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## Abstract Implications of the Rician distribution for fMRI generalized likelihood ratio tests (2004)

### Citations

273 | Analysis of functional MRI time-series.
- Friston, Jezzard, et al.
- 1994
(Show Context)
Citation Context ... better, at least if the correct probability density function (PDF) of the data is taken into account [8]. The most popular test currently applied to fMRI data is the general linear model test (GLMT) =-=[9]-=-. The GLMT is in fact a GLRT under the assumption of Gaussian-distributed noise. It is to be expected that the performance of the tests954 will suffer from the inaccuracy of the Gaussian approximation... |

146 |
Matched subspace detectors,”
- Scharf, Friedlander
- 1994
(Show Context)
Citation Context ...xpression for the modified GLR statistic can be obtained: 2lnk P 1 r2 jjm P P âa 1jj P0 2 h jjm P â P a P1 ˆb P b P rjj2i ð8Þ It can be shown that Eq. (8) will possess an v1 2 distribution under H0 =-=[16]-=-. This allows one to select a proper threshold so as to achieve a desired false alarm rate. Moreover, this means that under the assumption of Gaussian-distributed data, the test under concern will pos... |

80 |
The Rician distribution of noisy MRI data. Magn Reson Med.
- Gudbjartsson, Patz
- 1995
(Show Context)
Citation Context ...se variations due to various sources. However, because magnitude images are obtained by computing the magnitude of complex valued, Gaussian-distributed images, they are known to be Rician distributed =-=[2,3]-=-. Nevertheless, standard tests based on magnitude data generally rely on the assumption that these data are Gaussian distributed, which is a valid assumption only when the signal-to-noise ratio (SNR) ... |

34 |
Zijdenbos AP, Kollokian V, Sled JG, Kabani NJ, Holmes CJ, et al. Design and construction of a realistic digital brain phantom
- DL
- 1998
(Show Context)
Citation Context ...follows. First, a synthetic, noiseless MRI image was generated using an MRI brain simulator, which resembles to some extent real MRI brain data (available from http://www.bic.mni.mcgill.ca/ brainweb) =-=[19]-=-. For each voxel, an fMRI trace was generated using a similar activation curve as described in the first paragraphs of Section 4. Thereby, only in the three square zones activation was induced (see Fi... |

31 | I.: Activation detection in functional MRI using subspace modeling and maximum likelihood estimation.
- Ardekani, Kershaw, et al.
- 1999
(Show Context)
Citation Context ...ted for a number of cycles. The activation-baseline pattern can be represented by a periodic rectangular waveform with values of +1 and 1 representing activation and baseline conditions, respectively =-=[17]-=-. For this reason, for the sake of simplicity, a square wave was chosen as a reference function in our experiments. Note, however, that the theory presented in this paper, as well as the conclusions d... |

13 |
A complex way to compute fMRI activation. Neuroimage 2004;23:1078–1092
- DB, BR
(Show Context)
Citation Context ...ct small intensity variations generated by neural activation [4]. This would allow to correctly process fMRI series with higher spatial resolution or fMRI images with a large degree of signal dropout =-=[5]-=-. In the past few years, generalized likelihood ratio tests (GLRTs) were developed to account for low SNR fMRI data [5–7]. These tests are based on complex valued data in which the phase in each voxel... |

13 | Parameter estimation from magnitude MR Images
- AJ, Dyck, et al.
(Show Context)
Citation Context ...ion was induced (see Fig. 3A) with l =0.05, l =0.075 and l =0.10. Finally, all fMRI traces were polluted with Rician-distributed noise with standard deviations r =2.5, r =4.0 and r =5.0, respectively =-=[20]-=-. The differences in the parametric map for both the GLMT and the GLRTcan be visually appreciated from Fig. 3. The first column of Fig. 3 shows three square activation regions. The second and third co... |

9 |
Fundamentals of statistical signal processing Volume 2: Detection theory
- SM
- 1998
(Show Context)
Citation Context ... 953–959 It can be shown that, asymptotically (i.e., for NYl), the modified GLR statistic 2 ln _k possesses a vr 2 distribution, that is, a v 2 distribution with r degrees of freedom, when H0 is true =-=[11,12]-=-. If the model is linear in the parameters and the noise is Gaussian distributed, this not only holds asymptotically, but also for a finite number of observations. Knowledge of the statistic’s PDF all... |

9 |
den Dekker AJ. Maximum likelihood estimation of signal amplitude and noise variance from MR data. Magn Reson Med
- Sijbers
(Show Context)
Citation Context ...cussion, it will be assumed that the noise variance r 2 is known. This is usually a valid assumption, because the noise variance can mostly be estimated independently with high accuracy and precision =-=[13,14]-=-. In Section 3.1, we will derive a GLRT based on the assumption of Gaussian-distributed data, which will lead to the well-known GLMT. Next, in Section 3.2, we will derive a new GLRT based on Rician-di... |

8 |
Parameter estimation in the magnitude-only and complexvalued fMRI data models. Neuroimage 2005;25:1124–32
- DB
(Show Context)
Citation Context ... developed to account for low SNR fMRI data [5–7]. These tests are based on complex valued data in which the phase in each voxel is described by a constant phase model [5,6] or a general linear model =-=[7]-=-. However, it has recently been shown that GLRTs based on complex valued data are very sensitive to (even small) errors in the phase model [8]. Moreover, for an increasing number of parameters in the ... |

