Il Compressed Sensing

Introduzione al metodo del Compressed Sensing per il campionamento di segnali sparsi.

Matrix Designs and Methods for Secure and Efficient Compressed Sensing

The idea of balancing the resources spent in the acquisition and encoding of natural signals strictly to their intrinsic information content has interested nearly a decade of research under the name of compressed sensing. In this doctoral dissertation we develop some extensions and improvements upon this technique's foundations, by modifying the random sensing matrices on which the signals of interest are projected to achieve different objectives. Firstly, we propose two methods for the adaptation of sensing matrix ensembles to the second-order moments of natural signals. These techniques leverage the maximisation of different proxies for the quantity of information acquired by compressed sensing, and are efficiently applied in the encoding of electrocardiographic tracks with minimum-complexity digital hardware. Secondly, we focus on the possibility of using compressed sensing as a method to provide a partial, yet cryptanalysis-resistant form of encryption; in this context, we show how a random matrix generation strategy with a controlled amount of perturbations can be used to distinguish between multiple user classes with different quality of access to the encrypted information content. Finally, we explore the application of compressed sensing in the design of a multispectral imager, by implementing an optical scheme that entails a coded aperture array and Fabry-Pérot spectral filters. The signal recoveries obtained by processing real-world measurements show promising results, that leave room for an improvement of the sensing matrix calibration problem in the devised imager.

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.

Compressed sensing based cyclic feature spectrum sensing for cognitive radios

Spectrum sensing is currently one of the most challenging design problems in cognitive radio. A robust spectrum sensing technique is important in allowing implementation of a practical dynamic spectrum access in noisy and interference uncertain environments. In addition, it is desired to minimize the sensing time, while meeting the stringent cognitive radio application requirements. To cope with this challenge, cyclic spectrum sensing techniques have been proposed. However, such techniques require very high sampling rates in the wideband regime and thus are costly in hardware implementation and power consumption. In this thesis the concept of compressed sensing is applied to circumvent this problem by utilizing the sparsity of the two-dimensional cyclic spectrum. Compressive sampling is used to reduce the sampling rate and a recovery method is developed for re- constructing the sparse cyclic spectrum from the compressed samples. The reconstruction solution used, exploits the sparsity structure in the two-dimensional cyclic spectrum do-main which is different from conventional compressed sensing techniques for vector-form sparse signals. The entire wideband cyclic spectrum is reconstructed from sub-Nyquist-rate samples for simultaneous detection of multiple signal sources. After the cyclic spectrum recovery two methods are proposed to make spectral occupancy decisions from the recovered cyclic spectrum: a band-by-band multi-cycle detector which works for all modulation schemes, and a fast and simple thresholding method that works for Binary Phase Shift Keying (BPSK) signals only. In addition a method for recovering the power spectrum of stationary signals is developed as a special case. Simulation results demonstrate that the proposed spectrum sensing algorithms can significantly reduce sampling rate without sacrifcing performance. The robustness of the algorithms to the noise uncertainty of the wireless channel is also shown.

Compressed sensing approach to ultra-wideband receiver design

One of the scarcest resources in the wireless communication system is the limited frequency spectrum. Many wireless communication systems are hindered by the bandwidth limitation and are not able to provide high speed communication. However, Ultra-wideband (UWB) communication promises a high speed communication because of its very wide bandwidth of 7.5GHz (3.1GHz-10.6GHz). The unprecedented bandwidth promises many advantages for the 21st century wireless communication system. However, UWB has many hardware challenges, such as a very high speed sampling rate requirement for analog to digital conversion, channel estimation, and implementation challenges. In this thesis, a new method is proposed using compressed sensing (CS), a mathematical concept of sub-Nyquist rate sampling, to reduce the hardware complexity of the system. The method takes advantage of the unique signal structure of the UWB symbol. Also, a new digital implementation method for CS based UWB is proposed. Lastly, a comparative study is done of the CS-UWB hardware implementation methods. Simulation results show that the application of compressed sensing using the proposed method significantly reduces the number of hardware complexity compared to the conventional method of using compressed sensing based UWB receiver.

