Nonstationary noise estimation in functional MRI.

An important issue in functional MRI analysis is accurate characterisation of the noise processes present in the data. Whilst conventional fMRI noise representations often assume stationarity (or time-invariance) in the noise generating sources, such approaches may serve to suppress important dynamic information about brain function. As an alternative to these fixed temporal assumptions, we present in this paper two time-varying procedures for examining nonstationary noise structure in fMRI data. In the first procedure, we approximate nonstationary behaviour by means of a collection of simple but numerous time-varying parametric models. This is accomplished through the derivation of a locally parametric AutoRegressive (AR) plus drift model which tracks temporal covariance by allowing the model parameters to evolve over time. Before exploring time variation in these parameters, window-widths (bandwidths) that are well suited to the latent time-varying noise structure must be determined. To do this, we employ a bandwidth selection mechanism based on Stein's Unbiased Risk Estimator (SURE) criterion. In the second procedure, we describe the fMRI noise using a nonparametric method based on Functional Data Analysis (FDA). This process generates well-conditioned nonstationary covariance estimates that reflect temporal continuity in the underlying data structure whilst penalizing effective model dimension. We demonstrate both methods on simulated data and investigate the presence of nonstationary noise in resting fMRI data using the whitening capabilities of the locally parametric procedure. We evaluate the comparative behaviour of the stationary and nonstationary AR-based methods on data acquired at 1.5, 3 and 7 T magnetic field strengths and show that incorporation of time variation in the AR parameters leads to an overall decrease in the level of residual structure in the data. The FDA noise modelling technique is formulated within an activation mapping procedure and compared to the SPM (Statistical Parametric Mapping) toolbox on a cognitive face recognition task. Both the SPM and FDA methods show good sensitivity on this task, but we find that inclusion of the nonstationary FDA noise model seems to improve detection power in important task-related medial temporal regions.

A Bayesian decoding algorithm for analysis of information encoding in neural ensembles.

Developing optimal strategies for constructing and testing decoding algorithms is an important question in computational neuroscience, In this field, decoding algorithms are mathematical methods that model ensemble neural spiking activity as they dynamically represent a biological signal. We present a recursive decoding algorithm based on a Bayesian point process model of individual neuron spiking activity and a linear stochastic state-space model of the biological signal. We assess the accuracy of the algorithm by computing, along with the decoding error, the true coverage probability of the approximate 0.95 confidence regions for the individual signal estimates. We illustrate the new algorithm by analyzing the position and ensemble neural spiking activity of CA1 hippocampal neurons from a rat foraging in an open circular environment The median decoding error during 10 minutes of open foraging was 5.5 cm, and the true coverage probability for 0.95 confidence regions was 0.75 using 32 neurons. These findings improve significantly on our previous results and suggest an approach to reading dynamically information represented in ensemble neural spiking activity.

An analysis of neural receptive field plasticity by point process adaptive filtering.

Neural receptive fields are plastic: with experience, neurons in many brain regions change their spiking responses to relevant stimuli. Analysis of receptive field plasticity from experimental measurements is crucial for understanding how neural systems adapt their representations of relevant biological information. Current analysis methods using histogram estimates of spike rate functions in nonoverlapping temporal windows do not track the evolution of receptive field plasticity on a fine time scale. Adaptive signal processing is an established engineering paradigm for estimating time-varying system parameters from experimental measurements. We present an adaptive filter algorithm for tracking neural receptive field plasticity based on point process models of spike train activity. We derive an instantaneous steepest descent algorithm by using as the criterion function the instantaneous log likelihood of a point process spike train model. We apply the point process adaptive filter algorithm in a study of spatial (place) receptive field properties of simulated and actual spike train data from rat CA1 hippocampal neurons. A stability analysis of the algorithm is sketched in the. The adaptive algorithm can update the place field parameter estimates on a millisecond time scale. It reliably tracked the migration, changes in scale, and changes in maximum firing rate characteristic of hippocampal place fields in a rat running on a linear track. Point process adaptive filtering offers an analytic method for studying the dynamics of neural receptive fields.

Locally regularized spatiotemporal modeling and model comparison for functional MRI.

In this work we treat fMRI data analysis as a spatiotemporal system identification problem and address issues of model formulation, estimation, and model comparison. We present a new model that includes a physiologically based hemodynamic response and an empirically derived low-frequency noise model. We introduce an estimation method employing spatial regularization that improves the precision of spatially varying noise estimates. We call the algorithm locally regularized spatiotemporal (LRST) modeling. We develop a new model selection criterion and compare our model to the SPM-GLM method. Our findings suggest that our method offers a better approach to identifying appropriate statistical models for fMRI studies.

A signal estimation approach to functional MRI.

In the last half decade, fast methods of magnetic resonance imaging have led to the possibility, for the first time, of non-invasive dynamic brain imaging. This has led to an explosion of work in the Neurosciences. From a signal processing viewpoint the problems are those of nonlinear spatio-temporal system identification. In this paper, we develop new methods of identification using novel spatial regularization. We also develop a new model comparison technique and use that to compare our method with existing techniques on some experimental data.

Errors-in-variables modeling in optical flow estimation.

Gradient-based optical flow estimation methods typically do not take into account errors in the spatial derivative estimates. The presence of these errors causes an errors-in-variables (EIV) problem. Moreover, the use of finite difference methods to calculate these derivatives ensures that the errors are strongly correlated between pixels. Total least squares (TLS) has often been used to address this EIV problem. However, its application in this context is flawed as TLS implicitly assumes that the errors between neighborhood pixels are independent. In this paper, a new optical flow estimation method (EIVM) is formulated to properly treat the EIV problem in optical flow. EIVM is based on Sprent's (1966) procedure which allows the incorporation of a general EIV model in the estimation process. In EIVM, the neighborhood size acts as a smoothing parameter. Due to the weights in the EIVM objective function, the effect of changing the neighborhood size is more complex than in other local model methods such as Lucas and Kanade (1981). These weights, which are functions of the flow estimate, can alter the effective size and orientation of the neighborhood. In this paper, we also present a data-driven method for choosing the neighborhood size based on Stein's unbiased risk estimators (SURE).