Denoising di immagini mediante tecniche basate sulla Total Variation.

Il lavoro svolto in questa tesi è legato allo studio ed alla formulazione di metodi computazionali volti all’eliminazione del noise (rumore) presente nelle immagini, cioè il processo di “denoising” che è quello di ricostruire un’immagine corrotta da rumore avendo a disposizione una conoscenza a priori del fenomeno di degrado. Il problema del denoising è formulato come un problema di minimo di un funzionale dato dalla somma di una funzione che rappresenta l’adattamento dei dati e la Variazione Totale. I metodi di denoising di immagini saranno affrontati attraverso tecniche basate sullo split Bregman e la Total Variation (TV) pesata che è un problema mal condizionato, cioè un problema sensibile a piccole perturbazioni sui dati. Queste tecniche permettono di ottimizzare dal punto di vista della visualizzazione le immagini in esame.

Il metodo di steepest descent per la regolarizzazione di immagini

Scopo della tesi è la descrizione di un metodo per il calcolo di minimi di funzionali, basato sulla steepest descent. L'idea principale è quella di considerare un flusso nella direzione opposta al gradiente come soluzione di un problema di Cauchy in spazi di Banach, che sotto l'ipotesi di Palais-Smale permette di determinare minimi. Il metodo viene applicato al problema di denoising e segmentazione in elaborazione di immagini: vengono presentati metodi classici basati sull'equazione del calore, il total variation ed il Perona Malik. Nell'ultimo capitolo il grafico di un'immagine viene considerato come varietà, che induce una metrica sul suo dominio, e viene nuovamente utilizzato il metodo di steepest descent per costruire algoritmi che tengano conto delle caratteristiche geometriche dell'immagine.

Funzioni a variazione limitata per la ricolorazione di un'immagine

Nella tesi si intende ricolorare alcune porzioni di un'immagine delle quali è nota soltanto la scala dei grigi. Il colore viene considerato nello spazio RGB e decomposto in cromaticità e luminosità. Il problema viene espresso come problema di minimo di un funzionale detto di ``Total Variation'', definito sulle funzioni a variazione limitata BV. Si introduce la nozione di funzione BV di R^n, le principali proprietà di queste funzioni e in particolare si enuncia un teorema di compattezza. Si utilizzano infine tali risultati per ottenere l'esistenza di un punto di minimo per il funzionale che risolve il problema della ricolorazione.

Compressed sensing in digital tomosynthesis reconstruction

In this work we study a model for the breast image reconstruction in Digital Tomosynthesis, that is a non-invasive and non-destructive method for the three-dimensional visualization of the inner structures of an object, in which the data acquisition includes measuring a limited number of low-dose two-dimensional projections of an object by moving a detector and an X-ray tube around the object within a limited angular range. The problem of reconstructing 3D images from the projections provided in the Digital Tomosynthesis is an ill-posed inverse problem, that leads to a minimization problem with an object function that contains a data fitting term and a regularization term. The contribution of this thesis is to use the techniques of the compressed sensing, in particular replacing the standard least squares problem of data fitting with the problem of minimizing the 1-norm of the residuals, and using as regularization term the Total Variation (TV). We tested two different algorithms: a new alternating minimization algorithm (ADM), and a version of the more standard scaled projected gradient algorithm (SGP) that involves the 1-norm. We perform some experiments and analyse the performance of the two methods comparing relative errors, iterations number, times and the qualities of the reconstructed images. In conclusion we noticed that the use of the 1-norm and the Total Variation are valid tools in the formulation of the minimization problem for the image reconstruction resulting from Digital Tomosynthesis and the new algorithm ADM has reached a relative error comparable to a version of the classic algorithm SGP and proved best in speed and in the early appearance of the structures representing the masses.

Spatio-temporal variation of macrofaunal assemblages in the deep Blanes submarine canyon

