Analisi e processi di immagini astronomiche

Questa tesi riguarda l'analisi di immagini astronomiche. In particolare esamineremo tecniche che permettono l'elaborazione di immagini. Si parlerà di operazioni di base che comprendono le usuali operazioni matematiche e le trasformazioni geometriche fornendo alcuni esempi di applicazioni. Parleremo inoltre approfonditamente dell'operazione di convoluzione tra immagini e delle sue proprietà. Successivamente tratteremo in modo approfondito la teoria di Fourier, a partire dai suoi lavori sulle serie omonime fino allo sviluppo dell'algoritmo FFT. Vedremo inoltre svariate applicazioni della trasformata di Fourier all'analisi di immagini. Per concludere parleremo di deconvoluzione, analizzando in particolare due algoritmi deconvolutivi, l'algoritmo di Van Cittert e l'algoritmo di Richardson-Lucy.

Conjectures and theorems in the theory of entire functions

Motivated by the recent solution of Karlin's conjecture, properties of functions in the Laguerre-Polya class are investigated. The main result of this paper establishes new moment inequalities fur a class of entire functions represented by Fourier transforms. The paper concludes with several conjectures and open problems involving the Laguerre-Polya class and the Riemann xi -function.

On Fast Bilateral Filtering Using Fourier Kernels

It was demonstrated in earlier work that, by approximating its range kernel using shiftable functions, the nonlinear bilateral filter can be computed using a series of fast convolutions. Previous approaches based on shiftable approximation have, however, been restricted to Gaussian range kernels. In this work, we propose a novel approximation that can be applied to any range kernel, provided it has a pointwise-convergent Fourier series. More specifically, we propose to approximate the Gaussian range kernel of the bilateral filter using a Fourier basis, where the coefficients of the basis are obtained by solving a series of least-squares problems. The coefficients can be efficiently computed using a recursive form of the QR decomposition. By controlling the cardinality of the Fourier basis, we can obtain a good tradeoff between the run-time and the filtering accuracy. In particular, we are able to guarantee subpixel accuracy for the overall filtering, which is not provided by the most existing methods for fast bilateral filtering. We present simulation results to demonstrate the speed and accuracy of the proposed algorithm.

Studio e sviluppo di algoritmi di elaborazione di immagini da TC per analisi perfusionali

La Tomografia Computerizzata (TC) perfusionale rappresenta attualmente una importante tecnica di imaging radiologico in grado di fornire indicatori funzionali di natura emodinamica relativi alla vascolarizzazione dei tessuti investigati. Le moderne macchine TC consentono di effettuare analisi funzionali ad una elevata risoluzione spaziale e temporale, provvedendo ad una caratterizzazione più accurata di zone di interesse clinico attraverso l’analisi dinamica della concentrazione di un mezzo di contrasto, con dosi contenute per il paziente. Tale tecnica permette potenzialmente di effettuare una valutazione precoce dell’efficacia di trattamenti antitumorali, prima ancora che vengano osservate variazioni morfologiche delle masse tumorali, con evidenti benefici prognostici. I principali problemi aperti in questo campo riguardano la standardizzazione dei protocolli di acquisizione e di elaborazione delle sequenze perfusionali, al fine di una validazione accurata e consistente degli indicatori funzionali nella pratica clinica. Differenti modelli matematici sono proposti in letteratura al fine di determinare parametri di interesse funzionale a partire dall’analisi del profilo dinamico del mezzo di contrasto in differenti tessuti. Questa tesi si propone di studiare, attraverso l’analisi e l’elaborazione di sequenze di immagini derivanti da TC assiale perfusionale, due importanti modelli matematici di stima della perfusione. In particolare, vengono presentati ed analizzati il modello del massimo gradiente ed il modello deconvoluzionale, evidenziandone tramite opportune simulazioni le particolarità e le criticità con riferimento agli artefatti più importanti che influenzano il protocollo perfusionale. Inoltre, i risultati ottenuti dall’analisi di casi reali riguardanti esami perfusionali epatici e polmonari sono discussi al fine di valutare la consistenza delle misure quantitative ottenute tramite i due metodi con le considerazioni di natura clinica proposte dal radiologo.

