64]  V. Lee,et al.  Cardiovascular applications of phase-contrast MRI. , 2009, AJR. American journal of roentgenology.

[65]  Ian R. Greenshields,et al.  A Nonlocal Maximum Likelihood Estimation Method for Rician Noise Reduction in MR Images , 2009, IEEE Transactions on Medical Imaging.

[66]  Giampaolo Ferraioli,et al.  Relaxation Time Estimation from Complex Magnetic Resonance Images , 2010, Sensors.

[67]  Bing Wu,et al.  High-field (9.4T) MRI of brain dysmyelination by quantitative mapping of magnetic susceptibility , 2011, NeuroImage.

[68]  W. Hoge,et al.  Statistical noise analysis in GRAPPA using a parametrized noncentral Chi approximation model , 2011, Magnetic resonance in medicine.

[69]  S. Aja‐Fernández,et al.  Influence of noise correlation in multiple‐coil statistical models with sum of squares reconstruction , 2012, Magnetic resonance in medicine.

[70]  Jeny Rajan.  Estimation and removal of noise from single and multiple coil magnetic resonance images , 2012 .

[71]  Ferdinand Schweser,et al.  Quantitative susceptibility mapping for investigating subtle susceptibility variations in the human brain , 2012, NeuroImage.

[72]  Torsten Rohlfing,et al.  MRI estimates of brain iron concentration in normal aging using quantitative susceptibility mapping , 2011, NeuroImage.

[73]  D. Louis Collins,et al.  New methods for MRI denoising based on sparseness and self-similarity , 2012, Medical Image Anal..

[74]  José M. F. Moura,et al.  On the Product of Independent Complex Gaussians , 2012, IEEE Transactions on Signal Processing.

[75]  B. Martin.  PARAMETER ESTIMATION , 2012, Statistical Methods for Biomedical Research.

[76]  J. Sijbers,et al.  Nonlocal maximum likelihood estimation method for denoising multiple-coil magnetic resonance images. , 2012, Magnetic resonance imaging.

[77]  Ferdinand Schweser,et al.  Quantitative susceptibility mapping (QSM) as a means to measure brain iron? A post mortem validation study , 2012, NeuroImage.

[78]  A. Leemans,et al.  Comprehensive framework for accurate diffusion MRI parameter estimation , 2013, Magnetic resonance in medicine.

[79]  Santiago Aja-Fernández,et al.  Noise estimation in magnetic resonance SENSE reconstructed data , 2013, 2013 35th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC).

[80]  M. L. Lauzon,et al.  A statistical method for characterizing the noise in nonlinearly reconstructed images from undersampled MR data: the POCS example. , 2013, Magnetic resonance imaging.

[81]  Jan Sijbers,et al.  Weighted linear least squares estimation of diffusion MRI parameters: Strengths, limitations, and pitfalls , 2013, NeuroImage.

[82]  Santiago Aja-Fernández,et al.  Effective noise estimation and filtering from correlated multiple-coil MR data. , 2013, Magnetic resonance imaging.

[83]  Karen O. Egiazarian,et al.  Nonlocal Transform-Domain Filter for Volumetric Data Denoising and Reconstruction , 2013, IEEE Transactions on Image Processing.

[84]  C. Muravchik,et al.  Error bounds in diffusion tensor estimation using multiple-coil acquisition systems. , 2013, Magnetic resonance imaging.

[85]  Tatiana V. Yakovleva,et al.  Noise and signal estimation in MRI: two-parametric analysis of rice-distributed data by means of the maximum likelihood approach , 2013 .

[86]  Jan Sijbers,et al.  A new non-local maximum likelihood estimation method for Rician noise reduction in magnetic resonance images using the Kolmogorov-Smirnov test , 2014, Signal Process..

[87]  Haosen Zhang,et al.  Improve myocardial T1 measurement in rats with a new regression model: Application to myocardial infarction and beyond , 2014, Magnetic resonance in medicine.