## Sparse Signal Recovery From Incomplete And Perturbed Data (2016)

Robust Methods for Sensing and Reconstructing Sparse Signals

Compressed sensing (CS) is a recently introduced signal acquisition framework that goes against the traditional Nyquist sampling paradigm. CS demonstrates that a sparse, or compressible, signal can be acquired using a low rate acquisition process. Since noise is always present in practical data acquisition systems, sensing and reconstruction methods are developed assuming a Gaussian (light-tailed) model for the corrupting noise. However, when the underlying signal and/or the measurements are corrupted by impulsive noise, commonly employed linear sampling operators, coupled with Gaussian-derived reconstruction algorithms, fail to recover a close approximation of the signal. This dissertation develops robust sampling and reconstruction methods for sparse signals in the presence of impulsive noise. To achieve this objective, we make use of robust statistics theory to develop appropriate methods addressing the problem of impulsive noise in CS systems. We develop a generalized Cauchy distribution (GCD) ...

Carrillo, Rafael — University of Delaware

Inverse Scattering Procedures for the Reconstruction of One-Dimensional Permittivity Range Profiles

Inverse scattering is relevant to a very large class of problems, where the unknown structure of a scattering object is estimated by measuring the scattered field produced by known probing waves. Therefore, for more than three decades, the promises of non-invasive imaging inspection by electromagnetic probing radiations have been justifying a research interest on these techniques. Several application areas are involved, such as civil and industrial engineering, non-destructive testing and medical imaging as well as subsurface inspection for oil exploration or unexploded devices. In spite of this relevance, most scattering tomography techniques are not reliable enough to solve practical problems. Indeed, the nonlinear relationship between the scattered field and the object function and the robustness of the inversion algorithms are still open issues. In particular, microwave tomography presents a number of specific difficulties that make it much more involved to ...

Genovesi, Simone — University of Pisa

Tradeoffs and limitations in statistically based image reconstruction problems

Advanced nuclear medical imaging systems collect multiple attributes of a large number of photon events, resulting in extremely large datasets which present challenges to image reconstruction and assessment. This dissertation addresses several of these challenges. The image formation process in nuclear medical imaging can be posed as a parametric estimation problem where the image pixels are the parameters of interest. Since nuclear medical imaging applications are often ill-posed inverse problems, unbiased estimators result in very noisy, high-variance images. Typically, smoothness constraints and a priori information are used to reduce variance in medical imaging applications at the cost of biasing the estimator. For such problems, there exists an inherent tradeoff between the recovered spatial resolution of an estimator, overall bias, and its statistical variance; lower variance can only be bought at the price of decreased spatial resolution and/or increased overall bias. ...

Kragh, Tom — University of Michigan

Sparsity Models for Signals: Theory and Applications

Many signal and image processing applications have benefited remarkably from the theory of sparse representations. In its classical form this theory models signal as having a sparse representation under a given dictionary -- this is referred to as the "Synthesis Model". In this work we focus on greedy methods for the problem of recovering a signal from a set of deteriorated linear measurements. We consider four different sparsity frameworks that extend the aforementioned synthesis model: (i) The cosparse analysis model; (ii) the signal space paradigm; (iii) the transform domain strategy; and (iv) the sparse Poisson noise model. Our algorithms of interest in the first part of the work are the greedy-like schemes: CoSaMP, subspace pursuit (SP), iterative hard thresholding (IHT) and hard thresholding pursuit (HTP). It has been shown for the synthesis model that these can achieve a stable recovery ...

Giryes, Raja — Technion

Transmission over Time- and Frequency-Selective Mobile Wireless Channels

The wireless communication industry has experienced rapid growth in recent years, and digital cellular systems are currently designed to provide high data rates at high terminal speeds. High data rates give rise to intersymbol interference (ISI) due to so-called multipath fading. Such an ISI channel is called frequency selective. On the other hand, due to terminal mobility and/or receiver frequency offset the received signal is subject to frequency shifts (Doppler shifts). Doppler shift induces time-selectivity characteristics. The Doppler effect in conjunction with ISI gives rise to a so-called doubly selective channel (frequency- and time-selective). In addition to the channel effects, the analog front-end may suffer from an imbalance between the I and Q branch amplitudes and phases as well as from carrier frequency offset. These analog front-end imperfections then result in an additional and significant degradation in system performance, especially ...

