Locally adaptive image denoising by a statistical multiresolution criterion

We demonstrate how one can choose the smoothing parameter in image denoising by a statistical multiresolution criterion, both globally and locally. Using inhomogeneous diffusion and total variation regularization as examples for localized regularization schemes, we present an efficient method for locally adaptive image denoising. As expected, the smoothing parameter serves as an edge detector in this framework. Numerical examples illustrate the usefulness of our approach. We also present an application in confocal microscopy

A virtual world of paleontology

Computer-aided visualization and analysis of fossils has revolutionized the study of extinct organisms. Novel techniques allow fossils to be characterized in three dimensions and in unprecedented detail. This has enabled paleontologists to gain important insights into their anatomy, development, and preservation. New protocols allow more objective reconstructions of fossil organisms, including soft tissues, from incomplete remains. The resulting digital reconstructions can be used in functional analyses, rigorously testing long-standing hypotheses regarding the paleobiology of extinct organisms. These approaches are transforming our understanding of long-studied fossil groups, and of the narratives of organismal and ecological evolution that have been built upon them

Atomic super-resolution tomography

We consider the problem of reconstructing a nanocrystal at atomic resolution from electron microscopy images taken at a few tilt angles. A popular reconstruction approach called discrete tomography confines the atom locations to a coarse spatial grid, which is inspired by the physical a priori knowledge that atoms in a crystalline solid tend to form regular lattices. Although this constraint has proven to be powerful for solving this very under-determined inverse problem in many cases, its key limitation is that, in practice, defects may occur that cause atoms to deviate from regular lattice positions. Here we propose a grid-free discrete tomography algorithm that allows for continuous deviations of the atom locations similar to super-resolution approaches for microscopy. The new formulation allows us to define atomic interaction potentials explicitly, which results in a both meaningful and powerful incorporation of the available physical a priori knowledge about the crystal's properties. In computational experiments, we compare the proposed grid-free method to established grid-based approaches and show that our approach can indeed recover the atom positions more accurately for common lattice defects

The effects of packing structure on the effective thermal conductivity of granular media: A grain scale investigation

Structural characteristics are considered to be the dominant factors in determining the effective properties of granular media, particularly in the scope of transport phenomena. Towards improved heat management, thermal transport in granular media requires an improved fundamental understanding. In this study, the effects of packing structure on heat transfer in granular media are evaluated at macro- and grain-scales. At the grain-scale, a gas-solid coupling heat transfer model is adapted into a discrete-element-method to simulate this transport phenomenon. The numerical framework is validated by experimental data obtained using a plane source technique, and the Smoluschowski effect of the gas phase is found to be captured by this extension. By considering packings of spherical SiO2 grains with an interstitial helium phase, vibration induced ordering in granular media is studied, using the simulation methods developed here, to investigate how disorder-to-order transitions of packing structure enhance effective thermal conductivity. Grain-scale thermal transport is shown to be influenced by the local neighbourhood configuration of individual grains. The formation of an ordered packing structure enhances both global and local thermal transport. This study provides a structure approach to explain transport phenomena, which can be applied in properties modification for granular media.Comment: 11 figures, 29 page

Mathematical methods for magnetic resonance based electric properties tomography

Magnetic resonance-based electric properties tomography (MREPT) is a recent quantitative imaging technique that could provide useful additional information to the results of magnetic resonance imaging (MRI) examinations. Precisely, MREPT is a collective name that gathers all the techniques that elaborate the radiofrequency (RF) magnetic field B1 generated and measured by a MRI scanner in order to map the electric properties inside a human body. The range of uses of MREPT in clinical oncology, patient-specific treatment planning and MRI safety motivates the increasing scientific interest in its development. The main advantage of MREPT with respect to other techniques for electric properties imaging is the knowledge of the input field inside the examined body, which guarantees the possibility of achieving high-resolution. On the other hand, MREPT techniques rely on just the incomplete information that MRI scanners can measure of the RF magnetic field, typically limited to the transmit sensitivity B1+. In this thesis, the state of art is described in detail by analysing the whole bibliography of MREPT, started few years ago but already rich of contents. With reference to the advantages and drawbacks of each technique proposed for MREPT, the particular implementation based on the contrast source inversion method is selected as the most promising approach for MRI safety applications and is denoted by the symbol csiEPT. Motivated by this observation, a substantial part of the thesis is devoted to a thoroughly study of csiEPT. Precisely, a generalised framework based on a functional point of view is proposed for its implementation. In this way, it is possible to adapt csiEPT to various physical situations. In particular, an original formulation, specifically developed to take into account the effects of the conductive shield always employed in RF coils, shows how an accurate modelling of the measurement system leads to more precise estimations of the electric properties. In addition, a preliminary study for the uncertainty assessment of csiEPT, an imperative requirement in order to make the method reliable for in vivo applications, is performed. The uncertainty propagation through csiEPT is studied using the Monte Carlo method as prescribed by the Supplement 1 to GUM (Guide to the expression of Uncertainty in Measurement). The robustness of the method when measurements are performed by multi-channel TEM coils for parallel transmission confirms the eligibility of csiEPT for MRI safety applications

Outlier Mining Methods Based on Graph Structure Analysis

Outlier detection in high-dimensional datasets is a fundamental and challenging problem across disciplines that has also practical implications, as removing outliers from the training set improves the performance of machine learning algorithms. While many outlier mining algorithms have been proposed in the literature, they tend to be valid or efficient for specific types of datasets (time series, images, videos, etc.). Here we propose two methods that can be applied to generic datasets, as long as there is a meaningful measure of distance between pairs of elements of the dataset. Both methods start by defining a graph, where the nodes are the elements of the dataset, and the links have associated weights that are the distances between the nodes. Then, the first method assigns an outlier score based on the percolation (i.e., the fragmentation) of the graph. The second method uses the popular IsoMap non-linear dimensionality reduction algorithm, and assigns an outlier score by comparing the geodesic distances with the distances in the reduced space. We test these algorithms on real and synthetic datasets and show that they either outperform, or perform on par with other popular outlier detection methods. A main advantage of the percolation method is that is parameter free and therefore, it does not require any training; on the other hand, the IsoMap method has two integer number parameters, and when they are appropriately selected, the method performs similar to or better than all the other methods tested.Peer ReviewedPostprint (published version