Design of universal multicoset sampling patterns for compressed sensing of multiband sparse signals

Many problems in digital communications involve wideband radio signals. As the most recent example, the impressive advances in Cognitive Radio systems make even more necessary the development of sampling schemes for wideband radio signals with spectral holes. This is equivalent to considering a sparse multiband signal in the framework of Compressive Sampling theory. Starting from previous results on multicoset sampling and recent advances in compressive sampling, we analyze the matrix involved in the corresponding reconstruction equation and define a new method for the design of universal multicoset codes, that is, codes guaranteeing perfect reconstruction of the sparse multiband signal.

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.

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.

Remote sensing the vertical profile of cloud droplet effective radius, thermodynamic phase, and temperature

Cloud-aerosol interaction is a key issue in the climate system, affecting the water cycle, the weather, and the total energy balance including the spatial and temporal distribution of latent heat release. Information on the vertical distribution of cloud droplet microphysics and thermodynamic phase as a function of temperature or height, can be correlated with details of the aerosol field to provide insight on how these particles are affecting cloud properties and their consequences to cloud lifetime, precipitation, water cycle, and general energy balance. Unfortunately, today's experimental methods still lack the observational tools that can characterize the true evolution of the cloud microphysical, spatial and temporal structure in the cloud droplet scale, and then link these characteristics to environmental factors and properties of the cloud condensation nuclei. Here we propose and demonstrate a new experimental approach (the cloud scanner instrument) that provides the microphysical information missed in current experiments and remote sensing options. Cloud scanner measurements can be performed from aircraft, ground, or satellite by scanning the side of the clouds from the base to the top, providing us with the unique opportunity of obtaining snapshots of the cloud droplet microphysical and thermodynamic states as a function of height and brightness temperature in clouds at several development stages. The brightness temperature profile of the cloud side can be directly associated with the thermodynamic phase of the droplets to provide information on the glaciation temperature as a function of different ambient conditions, aerosol concentration, and type. An aircraft prototype of the cloud scanner was built and flew in a field campaign in Brazil. The CLAIM-3D (3-Dimensional Cloud Aerosol Interaction Mission) satellite concept proposed here combines several techniques to simultaneously measure the vertical profile of cloud microphysics, thermodynamic phase, brightness temperature, and aerosol amount and type in the neighborhood of the clouds. The wide wavelength range, and the use of multi-angle polarization measurements proposed for this mission allow us to estimate the availability and characteristics of aerosol particles acting as cloud condensation nuclei, and their effects on the cloud microphysical structure. These results can provide unprecedented details on the response of cloud droplet microphysics to natural and anthropogenic aerosols in the size scale where the interaction really happens.

Energy dissipation in depth-sensing indentation as a characteristic of the nanoscratch behavior of coatings

Wear behavior of coatings has usually been described in terms of mechanical properties such as hardness (H) and effective elastic modulus (E*). Alternatively, an energy approach appears as a promising analysis taking into account the influence of those properties. In a nanoindentation test, the dissipated energy depends not only on the hardness and elastic modulus, but also on the elastic recovery (W(e)). This work aims to establish a relation between plastic deformation energy (E(p)) during depth-sensing indentation method and the grooving resistance of coatings in nanoscratch tests. An energy dissipation coefficient (K(d)) was defined, calculated as the ratio of the plastic to the total deformation energy (E(p)/E(t)), which represents the energy dissipation of materials. Reactive depositions using titanium as the target and nitrogen and methane as reactive gases were obtained by triode magnetron sputtering, in order to assess wear and nanoindentation data. A topographical, chemical and microstructural characterization has been conducted using X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), wave dispersion spectroscopy (WDS), scanning electron (SEM) and atomic force microscopy (AFM) techniques. Nanoscratch results showed that the groove depth was well correlated to the energy dissipation coefficient of the coatings. On the other hand, a reduction in the coefficient was found when the elastic recovery was increased. (C) 2009 Elsevier B.V. All rights reserved.

