A bayesian signal detection procedure for scale‐space random fields

The authors consider the problem of searching for activation in brain images obtained from functional magnetic resonance imaging and the corresponding functional signal detection problem. They develop a Bayesian procedure to detect signals existing within noisy images when the image is modeled as a scale space random field. Their procedure is based on the Radon-Nikodym derivative, which is used as the Bayes factor for assessing the point null hypothesis of no signal. They apply their method to data from

[1]  E. Parzen.  An Approach to Time Series Analysis , 1961 .

[2]  Hung T. Nguyen,et al.  A course in stochastic processes , 1996 .

[3]  J B Poline,et al.  Enhanced Detection in Brain Activation Maps Using a Multifiltering Approach , 1994, Journal of cerebral blood flow and metabolism : official journal of the International Society of Cerebral Blood Flow and Metabolism.

[4]  R. Turner,et al.  Dynamic magnetic resonance imaging of human brain activity during primary sensory stimulation. , 1992, Proceedings of the National Academy of Sciences of the United States of America.

[5]  L. Fahrmeir,et al.  Bayesian Modeling of the Hemodynamic Response Function in BOLD fMRI , 2001, NeuroImage.

[6]  U. Grenander.  Stochastic processes and statistical inference , 1950 .

[7]  L. M. M.-T..  Theory of Probability , 1929, Nature.

[8]  S. R. Srinivasa Varadhan,et al.  Stochastic Processes , 2018, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics.

[9]  Karl J. Friston,et al.  Analysis of fMRI Time-Series Revisited—Again , 1995, NeuroImage.

[10]  Thomas Kailath,et al.  RKHS approach to detection and estimation problems-I: Deterministic signals in Gaussian noise , 1971, IEEE Trans. Inf. Theory.

[11]  Karl J. Friston,et al.  Analysis of fMRI Time-Series Revisited , 1995, NeuroImage.

[12]  Alan C. Evans,et al.  Scale space searches for a periodic signal in fMRI data with spatially varying hemodynamic response , 1997 .

[13]  N. Krylov,et al.  Introduction to the Theory of Random Processes , 2002 .

[14]  Karl J. Friston,et al.  Posterior probability maps and SPMs , 2003, NeuroImage.

[15]  Karl J. Friston,et al.  Classical and Bayesian Inference in Neuroimaging: Theory , 2002, NeuroImage.

[16]  Thomas Kailath,et al.  An RKHS approach to detection and estimation problems-II: Gaussian signal detection , 1975, IEEE Trans. Inf. Theory.

[17]  K. Worsley,et al.  Local Maxima and the Expected Euler Characteristic of Excursion Sets of χ 2, F and t Fields , 1994, Advances in Applied Probability.

[18]  Iwao Kanno,et al.  Application of Bayesian inference to fMRI data analysis , 1999, IEEE Transactions on Medical Imaging.

[19]  D. Siegmund,et al.  Testing for a Signal with Unknown Location and Scale in a Stationary Gaussian Random Field , 1995 .

[20]  Christopher R. Genovese,et al.  A Bayesian Time-Course Model for Functional Magnetic Resonance Imaging Data , 2000 .

[21]  Karl J. Friston,et al.  Analysis of functional MRI time‐series , 1994, Human Brain Mapping.

[22]  T. T. Kadota.  Optimum reception of binary sure and Gaussian signals , 1965 .

[23]  J. Berger.  Statistical Decision Theory and Bayesian Analysis , 1988 .

[24]  Azriel Rosenfeld,et al.  Digital Picture Processing , 1976 .

[25]  Karl J. Friston,et al.  Variational Bayesian inference for fMRI time series , 2003, NeuroImage.

[26]  Mark W. Woolrich,et al.  Multilevel linear modelling for FMRI group analysis using Bayesian inference , 2004, NeuroImage.

[27]  T. Kadota.  Optimum reception of binary Gaussian signals , 1964 .

[28]  Keith J. Worsley,et al.  Rotation space random fields with an application to fMRI data , 2003 .

[29]  K. Worsley.  Testing for signals with unknown location and scale in a χ2 random field, with an application to fMRI , 2001, Advances in Applied Probability.

[30]  James D. Hamilton.  Time Series Analysis , 1994 .

[31]  Tony Lindeberg,et al.  Scale-Space Theory in Computer Vision , 1993, Lecture Notes in Computer Science.

[32]  Alan C. Evans,et al.  A Three-Dimensional Statistical Analysis for CBF Activation Studies in Human Brain , 1992, Journal of cerebral blood flow and metabolism : official journal of the International Society of Cerebral Blood Flow and Metabolism.

[33]  E. Dubois,et al.  Digital picture processing , 1985, Proceedings of the IEEE.