Jörg Polzehl

Analyzing fMRI experiments with structural adaptive smoothing procedures

Data from functional magnetic resonance imaging (fMRI) consist of time series of brain images that are characterized by a low signal-to-noise ratio. In order to reduce noise and to improve signal detection, the fMRI data are spatially smoothed. However, the common application of a Gaussian filter does this at the cost of loss of information on spatial extent and shape of the activation area. We suggest to use the propagation-separation procedures introduced by Polzehl, J., Spokoiny, V. (2006). Propagation-separation approach for local likelihood estimation. Probab. Theory Relat. Fields, in print. instead. We show that this significantly improves the information on the spatial extent and shape of the activation region with similar results for the noise reduction. To complete the statistical analysis, signal detection is based on thresholds defined by random field theory. Effects of adaptive and non-adaptive smoothing are illustrated by artificial examples and an analysis of experimental data.

Diffusion tensor imaging: structural adaptive smoothing.

Diffusion Tensor Imaging (DTI) data is characterized by a high noise level. Thus, estimation errors of quantities like anisotropy indices or the main diffusion direction used for fiber tracking are relatively large and may significantly confound the accuracy of DTI in clinical or neuroscience applications. Besides pulse sequence optimization, noise reduction by smoothing the data can be pursued as a complementary approach to increase the accuracy of DTI. Here, we suggest an anisotropic structural adaptive smoothing procedure, which is based on the Propagation-Separation method and preserves the structures seen in DTI and their different sizes and shapes. It is applied to artificial phantom data and a brain scan. We show that this method significantly improves the quality of the estimate of the diffusion tensor, by means of both bias and variance reduction, and hence enables one either to reduce the number of scans or to enhance the input for subsequent analysis such as fiber tracking.

Adaptive smoothing of multi-shell diffusion weighted magnetic resonance data by msPOAS.

We present a novel multi-shell position-orientation adaptive smoothing (msPOAS) method for diffusion weighted magnetic resonance data. Smoothing in voxel and diffusion gradient space is embedded in an iterative adaptive multiscale approach. The adaptive character avoids blurring of the inherent structures and preserves discontinuities. The simultaneous treatment of all q-shells improves the stability compared to single-shell approaches such as the original POAS method. The msPOAS implementation simplifies and speeds up calculations, compared to POAS, facilitating its practical application. Simulations and heuristics support the face validity of the technique and its rigorousness. The characteristics of msPOAS were evaluated on single and multi-shell diffusion data of the human brain. Significant reduction in noise while preserving the fine structure was demonstrated for diffusion weighted images, standard DTI analysis and advanced diffusion models such as NODDI. MsPOAS effectively improves the poor signal-to-noise ratio in highly diffusion weighted multi-shell diffusion data, which is required by recent advanced diffusion micro-structure models. We demonstrate the superiority of the new method compared to other advanced denoising methods.

Image analysis and statistical inference in neuroimaging with R

R is a language and environment for statistical computing and graphics. It can be considered an alternative implementation of the S language developed in the 1970s and 1980s for data analysis and graphics (Becker and Chambers, 1984; Becker et al., 1988). The R language is part of the GNU project and offers versions that compile and run on almost every major operating system currently available. We highlight several R packages built specifically for the analysis of neuroimaging data in the context of functional MRI, diffusion tensor imaging, and dynamic contrast-enhanced MRI. We review their methodology and give an overview of their capabilities for neuroimaging. In addition we summarize some of the current activities in the area of neuroimaging software development in R.

