## 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

Accounting for channel constraints in joint source-channel video coding schemes

SoftCast based Linear Video Coding (LVC) schemes have been emerged in the last decade as a quasi analog joint-source-channel alternative to classical video coding schemes. Theoretical analyses have shown that analog coding is better than digital coding in a multicast scenario when the channel signal-to-noise ratios (C-SNR) differ among receivers. LVC schemes provide in such context a decoded video quality at different receivers proportional to their C-SNR. This thesis considers first the channel precoding and decoding matrix design problem for LVC schemes under a per-subchannel power constraint. Such constraint is found, e.g., on Power Line Telecommunication (PLT) channels and is similar to per-antenna power constraints in multi-antenna transmission system. An optimal design approach is proposed, involving a multi-level water filling algorithm and the solution of a structured Hermitian Inverse Eigenvalue problem. Three lower-complexity alternative suboptimal algorithms are also proposed. Extensive ...

Zheng, Shuo — TélécomParis

Reverberation consists of a complex acoustic phenomenon that occurs inside rooms. Many audio signal processing methods, addressing source localization, signal enhancement and other tasks, often assume absence of reverberation. Consequently, reverberant environments are considered challenging as state-ofthe-art methods can perform poorly. The acoustics of a room can be described using a variety of mathematical models, among which, physical models are the most complete and accurate. The use of physical models in audio signal processing methods is often non-trivial since it can lead to ill-posed inverse problems. These inverse problems require proper regularization to achieve meaningful results and involve the solution of computationally intensive large-scale optimization problems. Recently, however, sparse regularization has been applied successfully to inverse problems arising in different scientific areas. The increased computational power of modern computers and the development of new efficient optimization algorithms makes it possible ...

Antonello, Niccolò — KU Leuven

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

Linear Dynamical Systems with Sparsity Constraints: Theory and Algorithms

This thesis develops new mathematical theory and presents novel recovery algorithms for discrete linear dynamical systems (LDS) with sparsity constraints on either control inputs or initial state. The recovery problems in this framework manifest as the problem of reconstructing one or more sparse signals from a set of noisy underdetermined linear measurements. The goal of our work is to design algorithms for sparse signal recovery which can exploit the underlying structure in the measurement matrix and the unknown sparse vectors, and to analyze the impact of these structures on the efficacy of the recovery. We answer three fundamental and interconnected questions on sparse signal recovery problems that arise in the context of LDS. First, what are necessary and sufficient conditions for the existence of a sparse solution? Second, given that a sparse solution exists, what are good low-complexity algorithms that ...

Joseph, Geethu — Indian Institute of Science, Bangalore

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

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

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

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

Equalization, windowing and zero restoration for OFDM and single-carrier block transmission

Fourier transform (DFT). In the case of MCM, the transmitted data is encoded into blocks in the frequency domain, by using an inverse DFT (IDFT) at the transmitter. The receiver then consists of a DFT, followed by a one-tap complex equalizer for each tone. In SC-FDE the information is encoded into blocks in the time domain. At the receiver, the DFT and one-tap equalizer are followed by an extra IDFT. To avoid the loss of orthogonality between the tones, a guard interval (GI) is inserted between each two blocks. If the channel order doesn’t exceed the GI length, zero-forcing equalization is possible. For longer channels, a Per-Tone equalizer (PTEQ) can be used, which minimizes the mean square error of the received symbols. In practice, the individual bands are orthogonal but overlap, due to the slow roll-off of the DFT’s side ...

Cuypers, Gert — KU Leuven

Channel Modeling and Estimation For Wireless Communication Systems Using a Time-Frequency Approach

Broadband wireless communication is a very fast growing communication area. Multicarrier modulation techniques like Orthogonal Frequency Division Multiplexing (OFDM), Biorthogonal Frequency Division Multiplexing (BFDM), Pulse Shaping (PS) and Multi-Carrier Spread Spectrum (MCSS) have recently been introduced as robust techniques against intersymbol interference (ISI) and noise, compared to single carrier communication systems over fast fading multipath communication channels. Therefore, multicarrier modulation techniques have been considered as a candidate for new generation, high data rate broadband wireless communication systems and have been adopted as the related standards. Several examples are the European digital audio broadcasting (DAB) and digital video broadcasting (DVB), the IEEE standands for wireless local area networks (WLAN), 802.11a, and wireless metropolitan area networks (WMAN), 802.16a. However, Doppler frequency shifts, phase offset, local oscillator frequency shifts, and multi-path fading severely degrade the performance of multicarrier communication systems. For fast-varying channels, ...

Yalcin, Mahmut — Istanbul University

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

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

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

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