Ultra low power analog-to-information conversion by short-time compressed sensing

Il compressed sensing è un’innovativa tecnica per l’acquisizione dei dati, che mira all'estrazione del solo contenuto informativo intrinseco di un segnale. Ciò si traduce nella possibilità di acquisire informazione direttamente in forma compressa, riducendo la quantità di risorse richieste per tale operazione. In questa tesi è sviluppata un'architettura hardware per l'acquisizione di segnali analogici basata sul compressed sensing, specializzata al campionamento con consumo di potenza ridotto di segnali biomedicali a basse frequenze. Lo studio è svolto a livello di sistema mediante l'integrazione della modulazione richiesta dal compressed sensing in un convertitore analogico-digitale ad approssimazioni successive, modificandone la logica di controllo. Le prestazioni risultanti sono misurate tramite simulazioni numeriche e circuitali. Queste confermano la possibilità di ridurre la complessità hardware del sistema di acquisizione rispetto allo stato dell'arte, senza alterarne le prestazioni.

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.

Estimation of Symmetric Channels for Discrete Cosine Transform Type-I Multicarrier Systems: A Compressed Sensing Approach

The problem of channel estimation for multicarrier communications is addressed. We focus on systems employing the Discrete Cosine Transform Type-I (DCT1) even at both the transmitter and the receiver, presenting an algorithm which achieves an accurate estimation of symmetric channel filters using only a small number of training symbols. The solution is obtained by using either matrix inversion or compressed sensing algorithms. We provide the theoretical results which guarantee the validity of the proposed technique for the DCT1. Numerical simulations illustrate the good behaviour of the proposed algorithm.

Optimal sparsifying bases for frequency-domain optical-coherence tomography

We address the reconstruction problem in frequency-domain optical-coherence tomography (FDOCT) from under-sampled measurements within the framework of compressed sensing (CS). Specifically, we propose optimal sparsifying bases for accurate reconstruction by analyzing the backscattered signal model. Although one might expect Fourier bases to be optimal for the FDOCT reconstruction problem, it turns out that the optimal sparsifying bases are windowed cosine functions where the window is the magnitude spectrum of the laser source. Further, the windowed cosine bases can be phase locked, which allows one to obtain higher accuracy in reconstruction. We present experimental validations on real data. The findings reported in this Letter are useful for optimal dictionary design within the framework of CS-FDOCT. (C) 2012 Optical Society of America

Low order anti-aliasing filters for sparse signals in embedded applications

Major emphasis, in compressed sensing (CS) research, has been on the acquisition of sub-Nyquist number of samples of a signal that has a sparse representation on some tight frame or an orthogonal basis, and subsequent reconstruction of the original signal using a plethora of recovery algorithms. In this paper, we present compressed sensing data acquisition from a different perspective, wherein a set of signals are reconstructed at a sampling rate which is a multiple of the sampling rate of the ADCs that are used to measure the signals. We illustrate how this can facilitate usage of anti-aliasing filters with relaxed frequency specifications and, consequently, of lower order.

Low complexity joint estimation of synchronization impairments in sparse channel for MIMO-OFDM system

Low complexity joint estimation of synchronization impairments and channel in a single-user MIMO-OFDM system is presented in this paper. Based on a system model that takes into account the effects of synchronization impairments such as carrier frequency offset, sampling frequency offset, and symbol timing error, and channel, a Maximum Likelihood (ML) algorithm for the joint estimation is proposed. To reduce the complexity of ML grid search, the number of received signal samples used for estimation need to be reduced. The conventional channel estimation techniques using Least-Squares (LS) or Maximum a posteriori (MAP) methods fail for the reduced sample under-determined system, which results in poor performance of the joint estimator. The proposed ML algorithm uses Compressed Sensing (CS) based channel estimation method in a sparse fading scenario, where the received samples used for estimation are less than that required for an LS or MAP based estimation. The performance of the estimation method is studied through numerical simulations, and it is observed that CS based joint estimator performs better than LS and MAP based joint estimator. (C) 2013 Elsevier GmbH. All rights reserved.

Reduced Look Ahead Orthogonal Matching Pursuit

Compressed Sensing (CS) is an elegant technique to acquire signals and reconstruct them efficiently by solving a system of under-determined linear equations. The excitement in this field stems from the fact that we can sample at a rate way below the Nyquist rate and still reconstruct the signal provided some conditions are met. Some of the popular greedy reconstruction algorithms are the Orthogonal Matching Pursuit (OMP), the Subspace Pursuit (SP) and the Look Ahead Orthogonal Matching Pursuit (LAOMP). The LAOMP performs better than the OMP. However, when compared to the SP and the OMP, the computational complexity of LAOMP is higher. We introduce a modified version of the LAOMP termed as Reduced Look Ahead Orthogonal Matching Pursuit (Reduced LAOMP). Reduced LAOMP uses prior information from the results of the OMP and the SP in the quest to speedup the look ahead strategy in the LAOMP. Monte Carlo simulations of this algorithm deliver promising results.