7 |
Generalized likelihood ratio detection for fMRI using complex data.
- FY, RD
- 1999
(Show Context)
Citation Context ...elihood ratio tests (GLRTs) were developed to account for low SNR fMRI data [5–7]. These tests are based on complex valued data in which the phase in each voxel is described by a constant phase model =-=[5,6]-=- or a general linear model [7]. However, it has recently been shown that GLRTs based on complex valued data are very sensitive to (even small) errors in the phase model [8]. Moreover, for an increasin... |

6 |
Poline J-B, Holmes AP: Statistical limitations in functional neuroimaging I: non-inferential methods and statistical models
- KM, TE
- 1999
(Show Context)
Citation Context ...by both tests. The P value is defined as the probability that the test statistic would assume a value greater than or equal to the observed value under the assumption that H 0 (no activation) is true =-=[21]-=-. In other words, the P value is the smallest significance level at which the null hypothesis would be rejected for the set of observations. A small P value provides strong evidence against the null h... |

4 |
Vetterling WT, Teukolsky S-A, Flannery B-P. Numerical recipes
- WH
- 2001
(Show Context)
Citation Context ...bed above was evaluated, which will be described in Sections 4.1 and 4.2, respectively. For numerical optimization, while running the GLRT test, the routine Amoeba from Numerical Recipes was employed =-=[18]-=-. 4.1. CFAR property First, simulation experiments have been conducted so as to find out to what extent the tests under concern have the CFAR property, that is, whether a specified false alarm rate Pf... |

2 |
An evaluation of methods for detecting brain activations from PET or fMRI images
- AS, MN, et al.
- 1999
(Show Context)
Citation Context ...y statistically analyzing a sequence of MR brain images acquired over time. In the past, many statistical tests have been proposed for the construction of statistical parametric maps (see, e.g., Ref. =-=[1]-=- for an overview). Most of these tests are applied to magnitude MR images, because magnitude images have the advantage to be immune to incidental phase variations due to various sources. However, beca... |

2 |
Bovée WM. Parameter estimation from Rician-distributed data sets using a maximum likelihood estimator: application to T1 and perfusion measurements. Magn Reson Med
- OT, Verhagen
- 1999
(Show Context)
Citation Context ...se variations due to various sources. However, because magnitude images are obtained by computing the magnitude of complex valued, Gaussian-distributed images, they are known to be Rician distributed =-=[2,3]-=-. Nevertheless, standard tests based on magnitude data generally rely on the assumption that these data are Gaussian distributed, which is a valid assumption only when the signal-to-noise ratio (SNR) ... |

1 |
DJ, Hearshen DO, Lajiness-ONeill RR. Model-independent method for fMRI analysis
- Soltanian-Zadeh, Peck
(Show Context)
Citation Context ... is generally compromised. Therefore, it is of great interest to develop reliable methods that would work also on low SNR fMRI data to detect small intensity variations generated by neural activation =-=[4]-=-. This would allow to correctly process fMRI series with higher spatial resolution or fMRI images with a large degree of signal dropout [5]. In the past few years, generalized likelihood ratio tests (... |

1 |
den Dekker AJ. Generalized likelihood ratio tests for complex fMRI data: a simulation study
- Sijbers
(Show Context)
Citation Context ...by a constant phase model [5,6] or a general linear model [7]. However, it has recently been shown that GLRTs based on complex valued data are very sensitive to (even small) errors in the phase model =-=[8]-=-. Moreover, for an increasing number of parameters in the phase model, the detection rate of those GLRTs drops drastically. Hence, tests based on magnitude data instead of complex valued data are like... |

1 |
The Emeraude Environment, Reference
- unknown authors
- 1990
(Show Context)
Citation Context ... 953–959 It can be shown that, asymptotically (i.e., for NYl), the modified GLR statistic 2 ln _k possesses a vr 2 distribution, that is, a v 2 distribution with r degrees of freedom, when H0 is true =-=[11,12]-=-. If the model is linear in the parameters and the noise is Gaussian distributed, this not only holds asymptotically, but also for a finite number of observations. Knowledge of the statistic’s PDF all... |

1 |
Renou JP, Zanca M. Optimal measurement of magnitude and phase from MR data
- JM
- 1996
(Show Context)
Citation Context ...cussion, it will be assumed that the noise variance r 2 is known. This is usually a valid assumption, because the noise variance can mostly be estimated independently with high accuracy and precision =-=[13,14]-=-. In Section 3.1, we will derive a GLRT based on the assumption of Gaussian-distributed data, which will lead to the well-known GLMT. Next, in Section 3.2, we will derive a new GLRT based on Rician-di... |

1 |
Bos A. Handbook of measurement science
- den
(Show Context)
Citation Context ...ood function of the data is given by Lðz; mÞ 1 2pr 2 N 2 e 1 2r2jjm zjj2 ð5Þ Closed form expressions for the maximum likelihood estimators (MLEs) of the unspecified parameters can easily be derived =-=[15]-=-. Under H0, in which z =a1, the MLE â0 of the parameter a is given by P âa 1 P0 N m P T :1 ð6Þ Under H1, in which z =a1+br, the MLEs â1 and bˆ of the parameters a and b are given by P âa P1 ˆb P b !... |