Sparse image approximation with application to flexible image coding

Natural images are often modeled through piecewise-smooth regions. Region edges, which correspond to the contours of the objects, become, in this model, the main information of the signal. Contours have the property of being smooth functions along the direction of the edge, and irregularities on the perpendicular direction. Modeling edges with the minimum possible number of terms is of key importance for numerous applications, such as image coding, segmentation or denoising. Standard separable basis fail to provide sparse enough representation of contours, due to the fact that this kind of basis do not see the regularity of edges. In order to be able to detect this regularity, a new method based on (possibly redundant) sets of basis functions able to capture the geometry of images is needed. This thesis presents, in a first stage, a study about the features that basis functions should have in order to provide sparse representations of a piecewise-smooth image. This study emphasizes the need for edge-adapted basis functions, capable to accurately capture local orientation and anisotropic scaling of image structures. The need of different anisotropy degrees and orientations in the basis function set leads to the use of redundant dictionaries. However, redundant dictionaries have the inconvenience of giving no unique sparse image decompositions, and from all the possible decompositions of a signal in a redundant dictionary, just the sparsest is needed. There are several algorithms that allow to find sparse decompositions over redundant dictionaries, but most of these algorithms do not always guarantee that the optimal approximation has been recovered. To cope with this problem, a mathematical study about the properties of sparse approximations is performed. From this, a test to check whether a given sparse approximation is the sparsest is provided. The second part of this thesis presents a novel image approximation scheme, based on the use of a redundant dictionary. This scheme allows to have a good approximation of an image with a number of terms much smaller than the dimension of the signal. This novel approximation scheme is based on a dictionary formed by a combination of anisotropically refined and rotated wavelet-like mother functions and Gaussians. An efficient Full Search Matching Pursuit algorithm to perform the image decomposition in such a dictionary is designed. Finally, a geometric image coding scheme based on the image approximated over the anisotropic and rotated dictionary of basis functions is designed. The coding performances of this dictionary are studied. Coefficient quantization appears to be of crucial importance in the design of a Matching Pursuit based coding scheme. Thus, a quantization scheme for the MP coefficients has been designed, based on the theoretical energy upper bound of the MP algorithm and the empirical observations of the coefficient distribution and evolution. Thanks to this quantization, our image coder provides low to medium bit-rate image approximations, while it allows for on the fly resolution switching and several other affine image transformations to be performed directly in the transformed domain

Georisks in the Mediterranean and their mitigation

An international scientific conference organised by the Seismic Monitoring and Research Unit, Department of Geoscience, Faculty of Science, Department of Civil and Structural Engineering and Department of Construction and Property Management, Faculty of the Built Environment, University of Malta.Part of the SIMIT project: Integrated civil protection system for the Italo-Maltese cross-border area. Italia-Malta Programme – Cohesion Policy 2007-2013This conference is one of the activities organised within the SIMIT strategic project (Integrated Cross-Border Italo-Maltese System of Civil Protection), Italia-Malta Operational Programme 2007 – 2013. SIMIT aims to establish a system of collaboration in Civil Protection procedures and data management between Sicilian and Maltese partners, so as to guarantee the safety and protection of the citizens and infrastructure of the cross-border area. It is led by the Department of Civil Protection of the Sicilian region, and has as other partners the Department of Civil Protection of Malta and the Universities of Palermo, Catania and Malta. SIMIT was launched in March 2013, and will come to a close in October 2015. Ever since the initial formulation of the project, it has been recognised that a state of national preparedness and correct strategies in the face of natural hazards cannot be truly effective without a sound scientific knowledge of the hazards and related risks. The University of Malta, together with colleagues from other Universities in the project, has been contributing mostly to the gathering and application of scientific knowledge, both in earthquake hazard as well as in building vulnerability. The issue of seismic hazard in the cross-border region has been identified as deserving foremost importance. South-East Sicily in particular has suffered on more than one occasion the effects of large devastating earthquakes. Malta, although fortunately more removed from the sources of such large earthquakes, has not been completely spared of their damaging effects. The drastic increase in the building density over recent decades has raised the level of awareness and concern of citizens and authorities about our vulnerability. These considerations have spurred scientists from the cross-border region to work together towards a deeper understanding of the underlying causes and nature of seismic and associated hazards, such as landslide and tsunami. The SIMIT project has provided us with the means of improving earthquake surveillance and analysis in the Sicily Channel and further afield in the Mediterranean, as well as with facilities to study the behaviour of our rocks and buildings during earthquake shaking. The role of the civil engineering community in this endeavour cannot be overstated, and this is reflected in the incorporation, from the beginning, of the civil engineering component in the SIMIT project. Constructing safer buildings is now accepted to be the major option towards human loss mitigation during strong earthquakes, and this project has provided us with a welcome opportunity for interaction between the two disciplines. Finally the role of the Civil Protection authorities must occupy a central position, as we recognize the importance of their prevention, coordination and intervention efforts, aided by the input of the scientific community. This conference brings together a diversity of geoscientists and engineers whose collaboration is the only way forward to tackling issues and strategies for risk mitigation. Moreover we welcome the contribution of participants from farther afield than the Central Mediterranean, so that their varied experience may enhance our efforts. We are proud to host the conference in the historic city of Valletta, in the heart of the Mediterranean, which also serves as a constant reminder of the responsibility of all regions to protect and conserve our collective heritage.peer-reviewe