Ricostruzione di immagini in norma L1

In questa tesi è stato trattato il problema della ricostruzione di immagini di tomografia computerizzata considerando un modello che utilizza la variazione totale come termine di regolarizzazione e la norma 1 come fidelity term (modello TV/L1). Il problema è stato risolto modificando un metodo di minimo alternato utilizzato per il deblurring e denoising di immagini affette da rumore puntuale. Il metodo è stato testato nel caso di rumore gaussiano e geometria fan beam e parallel beam. Infine vengono riportati i risultati ottenuti dalle sperimentazioni.

Inversione della trasformata di Laplace mediante regolarizzazione con norma L1

I dati derivanti da spettroscopia NMR sono l'effetto di fenomeni descritti attraverso la trasformata di Laplace della sorgente che li ha prodotti. Ci si riferisce a un problema inverso con dati discreti ed in relazione ad essi nasce l'esigenza di realizzare metodi numerici per l'inversione della trasformata di Laplace con dati discreti che è notoriamente un problema mal posto e pertanto occorre ricorrere a metodi di regolarizzazione. In questo contesto si propone una variante ai modelli presenti il letteratura che fanno utilizzo della norma L2, introducendo la norma L1.

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.

Infrared image enhancement based on hybrid-domain consideration and data fusion methods

Au cours des dernières décennies, l’effort sur les applications de capteurs infrarouges a largement progressé dans le monde. Mais, une certaine difficulté demeure, en ce qui concerne le fait que les objets ne sont pas assez clairs ou ne peuvent pas toujours être distingués facilement dans l’image obtenue pour la scène observée. L’amélioration de l’image infrarouge a joué un rôle important dans le développement de technologies de la vision infrarouge de l’ordinateur, le traitement de l’image et les essais non destructifs, etc. Cette thèse traite de la question des techniques d’amélioration de l’image infrarouge en deux aspects, y compris le traitement d’une seule image infrarouge dans le domaine hybride espacefréquence, et la fusion d’images infrarouges et visibles employant la technique du nonsubsampled Contourlet transformer (NSCT). La fusion d’images peut être considérée comme étant la poursuite de l’exploration du modèle d’amélioration de l’image unique infrarouge, alors qu’il combine les images infrarouges et visibles en une seule image pour représenter et améliorer toutes les informations utiles et les caractéristiques des images sources, car une seule image ne pouvait contenir tous les renseignements pertinents ou disponibles en raison de restrictions découlant de tout capteur unique de l’imagerie. Nous examinons et faisons une enquête concernant le développement de techniques d’amélioration d’images infrarouges, et ensuite nous nous consacrons à l’amélioration de l’image unique infrarouge, et nous proposons un schéma d’amélioration de domaine hybride avec une méthode d’évaluation floue de seuil amélioré, qui permet d’obtenir une qualité d’image supérieure et améliore la perception visuelle humaine. Les techniques de fusion d’images infrarouges et visibles sont établies à l’aide de la mise en oeuvre d’une mise en registre précise des images sources acquises par différents capteurs. L’algorithme SURF-RANSAC est appliqué pour la mise en registre tout au long des travaux de recherche, ce qui conduit à des images mises en registre de façon très précise et des bénéfices accrus pour le traitement de fusion. Pour les questions de fusion d’images infrarouges et visibles, une série d’approches avancées et efficaces sont proposés. Une méthode standard de fusion à base de NSCT multi-canal est présente comme référence pour les approches de fusion proposées suivantes. Une approche conjointe de fusion, impliquant l’Adaptive-Gaussian NSCT et la transformée en ondelettes (Wavelet Transform, WT) est propose, ce qui conduit à des résultats de fusion qui sont meilleurs que ceux obtenus avec les méthodes non-adaptatives générales. Une approche de fusion basée sur le NSCT employant la détection comprime (CS, compressed sensing) et de la variation totale (TV) à des coefficients d’échantillons clairsemés et effectuant la reconstruction de coefficients fusionnés de façon précise est proposée, qui obtient de bien meilleurs résultats de fusion par le biais d’une pré-amélioration de l’image infrarouge et en diminuant les informations redondantes des coefficients de fusion. Une procédure de fusion basée sur le NSCT utilisant une technique de détection rapide de rétrécissement itératif comprimé (fast iterative-shrinking compressed sensing, FISCS) est proposée pour compresser les coefficients décomposés et reconstruire les coefficients fusionnés dans le processus de fusion, qui conduit à de meilleurs résultats plus rapidement et d’une manière efficace.