Segmentazione di immagini mammografiche con convolutional neural networks

Il tumore al seno si colloca al primo posto per livello di mortalità tra le patologie tumorali che colpiscono la popolazione femminile mondiale. Diversi studi clinici hanno dimostrato come la diagnosi da parte del radiologo possa essere aiutata e migliorata dai sistemi di Computer Aided Detection (CAD). A causa della grande variabilità di forma e dimensioni delle masse tumorali e della somiglianza di queste con i tessuti che le ospitano, la loro ricerca automatizzata è un problema estremamente complicato. Un sistema di CAD è generalmente composto da due livelli di classificazione: la detection, responsabile dell’individuazione delle regioni sospette presenti sul mammogramma (ROI) e quindi dell’eliminazione preventiva delle zone non a rischio; la classificazione vera e propria (classification) delle ROI in masse e tessuto sano. Lo scopo principale di questa tesi è lo studio di nuove metodologie di detection che possano migliorare le prestazioni ottenute con le tecniche tradizionali. Si considera la detection come un problema di apprendimento supervisionato e lo si affronta mediante le Convolutional Neural Networks (CNN), un algoritmo appartenente al deep learning, nuova branca del machine learning. Le CNN si ispirano alle scoperte di Hubel e Wiesel riguardanti due tipi base di cellule identificate nella corteccia visiva dei gatti: le cellule semplici (S), che rispondono a stimoli simili ai bordi, e le cellule complesse (C) che sono localmente invarianti all’esatta posizione dello stimolo. In analogia con la corteccia visiva, le CNN utilizzano un’architettura profonda caratterizzata da strati che eseguono sulle immagini, alternativamente, operazioni di convoluzione e subsampling. Le CNN, che hanno un input bidimensionale, vengono solitamente usate per problemi di classificazione e riconoscimento automatico di immagini quali oggetti, facce e loghi o per l’analisi di documenti.

Fast and accurate numerical solutions in some problems of particle and radiation transport: synthetic acceleration for the method of short characteristics, Doppler-broadened scattering kernel, remote sensing of the cryosphere

The aim of this work is to present various aspects of numerical simulation of particle and radiation transport for industrial and environmental protection applications, to enable the analysis of complex physical processes in a fast, reliable, and efficient way. In the first part we deal with speed-up of numerical simulation of neutron transport for nuclear reactor core analysis. The convergence properties of the source iteration scheme of the Method of Characteristics applied to be heterogeneous structured geometries has been enhanced by means of Boundary Projection Acceleration, enabling the study of 2D and 3D geometries with transport theory without spatial homogenization. The computational performances have been verified with the C5G7 2D and 3D benchmarks, showing a sensible reduction of iterations and CPU time. The second part is devoted to the study of temperature-dependent elastic scattering of neutrons for heavy isotopes near to the thermal zone. A numerical computation of the Doppler convolution of the elastic scattering kernel based on the gas model is presented, for a general energy dependent cross section and scattering law in the center of mass system. The range of integration has been optimized employing a numerical cutoff, allowing a faster numerical evaluation of the convolution integral. Legendre moments of the transfer kernel are subsequently obtained by direct quadrature and a numerical analysis of the convergence is presented. In the third part we focus our attention to remote sensing applications of radiative transfer employed to investigate the Earth's cryosphere. The photon transport equation is applied to simulate reflectivity of glaciers varying the age of the layer of snow or ice, its thickness, the presence or not other underlying layers, the degree of dust included in the snow, creating a framework able to decipher spectral signals collected by orbiting detectors.

Un metodo di tipo Newton per la ricostruzione di immagini con norma L1

Scopo dell'opera è implementare in maniera efficiente ed affidabile un metodo di tipo Newton per la ricostruzione di immagini con termine regolativo in norma L1. In particolare due metodi, battezzati "OWL-QN per inversione" e "OWL-QN precondizionato", sono presentati e provati con numerose sperimentazioni. I metodi sono generati considerando le peculiarità del problema e le proprietà della trasformata discreta di Fourier. I risultati degli esperimenti numerici effettuati mostrano la bontà del contributo proposto, dimostrando la loro superiorità rispetto al metodo OWL-QN presente in letteratura, seppure adattato alle immagini.

