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## Generalized likelihood ratio tests for complex FMRI data : a simulation study (2005)

Venue: | IEEE Trans. on Medical Imaging |

Citations: | 2 - 0 self |

### Citations

676 |
Nonlinear Regression
- Seber, Wild
- 2003
(Show Context)
Citation Context ...a closed-form expression for the GLR can be obtained (22) with and given by (17) and (21), respectively. Furthermore, it can be shown that the test statistic (23) is asymptotically -distributed under =-=[24]-=-. The test will decide if and only if the test statistic (23) exceeds a user specified threshold value. In order to achieve a specified false alarm rate , this threshold should be chosen equal to (i.e... |

317 | Analysis of fMRI data by blind separation into independent spatial components,”
- McKeown
- 1998
(Show Context)
Citation Context ... the incorporation of a hemodynamic response function. Furthermore, more flexible and general variants of the general linear model were developed such as tests based on independent component analysis =-=[16]-=-, [27], multiresolution analysis [4], and likelihood ratio tests [19], [22]. Although magnetic resonance data are intrinsically complex valued, statistical tests are generally applied to magnitude fMR... |

273 | Analysis of functional MRI time-series.
- Friston, Jezzard, et al.
- 1994
(Show Context)
Citation Context ...n order to achieve a specified false alarm rate , this threshold should be chosen equal to . Note that this test is identical to the well-known generalized linear model test applied to magnitude data =-=[6]-=-. IV. SIMULATION RESULTS AND DISCUSSION Monte Carlo simulation experiments were set up to compare the performance of the GLRT for magnitude data to the performance of the GLRTs based on complex data. ... |

251 |
Event-related fMRI: characterizing differential responses,”
- Friston, Fletcher, et al.
- 1998
(Show Context)
Citation Context ...with the Delft University of Technology, Delft Center for Systems and Control, 2628CD Delft, The Netherlands (e-mail: a.j.dendekker@dcsc.tudelft.nl). Digital Object Identifier 10.1109/TMI.2005.844075 =-=[5]-=-. A main advancement of the GLM test was the incorporation of a hemodynamic response function. Furthermore, more flexible and general variants of the general linear model were developed such as tests ... |

211 | Temporal autocorrelation in univariate linear modeling of FMRI data.
- Woolrich, Ripley, et al.
- 2001
(Show Context)
Citation Context ...own in the background (gray denotes stimulus). over thermal noise). However, if the data are observed to be correlated, they can be whitened based on an estimated autocorrelation structure [2], [19], =-=[29]-=-–[30]. Moreover, valuable methods exist to eliminate, for example, physiological noise from the fMRI time courses, prior to activation detection [3], [7], [28]. Hence, the conclusions of this work can... |

165 | The Rician distribution of noisy MRI data.
- Gudbjartsson, Patz
- 1995
(Show Context)
Citation Context ...tude data are derived from complex valued data of which the components are Gaussian distributed). The Rician PDF of magnitude data with deterministic signal component and noise variance , is given by =-=[8]-=-: (4) where is the zeroth order modified Bessel function of the first kind. With increasing SNR (defined as ), the Rician distribution tends to a Gaussian distribution [26]. 1) ML estimation under : T... |

153 |
Statistique exploratoire multidimensionelle. París: dunod Martínez de
- lebart, morineau, et al.
- 1998
(Show Context)
Citation Context ...hase model. However, the lack of CFAR property may be explained by the fact that for a random phase model the number of estimated parameters is very large in comparison with the number of data points =-=[14]-=-. These results, summarized in Table I, indicate that, for a very wide range of SNRs (simulations were run for SNRs larger than 1), a GLRT for magnitude data holds the CFAR property. On the other hand... |

148 |
A general statistical analysis for fMRI data,”
- Worsley, Liao, et al.
- 2002
(Show Context)
Citation Context ...n the background (gray denotes stimulus). over thermal noise). However, if the data are observed to be correlated, they can be whitened based on an estimated autocorrelation structure [2], [19], [29]–=-=[30]-=-. Moreover, valuable methods exist to eliminate, for example, physiological noise from the fMRI time courses, prior to activation detection [3], [7], [28]. Hence, the conclusions of this work can easi... |

107 |
Functional mapping of the human visual cortex by magnetic resonance imaging
- Belliveau, Kennedy, et al.
- 1991
(Show Context)
Citation Context ...s, often referred to as statistical parametric maps (SPMs). Initial detection methods were based on simple subtraction of images acquired during a resting state from images acquired during activation =-=[1]-=-, [31]. In order to improve the detection rate, activation detection methods using the -score, correlation coefficients, analysis of variance, or Student- test statistics were employed [20], [23]. Tho... |

87 |
Introduction to the theory of statistics. 3rd ed.
- Mood, Graybill, et al.
- 1985
(Show Context)
Citation Context ...s. the unknown parameter vector only. By regarding these parameters as variables, the so called likelihood function is obtained. Then the generalized likelihood-ratio (GLR) is defined as follows [9], =-=[18]-=-: (2) Note that is a function of the observations only. If these observations are replaced by their corresponding random variables , then we write for , that is, . Since is a function of the random ve... |