Transmission electron tomography: quality assessment and enhancement for three-dimensional imaging of nanostructures

Nanotechnology has revolutionised humanity's capability in building microscopic systems by manipulating materials on a molecular and atomic scale. Nan-osystems are becoming increasingly smaller and more complex from the chemical perspective which increases the demand for microscopic characterisation techniques. Among others, transmission electron microscopy (TEM) is an indispensable tool that is increasingly used to study the structures of nanosystems down to the molecular and atomic scale. However, despite the effectivity of this tool, it can only provide 2-dimensional projection (shadow) images of the 3D structure, leaving the 3-dimensional information hidden which can lead to incomplete or erroneous characterization. One very promising inspection method is Electron Tomography (ET), which is rapidly becoming an important tool to explore the 3D nano-world. ET provides (sub-)nanometer resolution in all three dimensions of the sample under investigation. However, the fidelity of the ET tomogram that is achieved by current ET reconstruction procedures remains a major challenge. This thesis addresses the assessment and advancement of electron tomographic methods to enable high-fidelity three-dimensional investigations. A quality assessment investigation was conducted to provide a quality quantitative analysis of the main established ET reconstruction algorithms and to study the influence of the experimental conditions on the quality of the reconstructed ET tomogram. Regular shaped nanoparticles were used as a ground-truth for this study. It is concluded that the fidelity of the post-reconstruction quantitative analysis and segmentation is limited, mainly by the fidelity of the reconstructed ET tomogram. This motivates the development of an improved tomographic reconstruction process. In this thesis, a novel ET method was proposed, named dictionary learning electron tomography (DLET). DLET is based on the recent mathematical theorem of compressed sensing (CS) which employs the sparsity of ET tomograms to enable accurate reconstruction from undersampled (S)TEM tilt series. DLET learns the sparsifying transform (dictionary) in an adaptive way and reconstructs the tomogram simultaneously from highly undersampled tilt series. In this method, the sparsity is applied on overlapping image patches favouring local structures. Furthermore, the dictionary is adapted to the specific tomogram instance, thereby favouring better sparsity and consequently higher quality reconstructions. The reconstruction algorithm is based on an alternating procedure that learns the sparsifying dictionary and employs it to remove artifacts and noise in one step, and then restores the tomogram data in the other step. Simulation and real ET experiments of several morphologies are performed with a variety of setups. Reconstruction results validate its efficiency in both noiseless and noisy cases and show that it yields an improved reconstruction quality with fast convergence. The proposed method enables the recovery of high-fidelity information without the need to worry about what sparsifying transform to select or whether the images used strictly follow the pre-conditions of a certain transform (e.g. strictly piecewise constant for Total Variation minimisation). This can also avoid artifacts that can be introduced by specific sparsifying transforms (e.g. the staircase artifacts the may result when using Total Variation minimisation). Moreover, this thesis shows how reliable elementally sensitive tomography using EELS is possible with the aid of both appropriate use of Dual electron energy loss spectroscopy (DualEELS) and the DLET compressed sensing algorithm to make the best use of the limited data volume and signal to noise inherent in core-loss electron energy loss spectroscopy (EELS) from nanoparticles of an industrially important material. Taken together, the results presented in this thesis demonstrates how high-fidelity ET reconstructions can be achieved using a compressed sensing approach.

Adaptive temporal compressive sensing for video

This paper introduces the concept of adaptive temporal compressive sensing (CS) for video. We propose a CS algorithm to adapt the compression ratio based on the scene's temporal complexity, computed from the compressed data, without compromising the quality of the reconstructed video. The temporal adaptivity is manifested by manipulating the integration time of the camera, opening the possibility to realtime implementation. The proposed algorithm is a generalized temporal CS approach that can be incorporated with a diverse set of existing hardware systems. © 2013 IEEE.

Compressive sensing in Clifford analysis

Compressed sensing is a new paradigm in signal processing which states that for certain matrices sparse representations can be obtained by a simple l1-minimization. In this thesis we explore this paradigm for higher-dimensional signal. In particular three cases are being studied: signals taking values in a bicomplex algebra, quaternionic signals, and complex signals which are representable by a nonlinear Fourier basis, a so-called Takenaka-Malmquist system.

Antipodal random sequences with prescribed second-order statistics: application to Compressive Sensing and UWB system based on DS-CDMA

It is usual to hear a strange short sentence: «Random is better than...». Why is randomness a good solution to a certain engineering problem? There are many possible answers, and all of them are related to the considered topic. In this thesis I will discuss about two crucial topics that take advantage by randomizing some waveforms involved in signals manipulations. In particular, advantages are guaranteed by shaping the second order statistic of antipodal sequences involved in an intermediate signal processing stages. The first topic is in the area of analog-to-digital conversion, and it is named Compressive Sensing (CS). CS is a novel paradigm in signal processing that tries to merge signal acquisition and compression at the same time. Consequently it allows to direct acquire a signal in a compressed form. In this thesis, after an ample description of the CS methodology and its related architectures, I will present a new approach that tries to achieve high compression by design the second order statistics of a set of additional waveforms involved in the signal acquisition/compression stage. The second topic addressed in this thesis is in the area of communication system, in particular I focused the attention on ultra-wideband (UWB) systems. An option to produce and decode UWB signals is direct-sequence spreading with multiple access based on code division (DS-CDMA). Focusing on this methodology, I will address the coexistence of a DS-CDMA system with a narrowband interferer. To do so, I minimize the joint effect of both multiple access (MAI) and narrowband (NBI) interference on a simple matched filter receiver. I will show that, when spreading sequence statistical properties are suitably designed, performance improvements are possible with respect to a system exploiting chaos-based sequences minimizing MAI only.