Multiscale adaptive smoothing models for the hemodynamic response function in fMRI

In the event-related functional magnetic resonance imaging (fMRI) data analysis, there is an extensive interest in accurately and robustly estimating the hemodynamic response function (HRF) and its associated statistics (e.g., the magnitude and duration of the activation). Most methods to date are developed in the time domain and they have utilized almost exclusively the temporal information of fMRI data without accounting for the spatial information. The aim of this paper is to develop a multiscale adaptive smoothing model (MASM) in the frequency domain by integrating the spatial and frequency information to adaptively and accurately estimate HRFs pertaining to each stimulus sequence across all voxels in a three-dimensional (3D) volume. We use two sets of simulation studies and a real data set to examine the finite sample performance of MASM in estimating HRFs. Our real and simulated data analyses confirm that MASM outperforms several other state-of-the-art methods, such as the smooth finite impulse response (sFIR) model.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS609 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

A kepstrum approach to filtering, smoothing and prediction

The kepstrum (or complex cepstrum) method is revisited and applied to the problem of spectral factorization where the spectrum is directly estimated from observations. The solution to this problem in turn leads to a new approach to optimal filtering, smoothing and prediction using the Wiener theory. Unlike previous approaches to adaptive and self-tuning filtering, the technique, when implemented, does not require a priori information on the type or order of the signal generating model. And unlike other approaches - with the exception of spectral subtraction - no state-space or polynomial model is necessary. In this first paper results are restricted to stationary signal and additive white noise

Regularized adaptive long autoregressive spectral analysis

This paper is devoted to adaptive long autoregressive spectral analysis when (i) very few data are available, (ii) information does exist beforehand concerning the spectral smoothness and time continuity of the analyzed signals. The contribution is founded on two papers by Kitagawa and Gersch. The first one deals with spectral smoothness, in the regularization framework, while the second one is devoted to time continuity, in the Kalman formalism. The present paper proposes an original synthesis of the two contributions: a new regularized criterion is introduced that takes both information into account. The criterion is efficiently optimized by a Kalman smoother. One of the major features of the method is that it is entirely unsupervised: the problem of automatically adjusting the hyperparameters that balance data-based versus prior-based information is solved by maximum likelihood. The improvement is quantified in the field of meteorological radar