Flexible methods for blind separation of complex signals

One of the main matter in Blind Source Separation (BSS) performed with a neural network approach is the choice of the nonlinear activation function (AF). In fact if the shape of the activation function is chosen as the cumulative density function (c.d.f.) of the original source the problem is solved. For this scope in this thesis a flexible approach is introduced and the shape of the activation functions is changed during the learning process using the so-called “spline functions”. The problem is complicated in the case of separation of complex sources where there is the problem of the dichotomy between analyticity and boundedness of the complex activation functions. The problem is solved introducing the “splitting function” model as activation function. The “splitting function” is a couple of “spline function” which wind off the real and the imaginary part of the complex activation function, each of one depending from the real and imaginary variable. A more realistic model is the “generalized splitting function”, which is formed by a couple of two bi-dimensional functions (surfaces), one for the real and one for the imaginary part of the complex function, each depending by both the real and imaginary part of the complex variable. Unfortunately the linear environment is unrealistic in many practical applications. In this way there is the need of extending BSS problem in the nonlinear environment: in this case both the activation function than the nonlinear distorting function are realized by the “splitting function” made of “spline function”. The complex and instantaneous separation in linear and nonlinear environment allow us to perform a complex-valued extension of the well-known INFOMAX algorithm in several practical situations, such as convolutive mixtures, fMRI signal analysis and bandpass signal transmission. In addition advanced characteristics on the proposed approach are introduced and deeply described. First of all it is shows as splines are universal nonlinear functions for BSS problem: they are able to perform separation in anyway. Then it is analyzed as the “splitting solution” allows the algorithm to obtain a phase recovery: usually there is a phase ambiguity. Finally a Cramér-Rao lower bound for ICA is discussed. Several experimental results, tested by different objective indexes, show the effectiveness of the proposed approaches

Flexible methods for blind separation of complex signals

One of the main matter in Blind Source Separation (BSS) performed with a neural network approach is the choice of the nonlinear activation function (AF). In fact if the shape of the activation function is chosen as the cumulative density function (c.d.f.) of the original source the problem is solved. For this scope in this thesis a flexible approach is introduced and the shape of the activation functions is changed during the learning process using the so-called “spline functions”. The problem is complicated in the case of separation of complex sources where there is the problem of the dichotomy between analyticity and boundedness of the complex activation functions. The problem is solved introducing the “splitting function” model as activation function. The “splitting function” is a couple of “spline function” which wind off the real and the imaginary part of the complex activation function, each of one depending from the real and imaginary variable. A more realistic model is the “generalized splitting function”, which is formed by a couple of two bi-dimensional functions (surfaces), one for the real and one for the imaginary part of the complex function, each depending by both the real and imaginary part of the complex variable. Unfortunately the linear environment is unrealistic in many practical applications. In this way there is the need of extending BSS problem in the nonlinear environment: in this case both the activation function than the nonlinear distorting function are realized by the “splitting function” made of “spline function”. The complex and instantaneous separation in linear and nonlinear environment allow us to perform a complex-valued extension of the well-known INFOMAX algorithm in several practical situations, such as convolutive mixtures, fMRI signal analysis and bandpass signal transmission. In addition advanced characteristics on the proposed approach are introduced and deeply described. First of all it is shows as splines are universal nonlinear functions for BSS problem: they are able to perform separation in anyway. Then it is analyzed as the “splitting solution” allows the algorithm to obtain a phase recovery: usually there is a phase ambiguity. Finally a Cramér-Rao lower bound for ICA is discussed. Several experimental results, tested by different objective indexes, show the effectiveness of the proposed approaches

Signals and Images in Sea Technologies

Life below water is the 14th Sustainable Development Goal (SDG) envisaged by the United Nations and is aimed at conserving and sustainably using the oceans, seas, and marine resources for sustainable development. It is not difficult to argue that signals and image technologies may play an essential role in achieving the foreseen targets linked to SDG 14. Besides increasing the general knowledge of ocean health by means of data analysis, methodologies based on signal and image processing can be helpful in environmental monitoring, in protecting and restoring ecosystems, in finding new sensor technologies for green routing and eco-friendly ships, in providing tools for implementing best practices for sustainable fishing, as well as in defining frameworks and intelligent systems for enforcing sea law and making the sea a safer and more secure place. Imaging is also a key element for the exploration of the underwater world for various scopes, ranging from the predictive maintenance of sub-sea pipelines and other infrastructure projects, to the discovery, documentation, and protection of sunken cultural heritage. The scope of this Special Issue encompasses investigations into techniques and ICT approaches and, in particular, the study and application of signal- and image-based methods and, in turn, exploration of the advantages of their application in the previously mentioned areas

