Related papers: Smooth Principal Component Analysis over two-dimen…
Automated quality assessment of structural brain MRI is an important prerequisite for reliable neuroimaging analysis, but yet remains challenging due to motion artifacts and poor generalization across acquisition sites. Existing approaches…
Image smoothing represents a fundamental component of many disparate computer vision and graphics applications. In this paper, we present a unified unsupervised (label-free) learning framework that facilitates generating flexible and…
Most biological data are multidimensional, posing a major challenge to human comprehension and computational analysis. Principal component analysis is the most popular approach to rendering two- or three-dimensional representations of the…
We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…
We propose a new data-driven method to select the optimal number of relevant components in Principal Component Analysis (PCA). This new method applies to correlation matrices whose time autocorrelation function decays more slowly than an…
Graph Signal Processing (GSP) is a promising framework to analyze multi-dimensional neuroimaging datasets, while taking into account both the spatial and functional dependencies between brain signals. In the present work, we apply…
In this thesis, we present robust and fully-automated methods for the subdivision of the entire human cerebral cortex based on connectivity information. Our contributions are four-fold: First, we propose a clustering approach to delineate a…
Research on manifold learning within a density ridge estimation framework has shown great potential in recent work for both estimation and de-noising of manifolds, building on the intuitive and well-defined notion of principal curves and…
Knowing how the Human brain is anatomically and functionally organized at the level of a group of healthy individuals or patients is the primary goal of neuroimaging research. Yet computing an average of brain imaging data defined over a…
Optimization over the Stiefel manifold is a fundamental computational problem in many scientific and engineering applications. Despite considerable research effort, high-dimensional optimization problems over the Stiefel manifold remain…
In this paper, auto-associative models are proposed as candidates to the generalization of Principal Component Analysis. We show that these models are dedicated to the approximation of the dataset by a manifold. Here, the word "manifold"…
We consider the challenges in extracting stimulus-related neural dynamics from other intrinsic processes and noise in naturalistic functional magnetic resonance imaging (fMRI). Most studies rely on inter-subject correlations (ISC) of…
We propose a new framework -- Square Root Principal Component Pursuit -- for low-rank matrix recovery from observations corrupted with noise and outliers. Inspired by the square root Lasso, this new formulation does not require prior…
We present a novel approach to automatically segment magnetic resonance (MR) images of the human brain into anatomical regions. Our methodology is based on a deep artificial neural network that assigns each voxel in an MR image of the brain…
Image normalization is a building block in medical image analysis. Conventional approaches are customarily utilized on a per-dataset basis. This strategy, however, prevents the current normalization algorithms from fully exploiting the…
We consider an unconstrained problem of minimizing a smooth convex function which is only available through noisy observations of its values, the noise consisting of two parts. Similar to stochastic optimization problems, the first part is…
Gradients play a pivotal role in neural networks explanation. The inherent high dimensionality and structural complexity of neural networks result in the original gradients containing a significant amount of noise. While several approaches…
Spatially localized deformation components are very useful for shape analysis and synthesis in 3D geometry processing. Several methods have recently been developed, with an aim to extract intuitive and interpretable deformation components.…
The hippocampus is one of the most studied neuroanatomical structures due to its involvement in attention, learning, and memory as well as its atrophy in ageing, neurological, and psychiatric diseases. Hippocampal shape changes, however,…
Recent developments in mechanical, aerospace, and structural engineering have driven a growing need for efficient ways to model and analyse structures at much larger and more complex scales than before. While established numerical methods…