Biomedical subjects

Dimitri Van De Ville

Publications and source records attributed to Dimitri Van De Ville.

8 recordsLinked to original sources

PubMed2006

Wavelet-based multi-resolution statistics for optical imaging signals: Application to automated detection of odour activated glomeruli in the mouse olfactory bulb.

Optical imaging techniques offer powerful solutions to capture brain networks processing in animals, especially when activity is distributed in functionally distinct spatial domains. Despite the progress in imaging techniques, the standard analysis procedures and statistical assessments for this type of data are still limited. In this paper, we perform two in vivo non-invasive optical recording techniques in the mouse olfactory bulb, using a genetically expressed activity reporter fluorescent protein (synaptopHfluorin) and intrinsic signals of the brain. For both imaging techniques, we show that the odour-triggered signals can be accurately parameterized using linear models. Fitting the models allows us to extract odour specific signals with a reduced level of noise compared to standard methods. In addition, the models serve to evaluate statistical significance, using a wavelet-based framework that exploits spatial correlation at different scales. We propose an extension of this framework to extract activation patterns at specific wavelet scales. This method is especially interesting to detect the odour inputs that segregate on the olfactory bulb in small spherical structures called glomeruli. Interestingly, with proper selection of wavelet scales, we can isolate significantly activated glomeruli and thus determine the odour map in an automated manner. Comparison against manual detection of glomeruli shows the high accuracy of the proposed method. Therefore, beyond the advantageous alternative to the existing treatments of optical imaging signals in general, our framework propose an interesting procedure to dissect brain activation patterns on multiple scales with statistical control.

Algorithms↗

PubMed2006

Determining significant connectivity by 4D spatiotemporal wavelet packet resampling of functional neuroimaging data.

An active area of neuroimaging research involves examining functional relationships between spatially remote brain regions. When determining whether two brain regions exhibit significant correlation due to true functional connectivity, one must account for the background spatial correlation inherent in neuroimaging data. We define background correlation as spatiotemporal correlation in the data caused by factors other than neurophysiologically based functional associations such as scanner induced correlations and image preprocessing. We develop a 4D spatiotemporal wavelet packet resampling method which generates surrogate data that preserves only the average background spatial correlation within an axial slice, across axial slices, and through each voxel time series, while excluding the specific correlations due to true functional relationships. We also extend an amplitude adjustment algorithm which adjusts our surrogate data to closely match the amplitude distribution of the original data. Our method improves upon existing wavelet-based methods and extends them to 4D. We apply our resampling technique to determine significant functional connectivity from resting state and motor task fMRI datasets.

Adult↗

PubMed2006

Polyharmonic smoothing splines and the multidimensional Wiener filtering of fractal-like signals.

Motivated by the fractal-like behavior of natural images, we develop a smoothing technique that uses a regularization functional which is a fractional iterate of the Laplacian. This type of functional was initially introduced by Duchon for the approximation of nonuniformily sampled, multidimensional data. He proved that the general solution is a smoothing spline that is represented by a linear combination of radial basis functions (RBFs). Unfortunately, this is tedious to implement for images because of the poor conditioning of RBFs and their lack of decay. Here, we present a much more efficient method for the special case of a uniform grid. The key idea is to express Duchon's solution in a fractional polyharmonic B-spline basis that spans the same space as the RBFs. This allows us to derive an algorithm where the smoothing is performed by filtering in the Fourier domain. Next, we prove that the above smoothing spline can be optimally tuned to provide the MMSE estimation of a fractional Brownian field corrupted by white noise. This is a strong result that not only yields the best linear filter (Wiener solution), but also the optimal interpolation space, which is not bandlimited. It also suggests a way of using the noisy data to identify the optimal parameters (order of the spline and smoothing strength), which yields a fully automatic smoothing procedure. We evaluate the performance of our algorithm by comparing it against an oracle Wiener filter, which requires the knowledge of the true noiseless power spectrum of the signal. We find that our approach performs almost as well as the oracle solution over a wide range of conditions.