The spatio-temporal variations in diversity and abundance of deep-sea macrofaunal assemblages (excluding meiofaunal taxa, as Nematoda, Copepoda and Ostracoda) from the Blanes Canyon (BC) and adjacent open slope are described. The Catalan Sea basin is characterized by the presence of numerous submarine canyons, which are globally acknowledged as biodiversity hot-spots, due to their disturbance regime and incremented conveying of organic matter. This area is subjected to local deep-sea fisheries activities, and to recurrent cold water cascading events from the shelf. The upper canyon (~900 m), middle slope (~1200 m) and lower slope (~1500 m) habitats were investigated during three different months (October 2008, May 2009 and September 2009). A total of 624 specimens belonging to 16 different taxa were found into 67 analyzed samples, which had been collected from the two study areas. Of these, Polychaeta, Mollusca and Crustacea were always the most abundant groups. As expected, the patterns of species diversity and evenness were different in time and space. Both in BC and open slope, taxa diversity and abundance are higher in the shallowest depth and lowest at -1500 m depth. This is probably due to different trophic regimes at these depths. The abundance of filter-feeders is higher inside BC than in the adjacent open slope, which is also related with an increment of predator polychaetes. Surface deposit-feeders are more abundant in the open slope than in BC, along with a decrement of filter-feeders and their predators. Probably these differences are due to higher quantities of suspended organic matter reaching the canyon. The multivariate analyses conducted on major taxa point out major differences effective taxa richness between depths and stations. In September 2009 the analyzed communities double their abundances, with a corresponding increase in richness of taxa. This could be related to a mobilizing event, like the release of accumulated food-supply in a nepheloid layer associated to the arrival of autumn. The highest abundance in BC is detected in the shallowest depth and in late summer (September), probably due to higher food availability caused by stronger flood events coming from Tordera River. The effects of such events seemed to involve adjacent open slope too. The nMDS conducted on major taxa abundance shows a slight temporal difference between the three campaigns samples, with a clear clustering between samples of Sept 09. All depth and all months were dominated by Polychaeta, which have been identified to family level and submitted to further analysis. Family richness have clearly minimum at the -1200 m depth of BC, highlighting the presence of a general impact affecting the populations in the middle slope. Three different matrices have been created, each with a different taxonomic level (All Taxa “AT”, Phylum Level “PL” and Polychaeta Families “PF”). Multivariate analysis (MDS, SIMPER) conducted on PL matrix showed a clear spatial differences between stations (BC and open slope) and depths. MDSs conducted on other two matrices (AT and PF) showed similar patterns, but different from PL analysis. A 2 nd stage analysis have been conducted to understand differences between different taxonomic levels, and PL level has been chosen as the most representative of variation. The faunal differences observed were explained by depth, station and season. All work has been accomplished in the Centre d’estudis avançats de Blanes (CEAB-CSIC), within the framework of Spanish PROMETEO project "Estudio Integrado de Cañones y Taludes PROfundos del MEdiTErráneo Occidental: un hábitat esencial", Ref. CTM2007-66316-C02- 01/MAR.

Are there genetic breaks between Atlantic and Pacific Yellowfin tuna (Thunnus albacares) populations? A preliminary study based on microsatellites gene variation

Yellowfin tuna (Thunnus albacares, YFT, Bonnaterre 1788) is one of the most important market tuna species in the world. The high mortality of juveniles is in part caused by their bycatch. Indeed, if unregulated, it could permanently destabilize stocks health. For this reason investigating and better knowing the stock boundaries represent a crucial concern. Aim of this thesis was to preliminary investigate the YFT population structure within and between Atlantic and Pacific Oceans through the analysis of genetic variation at eight microsatellite loci and assess the occurrence of barriers to the gene flow between Oceans. For this propouse we collected 4 geographical samples coming from Atlantic and Pacific Ocean and selected a panel of 8 microsatellites loci developped by Antoni et al., (2014). Samples 71-2-Y and 77-2-Y, came from rispectively west central pacific ocean (WCPO) and east central pacific ocean (ECPO), instead samples 41-1-Y and 34-2-Y derive from west central atlantic ocean (WCAO) and east central atlantic ocean (ECAO). Total 160 specimens were analyzed (40 per sample) and were carried out several genetic information as allele frequencies, allele number, allelic richness, HWE (using He and Ho) and pairwise Fst genetic distance. Results obtained, may support the panmictic theory of this species, only one of pairwise Fst obtained is statistically significant (Fst= 0.00927; pV= 0.00218) between 41-1-Y and 71-2-Y samples. Results suggest low genetic differentiation and consequent high level of gene flow between Atlantic and Pacific populations. Furthermore, we performed an analysis of molecular taxonomy through the use of ATCO (the flaking region between ATPse6 and cytochrome oxidase subunit III genes mt DNA, to discriminate within the gener Thunnus two of the related species (Yellofin and bigeye tuna) according with their difficult recognition at certain size (<40 cm). ATCO analysis in this thesis, has provided strong discriminate evidence between the target species proving to be one of the most reliable genetic tools capable to indagate within the genus Thunnus. Thus, our study has provided useful information for possible use of this protocol for conservation plans and management of this fish stocks.