KDP/PEDOT: PSS mixture as a new alternative in the fabrication of pressure sensing devices

In this work we studied the mixture of poly(3,4-ethylenedioxythiophene): poly(styrenesulfonate) (PEDOT:PSS), a commercial polymer, with monobasic potassium phosphate (KDP), a piezoelectric salt, as a possible novel material in the fabrication of a low cost, easy-to-make,flexible pressure sensing device. The mixture between KDP and PEDOT: PSS was painted in a flexible polyester substrate and dried. Afterwards, I x V curves were carried out. The samples containing KDP presented higher values of current in smaller voltages than the PEDOT: PSS without KDP. This can mean a change in the chain arrays. Other results showed that the material responds to directly applied pressure to the sample that can be useful to sensors fabrication. (c) 2008 Elsevier B.V. All rights reserved.

In silico analysis of candidate genes involved in light sensing and signal transduction pathways in soybean

Several aspects of photoperception and light signal transduction have been elucidated by studies with model plants. However, the information available for economically important crops, such as Fabaceae species, is scarce. In order to incorporate the existing genomic tools into a strategy to advance soybean research, we have investigated publicly available expressed sequence tag ( EST) sequence databases in order to identify Glycine max sequences related to genes involved in light-regulated developmental control in model plants. Approximately 38,000 sequences from open-access databases were investigated, and all bona fide and putative photoreceptor gene families were found in soybean sequence databases. We have identified G. max orthologs for several families of transcriptional regulators and cytoplasmic proteins mediating photoreceptor-induced responses, although some important Arabidopsis phytochrome-signaling components are absent. Moreover, soybean and Arabidopsis gene-family homologs appear to have undergone a distinct expansion process in some cases. We propose a working model of light perception, signal transduction and response-eliciting in G. max, based on the identified key components from Arabidopsis. These results demonstrate the power of comparative genomics between model systems and crop species to elucidate several aspects of plant physiology and metabolism.

Quorum sensing detected by atomic force microscopy imaging of corrals surrounding multicellular arrangement of bacteria

Connectivity of the glycocalyx covering of small communities of Acidithiobacillus ferrooxidans bacteria deposited on hydrophilic mica plates was imaged by atomic force microscopy. When part of the coverage was removed by water rinsing, an insoluble structure formed by corrals surrounding each individual bacterium was observed. A collective ring structure with clustered bacteria (>= 3) was observed, which indicates that the bacteria perceived the neighborhood in order to grow a protective structure that results in smaller production of exopolysaccharides material. The most surprising aspect of these collective corral structures was that they occur at a low bacterial cell density. The deposited layers were also analyzed by confocal Raman microscopy and shown to contain polysaccharides, protein, and glucoronic acid.

Phosphatidylinositol phospholipase C mediates carbon sensing and vegetative nuclear duplication rates in Aspergillus nidulans

In this work, we disrupted one of three putative phosphatidylinositol phospholipase C genes of Aspergillus nidulans and studied its effect on carbon source sensing linked to vegetative mitotic nuclear division. We showed that glucose does not affect nuclear division rates during early vegetative conidial germination (6-7 h) in either the wild type or the plcA-deficient mutant. Only after 8 h of cultivation on glucose did the mutant strain present some decrease in nuclear duplication. However, decreased nuclear division rates were observed in the wild type when cultivated in media amended with polypectate, whereas our plcA-deficient mutant did not show slow nuclear duplication rates when grown on this carbon source, even though it requires induction and secretion of multiple pectinolytic enzymes to be metabolized. Thus, plcA appears to be directly linked to high-molecular-weight carbon source sensing.