AMIS

AMIS project summary

Imaging Science (IS) is a highly interdisciplinary field of increasing importance in Applied Sciences which combines many aspects that involve images, intended as two-dimensional or multidimensional signals. It is concerned with the detection, processing, analysis, modification and, visualization of images. The measured signals phenomena can be visible or invisible to the human eye, affecting the entire spectrum of electromagnetic waves (EM) and mechanical waves, in particular: visible light, radar signals, seismic waves, brain waves, etc. Therefore, IS finds applications in many scientific fields. The main applications for the studied methodologies are medical diagnostics and geophysical diagnostics applied to geotechnics, environment, agriculture, archeology and cultural heritage in general.
Regarding medical applications, a large number of modern diagnostic tools require careful processing of the involved measured signals in order to get an appropriate diagnosis. The best known examples are nuclear magnetic resonance (NMR) and computerized axial tomography (CAT). In this field, the theory of integral equations and, more in general, of inverse problems are of particular importance. The models are typically characterized by the lack of uniqueness of the solution and by a very strong sensitivity to the propagation of experimental and rounding errors (ill-conditioning). Recently, theory of complex networks has assumed an essential role in the analysis of brain waves, since the brain activity can be considered as a graph in which the nerve centers assume the role of nodes and the edges represent the activation of a connection between them. This made it possible to use network analysis methodologies already developed in other areas, but with specific implementation difficulties due to the large number of collected data and to the dependence on time of active connections, with consequences both from the numerical and modeling points of view. Finally, for diagnostics the problem of the acquired images cassification, for example by a microscope, is important in order to recognize particular structures that can be associated with any pathologies. A typical approach for this problem is to resort to pattern recognition techniques to classify the image within a pre-established database.
Among the applications of Applied Geophysics, in addition to those relating to petroleum and mining research in general (areas in which Geophysics has had greater diffusion and development), also the ones concerning geotechnical characterizations of soils, the identification and monitoring of contaminants in soils and aquifers, the estimation and monitoring of water content and salinity of agricultural soils, as well as the identification and characterization of buried structures in archaeology are of particular importance. The most widely used investigation methods for these applications are seismic methods, based on the propagation of seismic waves, high frequency electromagnetic methods (georadar), based on the propagation of electromagnetic waves, low frequency electromagnetic methods, based on the diffusion of electromagnetic fields in electrically conductive media, and geoelectric methods, based on the propagation of direct or alternating low frequency electric currents. In any case, the physical parameters of the investigated object (soil or other structures) are estimated by solving an inverse problem that makes them congruent with the experimental data. This generates a parallelism with the used methodologies, for example, in medical tomography both from the modeling point of view, lack of uniqueness of the solution and strong propagation of experimental errors, and from the numerical point of view, because of the necessity of regularization methods for large-scale problems. In particular, as will be better explained next, from the modeling point of view the inverse problem of tomography is analogous to the inverse problem of geometrical optics. The latter consists of determining a suitable model of differential equations that describes light propagation in terms of rays. The ray in geometrical optics is useful for approximating the paths along which light propagates under certain circumstances. Similarly, in tomography it is important to determine the speed of radio propagation (seismic or X-ray depending on the application), which is, in general, a function which dependends on the position.
In Archeology, in addition to the investigation techniques aimed at detecting the presence of archaeological finds in the subsoil, the techniques of support for the interpretation of the data that are based, for example, on the classification (physical and spatial) of the collected signals, are becoming increasingly important. Placing assemblages or artifacts from different sites in the same culture is called seriation. This is a problem which can be found in other applications, such as Genetics, and is connected to important algebraic problems, such as the reduction of the bandwith in sparse matrices and the "consecutive ones problem". The problem can be represented by a bipartite graph and analyzed with Complex Network analysis techniques. In the context of archaeological finds documentation, and in particular of petroglyphs (wall incisions as a form of rock art) and bas-reliefs, the creation of three-dimensional virtual models that can be analyzed on the computer and reproduced using 3D printers plays an important role.This allows the access to finds that are located in sites that are difficult to reach and / or preserve them from uses. The so-called "shape from shading" methodologies, typical in Computer Vision, allow the realization of such models starting from photographic images. The "photometric stereo" and "multiview" techniques are the most used for this purpose and require the solution of large scale least squares problems and systems of partial differential equations (PDE).
As just observed, the common point between so different application is that their study requires strong mathematical skills concerning algorithms and models, as well as, of course, a deep knowledge of physical phenomena involved in the specific areas.
The project is divided into four main research lines:

Inverse problems in Geophysics,
Complex Network Analysis and Neuro-Imaging,
Image Processing and Pattern Recognition,
Shape from Shading and Archeology.