Barhumi, Imad — Katholieke Universiteit Leuven

Filter Bank Techniques for the Physical Layer in Wireless Communications

Filter bank based multicarrier is an evolution with many advantages over the widespread OFDM multicarrier scheme. The author of the thesis stands behind this statement and proposes various solutions for practical physical layer problems based on filter bank processing of wireless communications signals. Filter banks are an evolved form of subband processing, harnessing the key advantages of original efficient subband processing based on the fast Fourier transforms and addressing some of its shortcomings, at the price of a somewhat increased implementation complexity. The main asset of the filter banks is the possibility to design very frequency selective subband filters to compartmentalize the overall spectrum into well isolated subbands, while still making very efficient use of the assigned bandwidth. This thesis first exploits this main feature of the filter banks in the subband system configuration, in which the analysis filter bank ...

Hidalgo Stitz, Tobias — Tampere University of Technology

MIMO Designs for filter bank multicarrier and multiantenna systems based on OQAM

From the perspective of increasingly data rate requirements in mobile communications, it is deemed necessary to do further research so that the future goals can be reached. To that end, the radio-based communications are resorting to multicarrier modulations and spatial diversity. Until today, the orthogonal frequency division multiplexing (OFDM) modulation is regarded as the dominant technology. On one hand, the OFDM modulation is able to accommodate multiantenna configurations in a very straightforward manner. On the other hand, the poor stopband attenuation exhibited by the OFDM modulation, highlights that a definitely tight synchronization is required. In addition, the cyclic prefix (CP) has to be sufficiently long to avoid inter-block interference, which may substantially reduce the spectral efficiency. In order to overcome the OFDM drawbacks, the filter bank multicarrier modulation based on OQAM (FBMC/OQAM) is introduced. This modulation does not need any ...

López, Màrius Caus — Universitat Politècnica de Catalunya (UPC)

Performance Evaluation of Practical OFDM Systems with Imperfect Synchronization

This work aims to expose the potential performance loss due to synchronization errors in the downlink of the two major cellular standards of OFDM systems, i.e., the WiMAX OFDM physical layer and the LTE. Different to most results in literature, the physical layer coded throughput is utilized as the major performance measure. The influence of an imperfect carrier frequency synchronization or symbol timing is evaluated via analytical modeling and standard compliant link level simulations. In the frequency aspect, a modified differential estimator for the residual frequency offset in WiMAX is proposed. It is shown that the theoretical performance of such an estimator approaches the Cramer-Rao lower bound and provides a significant gain in terms of the mean squared error. However, such an improvement becomes negligible in terms of the coded throughput. Therefore, a throughput loss prediction model is proposed for ...

Wang, Qi — Vienna University of Technology

Direction Finding In The Presence of Array Imperfections, Model Mismatches and Multipath

In direction finding (DF) applications, there are several factors affecting the estimation accuracy of the direction-of-arrivals (DOA) of unknown source locations. The major distortions in the estimation process are due to the array imperfections, model mismatches and multipath. The array imperfections usually exist in practical applications due to the nonidealities in the antenna array such as mutual coupling (MC) and gain/phase uncertainties. The model mismatches usually occur when the model of the received signal differs from the signal model used in the processing stage of the DF system. Another distortion is due to multipath signals. In the multipath scenario, the antenna array receives the transmitted signal from more than one path with different directions and the array covariance matrix is rank-deficient. In this thesis, three new methods are proposed for the problems in DF applications in the presence of array ...

Elbir, Ahmet M. — Middle East Technical Univresity

Bayesian Compressed Sensing using Alpha-Stable Distributions

During the last decades, information is being gathered and processed at an explosive rate. This fact gives rise to a very important issue, that is, how to effectively and precisely describe the information content of a given source signal or an ensemble of source signals, such that it can be stored, processed or transmitted by taking into consideration the limitations and capabilities of the several digital devices. One of the fundamental principles of signal processing for decades is the Nyquist-Shannon sampling theorem, which states that the minimum number of samples needed to reconstruct a signal without error is dictated by its bandwidth. However, there are many cases in our everyday life in which sampling at the Nyquist rate results in too many data and thus, demanding an increased processing power, as well as storage requirements. A mathematical theory that emerged ...