80 | Image-based method for retrospective correction of physiological motion effects in fMRI: RETROICOR,"
- Glover, Li, et al.
- 2000
(Show Context)
Citation Context ...stimated autocorrelation structure [2], [19], [29]–[30]. Moreover, valuable methods exist to eliminate, for example, physiological noise from the fMRI time courses, prior to activation detection [3], =-=[7]-=-, [28]. Hence, the conclusions of this work can easily be extended to more realistic noise models that incorporate colored noise. The organization of this paper is as follows. Section II briefly revie... |

41 | Functional magnetic resonance imaging of complex human movements. - Rao, Binder, et al. - 1993 |

41 |
Functional topographic mapping of the cortical ribbon in human vision with conventional MRI scanners.
- Schneider, Noll, et al.
- 1993
(Show Context)
Citation Context ...ation [1], [31]. In order to improve the detection rate, activation detection methods using the -score, correlation coefficients, analysis of variance, or Student- test statistics were employed [20], =-=[23]-=-. Those tests all fit into the framework of the so-called general linear model (GLM) test Manuscript received November 17, 2004; revised January 6, 2005. The Associate Editor responsible for coordinat... |

39 |
Introduction to Statistical Theory.
- Hoel, Port, et al.
- 1971
(Show Context)
Citation Context ...trices. the unknown parameter vector only. By regarding these parameters as variables, the so called likelihood function is obtained. Then the generalized likelihood-ratio (GLR) is defined as follows =-=[9]-=-, [18]: (2) Note that is a function of the observations only. If these observations are replaced by their corresponding random variables , then we write for , that is, . Since is a function of the ran... |

39 |
Diagnosis and exploration of massively univariate neuroimaging models.
- Luo, Nichols
- 2003
(Show Context)
Citation Context ... apply a GLRT based on magnitude data?”. In order to simplify the discussion (as was also done by Nan and Nowak), the noise disturbing the fMRI time series is assumed to be Gaussian white noise [13], =-=[15]-=-, [19]. The white noise model may be an oversimplification of the noises inherent in fMRI (especially if physiological noise is dominant 0278-0062/$20.00 © 2005 IEEE SIJBERS AND DEN DEKKER: GLRTS FOR ... |

35 |
Generalized likelihood ratio detection for fMRI using complex data.
- Nan, Nowak
- 1999
(Show Context)
Citation Context ... the past five years, new tests were developed that incorporate the complex nature of fMRI data. In particular, a generalized likelihood ratio test (GLRT) was proposed based on a constant phase model =-=[19]-=-. In this work, we evaluate the sensitivity of GLRTs for complex data to small misspecifications of the phase model by means of simulation experiments. It is argued that, in practical situations, GLRT... |

33 |
Postacquisition suppression of large-vessel BOLD signals in high-resolution fMRI.
- Menon
- 2002
(Show Context)
Citation Context ... exhibit activation-dependent modulations, especially for voxels with large venous blood fractions (i.e., voxels with high blood volume fractions show a time-dependency related to the paradigm) [10], =-=[17]-=-. On the other hand, since in most fMRI studies, a voxel contains a large ensemble of vessels with various orientations and sizes, the assumption of a constant phase value may still be appropriate. Ho... |

33 | A complex way to compute fMRI activation.
- Rowe, Logan
- 2004
(Show Context)
Citation Context ...most of the tests available for fMRI data analysis were specifically developed for magnitude (i.e., single-valued) times series. Only recently, tests were developed for complex valued data [3], [19], =-=[21]-=-. In this respect, Nan and Nowak showed how to construct a generalized likelihood ratio test (GLRT) for complex fMRI data with constant phase values [19]. Thereby, it was shown that, under the assumpt... |

31 |
Independent component analysis: an introduction
- Stone
- 2002
(Show Context)
Citation Context ...ncorporation of a hemodynamic response function. Furthermore, more flexible and general variants of the general linear model were developed such as tests based on independent component analysis [16], =-=[27]-=-, multiresolution analysis [4], and likelihood ratio tests [19], [22]. Although magnetic resonance data are intrinsically complex valued, statistical tests are generally applied to magnitude fMRI imag... |

25 |
Independent component analysis of fMRI data
- Calhoun, Adali, et al.
- 2002
(Show Context)
Citation Context ...n. Indeed, most of the tests available for fMRI data analysis were specifically developed for magnitude (i.e., single-valued) times series. Only recently, tests were developed for complex valued data =-=[3]-=-, [19], [21]. In this respect, Nan and Nowak showed how to construct a generalized likelihood ratio test (GLRT) for complex fMRI data with constant phase values [19]. Thereby, it was shown that, under... |