In section Research lines the different aspects of these topics are described in detail.

Overall objectives

Inverse Problems in Geophysics

Development of an iterative regularization method for large-scale nonlinear problems, based on the combination of the Tikhonov method with the TSVD.
Realization of a numerical procedure for the solution of integral equations of the first and second kind, based on the Gaussian and anti-Gaussian formulas leading to a more accurate approximation of the solution and providing an upper limit for the approximation error.
Setting the inverse problem in Geometrical Optics in the case in which the light propagation occurs in an inhomogeneous medium. In this regard, we intend to determine the system of differential equations that must be satisfied by the refractive index and to develop analytical and numerical procedures to solve it.
Deduction and resolution of models in the anisotropic case, both analytically and numerically, under the assumption that the wavelength of radiation is not negligible, using the laws of Physical Optics and, in particular, Maxwell's equations.
Development of an inversion procedure that combines the FWI of seismic data with the nonlinear inversion of electromagnetic data. The integration of electromagnetic data, sensitive to the hydraulic characteristics of the medium (porosity, characteristics of the fluids, etc.), with seismic data, sensitive to the viscoelastic characteristics of the medium, produces soil models with a smaller number of uncertainties leading to a great utility in environmental diagnostics. This procedure, repeated over time, can provide an excellent geophysical tool for environmental monitoring of surface soils and for monitoring the capture and geological sequestration of CO2.
In the microgeophysical field, techniques for extracting significant information from thermographic and multispectral data will be applied. One of the specific aims of these applications will be to process large amounts of data with PCA techniques or similar, in order to be able to perform uniform diagnostics on large valuable surfaces.

Complex Network Analysis and Neuro-Imaging

Application of Krylov algorithms to the analysis of multilayer networks, exploiting ranking metrics for nodes based on functions of the incidence matrix. Similar techniques will be applied to bipartite graphs associated with seriation problems.
Analysis of EEG brain signals and comparison between the most common techniques used so far for the characterization of the functional network. A new approach based on multilayer analysis that allows to take into account both the distribution of the signal on the various brain rhythms and the temporal evolution of the functional network

Image Processing and Pattern Recognition

Implementation of fast and accurate algorithms for the analysis and processing of images based on orthogonal moments, with particular attention to images in the biomedical field. Verification of their effectiveness on public datasets, in view of an application in the diagnostic field.
Regarding thermal remote sensing, it is aimed the development of methods for the detection of anomalies in non-stationary time series and its correlation with the seismic activity of the observed areas by applying pattern detection techniques.
Application of analogous pattern detection techniques to geophysical data for archeology, in order to classify the detected anomalies both by using the information of the individual traces or families, and by looking for particular structures or geometrical properties of their three-dimensional distributions.

Shape from Shading and Archeology

Create an open source software for archaeological research, usable by non-expert personnel, which allows to build in real time accurate 3D models of petroglyphs observed during excavation.

Tools and resources available for the project

Different high-performance computers equipped with scientific softwares available online both as calculation engines and as servers.
Geophysical instrumentation: 120-channel seismometric units, monostatic and bistatic GPR units, multichannel GPR system (16 antennas, 200 MHz), TDEM and FDEM instrumentation (different investigation depths), Syscal Pro all-in-one multinode resistivity, thermal imaging camera with programmable acquisition, instrumentation for multispectral reflectography.
Biomedical instruments: Choosemuse wireless EEG 7 dry channels, Enobio 8 wireless EEG 8 channels, Micromed Brain quick HD EEG 64 channels.