Array Manifold Calibration for Multichannel SAR Sounders

This dissertation demonstrates airborne synthetic aperture radar (SAR) sounder array manifold calibration to improve outcomes in two-dimensional and three-dimensional image formation of ice sheet and glacier subsurfaces. The methodology relies on the creation of snapshot databases that aid in both the identification of calibration pixels as well as the validation of proposed calibration strategies. A parametric estimator of nonlinear SAR sounder manifold parameters is derived given a superset of statistically independent and spatially diverse subsets, assuming knowledge of the manifold model. Both measurements-based and computational electromagnetic modeling (CEM) approaches are pursued in obtaining a parametric representation of the manifold that enables the application of this estimator. The former relies on a principal components based characterization of SAR sounder manifolds. By incorporating a subspace clustering technique to identify pixels with a single dominant source, the algorithm circumvents an assumption of single source observations that underlies the formulation of nonparametric methods and traditionally limits the applicability of these techniques to the SAR sounder problem. Three manifolds are estimated and tested against a nominal manifold model in angle estimation and tomography. Measured manifolds on average reduce angle estimation error by a factor of 4.8 and lower vertical elevation uncertainty of SAR sounder derived digital elevation models by a factor of 3.7. Application of the measured manifolds in angle estimation produces 3-D images with more focused scattering signatures and higher intensity pixels that improve automated surface extraction outcomes. Measured manifolds are studied against Method of Moments predictions of the array's response to plane wave excitation obtained with a detailed model of the sounder's array that includes the airborne platform and fairing housing. CEM manifolds reduce angle estimation uncertainty off nadir on average by a factor of 3 when applied to measurements, providing initial confirmation of the utility of the CEM model in predicting angle estimation performance of the sounder's airborne arrays. The research findings of this dissertation indicate that SAR sounder manifold calibration will significantly increase the scientific value of legacy ice sheet and glacier sounding data sets and lead to optimized designs of future remote sensing instrumentation for surveying the cryosphere

Compressive Sensing Applications in Measurement: Theoretical issues, algorithm characterization and implementation

At its core, signal acquisition is concerned with efficient algorithms and protocols capable to capture and encode the signal information content. For over five decades, the indisputable theoretical benchmark has been represented by the wellknown Shannon’s sampling theorem, and the corresponding notion of information has been indissolubly related to signal spectral bandwidth. The contemporary society is founded on almost instantaneous exchange of information, which is mainly conveyed in a digital format. Accordingly, modern communication devices are expected to cope with huge amounts of data, in a typical sequence of steps which comprise acquisition, processing and storage. Despite the continual technological progress, the conventional acquisition protocol has come under mounting pressure and requires a computational effort not related to the actual signal information content. In recent years, a novel sensing paradigm, also known as Compressive Sensing, briefly CS, is quickly spreading among several branches of Information Theory. It relies on two main principles: signal sparsity and incoherent sampling, and employs them to acquire the signal directly in a condensed form. The sampling rate is related to signal information rate, rather than to signal spectral bandwidth. Given a sparse signal, its information content can be recovered even fromwhat could appear to be an incomplete set of measurements, at the expense of a greater computational effort at reconstruction stage. My Ph.D. thesis builds on the field of Compressive Sensing and illustrates how sparsity and incoherence properties can be exploited to design efficient sensing strategies, or to intimately understand the sources of uncertainty that affect measurements. The research activity has dealtwith both theoretical and practical issues, inferred frommeasurement application contexts, ranging fromradio frequency communications to synchrophasor estimation and neurological activity investigation. The thesis is organised in four chapters whose key contributions include: • definition of a general mathematical model for sparse signal acquisition systems, with particular focus on sparsity and incoherence implications; • characterization of the main algorithmic families for recovering sparse signals from reduced set of measurements, with particular focus on the impact of additive noise; • implementation and experimental validation of a CS-based algorithmfor providing accurate preliminary information and suitably preprocessed data for a vector signal analyser or a cognitive radio application; • design and characterization of a CS-based super-resolution technique for spectral analysis in the discrete Fourier transform(DFT) domain; • definition of an overcomplete dictionary which explicitly account for spectral leakage effect; • insight into the so-called off-the-grid estimation approach, by properly combining CS-based super-resolution and DFT coefficients polar interpolation; • exploration and analysis of sparsity implications in quasi-stationary operative conditions, emphasizing the importance of time-varying sparse signal models; • definition of an enhanced spectral content model for spectral analysis applications in dynamic conditions by means of Taylor-Fourier transform (TFT) approaches

Fisher Information and entanglement of non-Gaussian spin states

In this thesis, we study a novel method to extract the Fisher information of quantum states from direct measurements without the need for state reconstruction. Our method characterizes the distinguishability of experimental probability distributions of the collective spin. The Fisher information is obtained via the observed rate of change of their statistical distance as a function of an experimental control parameter, which constitutes a phase transformation of the quantum state. The employed experimental system is a binary Bose-Einstein condensate of several hundred atoms. We use a combination of coherent collisional interaction and linear Rabi coupling of the two atomic states to generate collective non-classical spin states via quantum dynamics close to an unstable fixed point of the corresponding classical system. The fast redistribution of quantum uncertainty results in Gaussian spin-squeezed states for short evolution times which turn into non-Gaussian states on an experimentally feasible time scale. For the generated non-Gaussian states we observe a Fisher information larger than the number of atoms in the detected ensemble, which is a signature of particle entanglement, in a regime where no spin-squeezing is present. We confirm the implied resource for quantumenhanced measurements with the implementation of a model-free Bayesian protocol which obtains a sensitivity beyond the standard quantum limit in accordance with the extracted Fisher information