Classification of fMRI time series in a low-dimensional subspace with a spatial prior.

We propose a new method for detecting activation in functional magnetic resonance imaging (fMRI) data. We project the fMRI time series on a low-dimensional subspace spanned by wavelet packets in order to create projections that are as non-Gaussian as possible. Our approach achieves two goals: it reduces the dimensionality of the problem by explicitly constructing a sparse approximation to the dataset and it also creates meaningful clusters allowing the separation of the activated regions from the clutter formed by the background time series. We use a mixture of Gaussian densities to model the distribution of the wavelet packet coefficients. We expect activated areas that are connected, and impose a spatial prior in the form of a Markov random field. Our approach was validated with in vivo data and realistic synthetic data, where it outperformed a linear model equipped with the knowledge of the true hemodynamic response.

Fast adaptive wavelet packet image compression.

Wavelets are ill-suited to represent oscillatory patterns: rapid variations of intensity can only be described by the small scale wavelet coefficients, which are often quantized to zero, even at high bit rates. Our goal is to provide a fast numerical implementation of the best wavelet packet algorithm in order to demonstrate that an advantage can be gained by constructing a basis adapted to a target image. Emphasis is placed on developing algorithms that are computationally efficient. We developed a new fast two-dimensional (2-D) convolution decimation algorithm with factorized nonseparable 2-D filters. The algorithm is four times faster than a standard convolution-decimation. An extensive evaluation of the algorithm was performed on a large class of textured images. Because of its ability to reproduce textures so well, the wavelet packet coder significantly out performs one of the best wavelet coder on images such as Barbara and fingerprints, both visually and in term of PSNR.

Tracking myocardial deformation using phase contrast MR velocity fields: a stochastic approach.

The authors propose a new approach for tracking the deformation of the left-ventricular (LV) myocardium from two-dimensional (2-D) magnetic resonance (MR) phase contrast velocity fields. The use of phase contrast MR velocity data in cardiac motion problems has been introduced by others (N.J. Pelc et al., 1991) and shown to be potentially useful for tracking discrete tissue elements, and therefore, characterizing LV motion. However, the authors show here that these velocity data: 1) are extremely noisy near the LV borders; and 2) cannot alone be used to estimate the motion and the deformation of the entire myocardium due to noise in the velocity fields. In this new approach, the authors use the natural spatial constraints of the endocardial and epicardial contours, detected semiautomatically in each image frame, to help remove noisy velocity vectors at the LV contours. The information from both the boundaries and the phase contrast velocity data is then integrated into a deforming mesh that is placed over the myocardium at one time frame and then tracked over the entire cardiac cycle. The deformation is guided by a Kalman filter that provides a compromise between 1) believing the dense field velocity and the contour data when it is crisp and coherent in a local spatial and temporal sense and 2) employing a temporally smooth cyclic model of cardiac motion when contour and velocity data are not trustworthy. The Kalman filter is particularly well suited to this task as it produces an optimal estimate of the left ventricle's kinematics (in the sense that the error is statistically minimized) given incomplete and noise corrupted data, and given a basic dynamical model of the left ventricle. The method has been evaluated with simulated data; the average error between tracked nodes and theoretical position was 1.8% of the total path length. The algorithm has also been evaluated with phantom data; the average error was 4.4% of the total path length. The authors show that in their initial tests with phantoms that the new approach shows small, but concrete improvements over previous techniques that used primarily phase contrast velocity data alone. They feel that these improvements will be amplified greatly as they move to direct comparisons in in vivo and three-dimensional (3-D) datasets.