Algorithms↗

PubMed2005

Isotropic polyharmonic B-splines: scaling functions and wavelets.

In this paper, we use polyharmonic B-splines to build multidimensional wavelet bases. These functions are nonseparable, multidimensional basis functions that are localized versions of radial basis functions. We show that Rabut's elementary polyharmonic B-splines do not converge to a Gaussian as the order parameter increases, as opposed to their separable B-spline counterparts. Therefore, we introduce a more isotropic localization operator that guarantees this convergence, resulting into the isotropic polyharmonic B-splines. Next, we focus on the two-dimensional quincunx subsampling scheme. This configuration is of particular interest for image processing because it yields a finer scale progression than the standard dyadic approach. However, up until now, the design of appropriate filters for the quincunx scheme has mainly been done using the McClellan transform. In our approach, we start from the scaling functions, which are the polyharmonic B-splines and, as such, explicitly known, and we derive a family of polyharmonic spline wavelets corresponding to different flavors of the semi-orthogonal wavelet transform; e.g., orthonormal, B-spline, and dual. The filters are automatically specified by the scaling relations satisfied by these functions. We prove that the isotropic polyharmonic B-spline wavelet converges to a combination of four Gabor atoms, which are well separated in the frequency domain. We also show that these wavelets are nearly isotropic and that they behave as an iterated Laplacian operator at low frequencies. We describe an efficient fast Fourier transform-based implementation of the discrete wavelet transform based on polyharmonic B-splines.

Algorithms↗

PubMed2004

Complex wavelets for extended depth-of-field: a new method for the fusion of multichannel microscopy images.

Microscopy imaging often suffers from limited depth-of-field. However, the specimen can be "optically sectioned" by moving the object along the optical axis. Then different areas appear in focus in different images. Extended depth-of-field is a fusion algorithm that combines those images into one single sharp composite. One promising method is based on the wavelet transform. Here, we show how the wavelet-based image fusion technique can be improved and easily extended to multichannel data. First, we propose the use of complex-valued wavelet bases, which seem to outperform traditional real-valued wavelet transforms. Second, we introduce a way to apply this technique for multichannel images that suppresses artifacts and does not introduce false colors, an important requirement for multichannel optical microscopy imaging. We evaluate our method on simulated image stacks and give results relevant to biological imaging.

Animals↗

PubMed2004

Integrated wavelet processing and spatial statistical testing of fMRI data.

We introduce an integrated framework for detecting brain activity from fMRI data, which is based on a spatial discrete wavelet transform. Unlike the standard wavelet-based approach for fMRI analysis, we apply the suitable statistical test procedure in the spatial domain. For a desired significance level, this scheme has one remaining degree of freedom, characterizing the wavelet processing, which is optimized according to the principle of minimal approximation error. This allows us to determine the threshold values in a way that does not depend on data. While developing our framework, we make only conservative assumptions. Consequently, the detection of activation is based on strong evidence. We have implemented this framework as a toolbox (WSPM) for the SPM2 software, taking advantage of multiple options and functions of SPM such as the setup of the linear model and the use of the hemodynamic response function. We show by experimental results that our method is able to detect activation patterns; the results are comparable to those obtained by SPM even though statistical assumptions are more conservative.

Attention↗

PubMed2004

Hex-splines: a novel spline family for hexagonal lattices.

This paper proposes a new family of bivariate, nonseparable splines, called hex-splines, especially designed for hexagonal lattices. The starting point of the construction is the indicator function of the Voronoi cell, which is used to define in a natural way the first-order hex-spline. Higher order hex-splines are obtained by successive convolutions. A mathematical analysis of this new bivariate spline family is presented. In particular, we derive a closed form for a hex-spline of arbitrary order. We also discuss important properties, such as their Fourier transform and the fact they form a Riesz basis. We also highlight the approximation order. For conventional rectangular lattices, hex-splines revert to classical separable tensor-product B-splines. Finally, some prototypical applications and experimental results demonstrate the usefulness of hex-splines for handling hexagonally sampled data.

Algorithms↗

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Surfing the brain.

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Algorithms↗