18 |
Multiresolution analysis in fMRI: sensitivity and specificity in the detection of brain activation. Hum Brain Mapp 2001;14:16–27
- Desco, JA, et al.
(Show Context)
Citation Context ...esponse function. Furthermore, more flexible and general variants of the general linear model were developed such as tests based on independent component analysis [16], [27], multiresolution analysis =-=[4]-=-, and likelihood ratio tests [19], [22]. Although magnetic resonance data are intrinsically complex valued, statistical tests are generally applied to magnitude fMRI images, since only the signal ampl... |

13 |
vivo measurement of changes in venous blood-oxygenation with high resolution functional MRI at .95 Tesla by measuring changes in susceptibility and velocity
- Hoogenrad, Reichenbach, et al.
- 1998
(Show Context)
Citation Context ...es may exhibit activation-dependent modulations, especially for voxels with large venous blood fractions (i.e., voxels with high blood volume fractions show a time-dependency related to the paradigm) =-=[10]-=-, [17]. On the other hand, since in most fMRI studies, a voxel contains a large ensemble of vessels with various orientations and sizes, the assumption of a constant phase value may still be appropria... |

13 | Parameter estimation from magnitude MR Images
- AJ, Dyck, et al.
(Show Context)
Citation Context ...noise variance , is given by [8]: (4) where is the zeroth order modified Bessel function of the first kind. With increasing SNR (defined as ), the Rician distribution tends to a Gaussian distribution =-=[26]-=-. 1) ML estimation under : The likelihood function under is given by (5) Maximizing with respect to yields the MLEs of and under , denoted as and , respectively. 2) ML estimation under : The likelihoo... |

11 |
den Dekker, “Maximum Likelihood estimation of signal amplitude and noise variance from MR data”. Magn Reson Med 51(3):586—594
- Sijbers, J
- 2004
(Show Context)
Citation Context ...ect to . For to be a maximum, the first order derivatives of the likelihood function with respect to , , and should be zero. Solving the resulting system of equations yields the MLEs of , , and under =-=[25]-=-: (14) (15) (16) (17) b) ML estimation under : Under (i.e., ), maximizing in (12) with respect to yields the following MLEs of , , , and : (18) (19) (20) (21) Note that no numerical optimization is re... |

4 |
Testing a model for MR imager noise
- Kisner, Talavage, et al.
(Show Context)
Citation Context ...rather apply a GLRT based on magnitude data?”. In order to simplify the discussion (as was also done by Nan and Nowak), the noise disturbing the fMRI time series is assumed to be Gaussian white noise =-=[13]-=-, [15], [19]. The white noise model may be an oversimplification of the noises inherent in fMRI (especially if physiological noise is dominant 0278-0062/$20.00 © 2005 IEEE SIJBERS AND DEN DEKKER: GLRT... |

2 |
Measurement of brain activity with bolus administration of contrast agent and gradient-echo MR imaging.
- Zigun, Frank, et al.
- 1993
(Show Context)
Citation Context ...ten referred to as statistical parametric maps (SPMs). Initial detection methods were based on simple subtraction of images acquired during a resting state from images acquired during activation [1], =-=[31]-=-. In order to improve the detection rate, activation detection methods using the -score, correlation coefficients, analysis of variance, or Student- test statistics were employed [20], [23]. Those tes... |

1 |
Estimation and detection of fMRI eventrelated signals: a statistically efficient and unbiased approach
- Burock, Dale
- 2000
(Show Context)
Citation Context ...adigm is shown in the background (gray denotes stimulus). over thermal noise). However, if the data are observed to be correlated, they can be whitened based on an estimated autocorrelation structure =-=[2]-=-, [19], [29]–[30]. Moreover, valuable methods exist to eliminate, for example, physiological noise from the fMRI time courses, prior to activation detection [3], [7], [28]. Hence, the conclusions of t... |

1 |
Talavage, “Testing the distribution of nonstationary MRI data
- Kisner, M
(Show Context)
Citation Context ...may also be other causes for nonconstant phases as a function of time. For example, due to physiological processes or instabilities of the MR imaging system, the phase may show a slowly varying drift =-=[12]-=-. Similar phase behavior was found in our experimental fMRI data sets: though most data sets show constant phase values as a function of time, some of those data sets clearly revealed linear phase dri... |

1 |
Detection of brain activation from MRI data by likelihood-ratio test
- Ruan, Jaggi, et al.
- 1995
(Show Context)
Citation Context ...exible and general variants of the general linear model were developed such as tests based on independent component analysis [16], [27], multiresolution analysis [4], and likelihood ratio tests [19], =-=[22]-=-. Although magnetic resonance data are intrinsically complex valued, statistical tests are generally applied to magnitude fMRI images, since only the signal amplitude is assumed to be related to neura... |

1 |
Separation of movement and task related fMRI signal changes in a simulated data set by independent component analysis
- Vanello, Positano, et al.
- 2003
(Show Context)
Citation Context ...ted autocorrelation structure [2], [19], [29]–[30]. Moreover, valuable methods exist to eliminate, for example, physiological noise from the fMRI time courses, prior to activation detection [3], [7], =-=[28]-=-. Hence, the conclusions of this work can easily be extended to more realistic noise models that incorporate colored noise. The organization of this paper is as follows. Section II briefly reviews the... |