Position-orientation adaptive smoothing of diffusion weighted magnetic resonance data (POAS)

We introduce an algorithm for diffusion weighted magnetic resonance imaging data enhancement based on structural adaptive smoothing in both voxel space and diffusion-gradient space. The method, called POAS, does not refer to a specific model for the data, like the diffusion tensor or higher order models. It works by embedding the measurement space into a space with defined metric, in this case the Lie group of three-dimensional Euclidean motion SE(3). Subsequently, pairwise comparisons of the values of the diffusion weighted signal are used for adaptation. POAS preserves the edges of the observed fine and anisotropic structures. It is designed to reduce noise directly in the diffusion weighted images and consequently also to reduce bias and variability of quantities derived from the data for specific models. We evaluate the algorithm on simulated and experimental data and demonstrate that it can be used to reduce the number of applied diffusion gradients and hence acquisition time while achieving a similar quality of data, or to improve the quality of data acquired in a clinically feasible scan time setting.

Modeling the orientation distribution function by mixtures of angular central Gaussian distributions.

In this paper we develop a tensor mixture model for diffusion weighted imaging data using an automatic model order selection criterion for the number of tensor components in a voxel. We show that the weighted orientation distribution function for this model can be expanded into a mixture of angular central Gaussian distributions. We investigate properties of this model in extensive simulations and in a high angular resolution scan of a human brain. The results suggest that the model improves imaging of cerebral fiber tracts. In addition, inference on canonical model parameters could potentially provide novel clinical markers of altered white matter. Software to compute the tensor mixture model from diffusion weighted MRI data is made available in the programming language R.

Structural adaptive segmentation for statistical parametric mapping.

Functional Magnetic Resonance Imaging inherently involves noisy measurements and a severe multiple test problem. Smoothing is usually used to reduce the effective number of multiple comparisons and to locally integrate the signal and hence increase the signal-to-noise ratio. Here, we provide a new structural adaptive segmentation algorithm (AS) that naturally combines the signal detection with noise reduction in one procedure. Moreover, the new method is closely related to a recently proposed structural adaptive smoothing algorithm and preserves shape and spatial extent of activation areas without blurring their borders.

Functional and dynamic magnetic resonance imaging using vector adaptive weights smoothing

We consider the problem of statistical inference for functional and dynamic magnetic resonance imaging (MRI). A new approach is proposed which extends the adaptive weights smoothing procedure of Polzehl and Spokoiny that was originally designed for image denoising. We demonstrate how the adaptive weights smoothing method can be applied to time series of images, which typically occur in functional and dynamic MRI. It is shown how signal detection in functional MRI and the analysis of dynamic MRI can benefit from spatially adaptive smoothing. The performance of the procedure is illustrated by using real and simulated data.

High-resolution fMRI: overcoming the signal-to-noise problem.

Increasing the spatial resolution in functional Magnetic Resonance Imaging (fMRI) inherently lowers the signal-to-noise ratio (SNR). In order to still detect functionally significant activations in high-resolution images, spatial smoothing of the data is required. However, conventional non-adaptive smoothing comes with a reduced effective resolution, foiling the benefit of the higher acquisition resolution. We show how our recently proposed structural adaptive smoothing procedure for functional MRI data can improve signal detection of high-resolution fMRI experiments regardless of the lower SNR. The procedure is evaluated on human visual and sensory-motor mapping experiments. In these applications, the higher resolution could be fully utilized and high-resolution experiments were outperforming normal resolution experiments by means of both statistical significance and information content.

Accurate Localization of Brain Activity in Presurgical fMRI by Structure Adaptive Smoothing

An important problem of the analysis of functional magnetic resonance imaging (fMRI) experiments is to achieve some noise reduction of the data without blurring the shape of the activation areas. As a novel solution to this problem, recently the propagation-separation (PS) approach has been proposed. PS is a structure adaptive smoothing method that adapts to different shapes of activation areas. In this paper, we demonstrate how this method results in a more accurate localization of brain activity. First, it is shown in numerical simulations that PS is superior over Gaussian smoothing with respect to the accurate description of the shape of activation clusters and results in less false detections. Second, in a study of 37 presurgical planning cases we found that PS and Gaussian smoothing often yield different results, and we present examples showing aspects of the superiority of PS as applied to presurgical planning.