Scalable Learning-Based Sampling Optimization for Compressive Dynamic MRI
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Magnetic resonance spectroscopic imaging (MRSI) is a rapidly developing medical imaging modality, capable of conferring both spatial and spectral information content, and has become a powerful clinical tool. The ability to non-invasively observe spatial ma ...
Probabilistic programming is a powerful high-level paradigm for probabilistic modeling and inference. We present Odds, a small domain-specific language (DSL) for probabilistic programming, embedded in Scala. Odds provides first-class support for random var ...
The Poisson summation formula (PSF), which relates the sampling of an analog signal with the periodization of its Fourier transform, plays a key role in the classical sampling theory. In its current forms, the formula is only applicable to a limited class ...
In this work we consider the problem of approximating the statistics of a given Quantity of Interest (QoI) that depends on the solution of a linear elliptic PDE defined over a random domain parameterized by N random variables. The elliptic problem is remap ...
We address adaptive multivariate polynomial approximation by means of the discrete least-squares method with random evaluations, to approximate in the L2 probability sense a smooth function depending on a random variable distributed according to a given pr ...
This thesis addresses the problem of a statistical description of the transport of sediment as bed load. It highlights the role of fluctuations arising during the transport process, and their impact on macroscopic averages. The results presented here are b ...
We present a new information-theoretic result which we call the Chaining Lemma. It considers a so-called "chain" of random variables, defined by a source distribution X-(0) with high min-entropy and a number (say, t in total) of arbitrary functions (T-1,.. ...
The characteristic functional is the infinite-dimensional generalization of the Fourier transform for measures on function spaces. It characterizes the statistical law of the associated stochastic process in the same way as a characteristic function specif ...
We consider the simple random walk on , d > 3, evolving in a potential of the form beta V, where are i.i.d. random variables taking values in [0, + a), and beta > 0. When the potential is integrable, the asymptotic behaviours as beta tends to 0 of the asso ...
Many pharmaceutical products find their way into receiving waters, giving rise to concerns regarding their environmental impact. A procedure was proposed that enables ranking of the hazard to aquatic species and human health due to such products. In the pr ...