Tzagkarakis, George — University of Crete

OFDM Air-Interface Design for Multimedia Communications

The aim of this dissertation is the investigation of the key issues encountered in the development of wideband radio air-interfaces. Orthogonal frequency-division multiplexing (OFDM) is considered as the enabling technology for transmitting data at extremely high rates over time-dispersive radio channels. OFDM is a transmission scheme, which splits up the data stream, sending the data symbols simultaneously at a drastically reduced symbol rate over a set of parallel sub-carriers. The first part of this thesis deals with the modeling of the time-dispersive and frequency-selective radio channel, utilizing second order Gaussian stochastic processes. A novel channel measurement technique is developed, in which the RMS delay spread of the channel is estimated from the level-crossing rate of the frequency-selective channel transfer function. This method enables the empirical channel characterization utilizing simplified non-coherent measurements of the received power versus frequency. Air-interface and multiple ...

Witrisal, Klaus — Delft University of Technology

Modeling and Digital Mitigation of Transmitter Imperfections in Radio Communication Systems

To satisfy the continuously growing demands for higher data rates, modern radio communication systems employ larger bandwidths and more complex waveforms. Furthermore, radio devices are expected to support a rich mixture of standards such as cellular networks, wireless local-area networks, wireless personal area networks, positioning and navigation systems, etc. In general, a "smart'' device should be flexible to support all these requirements while being portable, cheap, and energy efficient. These seemingly conflicting expectations impose stringent radio frequency (RF) design challenges which, in turn, call for their proper understanding as well as developing cost-effective solutions to address them. The direct-conversion transceiver architecture is an appealing analog front-end for flexible and multi-standard radio systems. However, it is sensitive to various circuit impairments, and modern communication systems based on multi-carrier waveforms such as Orthogonal Frequency Division Multiplexing (OFDM) and Orthogonal Frequency Division Multiple ...

Kiayani, Adnan — Tampere University of Technology

Signal acquisition is a main topic in signal processing. The well-known Shannon-Nyquist theorem lies at the heart of any conventional analog to digital converters stating that any signal has to be sampled with a constant frequency which must be at least twice the highest frequency present in the signal in order to perfectly recover the signal. However, the Shannon-Nyquist theorem provides a worst-case rate bound for any bandlimited data. In this context, Compressive Sensing (CS) is a new framework in which data acquisition and data processing are merged. CS allows to compress the data while is sampled by exploiting the sparsity present in many common signals. In so doing, it provides an efficient way to reduce the number of measurements needed for perfect recovery of the signal. CS has exploded in recent years with thousands of technical publications and applications ...

Lagunas, Eva — Universitat Politecnica de Catalunya

Bayesian Fusion of Multi-band Images: A Powerful Tool for Super-resolution

Hyperspectral (HS) imaging, which consists of acquiring a same scene in several hundreds of contiguous spectral bands (a three dimensional data cube), has opened a new range of relevant applications, such as target detection [MS02], classification [C.-03] and spectral unmixing [BDPD+12]. However, while HS sensors provide abundant spectral information, their spatial resolution is generally more limited. Thus, fusing the HS image with other highly resolved images of the same scene, such as multispectral (MS) or panchromatic (PAN) images is an interesting problem. The problem of fusing a high spectral and low spatial resolution image with an auxiliary image of higher spatial but lower spectral resolution, also known as multi-resolution image fusion, has been explored for many years [AMV+11]. From an application point of view, this problem is also important as motivated by recent national programs, e.g., the Japanese next-generation space-borne ...

Wei, Qi — University of Toulouse

Waveform Advancements and Synchronization Techniques for Generalized Frequency Division Multiplexing

To enable a new level of connectivity among machines as well as between people and machines, future wireless applications will demand higher requirements on data rates, response time, and reliability from the communication system. This will lead to a different system design, comprising a wide range of deployment scenarios. One important aspect is the evolution of physical layer (PHY), specifically the waveform modulation. The novel generalized frequency division multiplexing (GFDM) technique is a prominent proposal for a flexible block filtered multicarrier modulation. This thesis introduces an advanced GFDM concept that enables the emulation of other prominent waveform candidates in scenarios where they perform best. Hence, a unique modulation framework is presented that is capable of addressing a wide range of scenarios and to upgrade the PHY for 5G networks. In particular, for a subset of system parameters of the modulation ...

Gaspar, Ivan — Technische Universität Dresden

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