On the Mixed Modulus of Smoothness and a Class of Double Fourier Series

MSC 2010: 42A32; 42A20

Adaptive instantaneous frequency estimation: Techniques and algorithms

This thesis deals with the problem of the instantaneous frequency (IF) estimation of sinusoidal signals. This topic plays significant role in signal processing and communications. Depending on the type of the signal, two major approaches are considered. For IF estimation of single-tone or digitally-modulated sinusoidal signals (like frequency shift keying signals) the approach of digital phase-locked loops (DPLLs) is considered, and this is Part-I of this thesis. For FM signals the approach of time-frequency analysis is considered, and this is Part-II of the thesis. In part-I we have utilized sinusoidal DPLLs with non-uniform sampling scheme as this type is widely used in communication systems. The digital tanlock loop (DTL) has introduced significant advantages over other existing DPLLs. In the last 10 years many efforts have been made to improve DTL performance. However, this loop and all of its modifications utilizes Hilbert transformer (HT) to produce a signal-independent 90-degree phase-shifted version of the input signal. Hilbert transformer can be realized approximately using a finite impulse response (FIR) digital filter. This realization introduces further complexity in the loop in addition to approximations and frequency limitations on the input signal. We have tried to avoid practical difficulties associated with the conventional tanlock scheme while keeping its advantages. A time-delay is utilized in the tanlock scheme of DTL to produce a signal-dependent phase shift. This gave rise to the time-delay digital tanlock loop (TDTL). Fixed point theorems are used to analyze the behavior of the new loop. As such TDTL combines the two major approaches in DPLLs: the non-linear approach of sinusoidal DPLL based on fixed point analysis, and the linear tanlock approach based on the arctan phase detection. TDTL preserves the main advantages of the DTL despite its reduced structure. An application of TDTL in FSK demodulation is also considered. This idea of replacing HT by a time-delay may be of interest in other signal processing systems. Hence we have analyzed and compared the behaviors of the HT and the time-delay in the presence of additive Gaussian noise. Based on the above analysis, the behavior of the first and second-order TDTLs has been analyzed in additive Gaussian noise. Since DPLLs need time for locking, they are normally not efficient in tracking the continuously changing frequencies of non-stationary signals, i.e. signals with time-varying spectra. Nonstationary signals are of importance in synthetic and real life applications. An example is the frequency-modulated (FM) signals widely used in communication systems. Part-II of this thesis is dedicated for the IF estimation of non-stationary signals. For such signals the classical spectral techniques break down, due to the time-varying nature of their spectra, and more advanced techniques should be utilized. For the purpose of instantaneous frequency estimation of non-stationary signals there are two major approaches: parametric and non-parametric. We chose the non-parametric approach which is based on time-frequency analysis. This approach is computationally less expensive and more effective in dealing with multicomponent signals, which are the main aim of this part of the thesis. A time-frequency distribution (TFD) of a signal is a two-dimensional transformation of the signal to the time-frequency domain. Multicomponent signals can be identified by multiple energy peaks in the time-frequency domain. Many real life and synthetic signals are of multicomponent nature and there is little in the literature concerning IF estimation of such signals. This is why we have concentrated on multicomponent signals in Part-H. An adaptive algorithm for IF estimation using the quadratic time-frequency distributions has been analyzed. A class of time-frequency distributions that are more suitable for this purpose has been proposed. The kernels of this class are time-only or one-dimensional, rather than the time-lag (two-dimensional) kernels. Hence this class has been named as the T -class. If the parameters of these TFDs are properly chosen, they are more efficient than the existing fixed-kernel TFDs in terms of resolution (energy concentration around the IF) and artifacts reduction. The T-distributions has been used in the IF adaptive algorithm and proved to be efficient in tracking rapidly changing frequencies. They also enables direct amplitude estimation for the components of a multicomponent

Color and texture feature fusion using kernel PCA with application to object-based vegetation species classification

A good object representation or object descriptor is one of the key issues in object based image analysis. To effectively fuse color and texture as a unified descriptor at object level, this paper presents a novel method for feature fusion. Color histogram and the uniform local binary patterns are extracted from arbitrary-shaped image-objects, and kernel principal component analysis (kernel PCA) is employed to find nonlinear relationships of the extracted color and texture features. The maximum likelihood approach is used to estimate the intrinsic dimensionality, which is then used as a criterion for automatic selection of optimal feature set from the fused feature. The proposed method is evaluated using SVM as the benchmark classifier and is applied to object-based vegetation species classification using high spatial resolution aerial imagery. Experimental results demonstrate that great improvement can be achieved by using proposed feature fusion method.