Showing papers in "IEEE Journal of Selected Topics in Signal Processing in 2010"

From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals

Abstract: Conventional sub-Nyquist sampling methods for analog signals exploit prior information about the spectral support. In this paper, we consider the challenging problem of blind sub-Nyquist sampling of multiband signals, whose unknown frequency support occupies only a small portion of a wide spectrum. Our primary design goals are efficient hardware implementation and low computational load on the supporting digital processing. We propose a system, named the modulated wideband converter, which first multiplies the analog signal by a bank of periodic waveforms. The product is then low-pass filtered and sampled uniformly at a low rate, which is orders of magnitude smaller than Nyquist. Perfect recovery from the proposed samples is achieved under certain necessary and sufficient conditions. We also develop a digital architecture, which allows either reconstruction of the analog input, or processing of any band of interest at a low rate, that is, without interpolating to the high Nyquist rate. Numerical simulations demonstrate many engineering aspects: robustness to noise and mismodeling, potential hardware simplifications, real-time performance for signals with time-varying support and stability to quantization effects. We compare our system with two previous approaches: periodic nonuniform sampling, which is bandwidth limited by existing hardware devices, and the random demodulator, which is restricted to discrete multitone signals and has a high computational load. In the broader context of Nyquist sampling, our scheme has the potential to break through the bandwidth barrier of state-of-the-art analog conversion technologies such as interleaved converters.

Signal Recovery From Incomplete and Inaccurate Measurements Via Regularized Orthogonal Matching Pursuit

Abstract: We demonstrate a simple greedy algorithm that can reliably recover a vector v ? ?d from incomplete and inaccurate measurements x = ?v + e. Here, ? is a N x d measurement matrix with N<

Signal Processing With Compressive Measurements

Abstract: The recently introduced theory of compressive sensing enables the recovery of sparse or compressible signals from a small set of nonadaptive, linear measurements. If properly chosen, the number of measurements can be much smaller than the number of Nyquist-rate samples. Interestingly, it has been shown that random projections are a near-optimal measurement scheme. This has inspired the design of hardware systems that directly implement random measurement protocols. However, despite the intense focus of the community on signal recovery, many (if not most) signal processing problems do not require full signal recovery. In this paper, we take some first steps in the direction of solving inference problems-such as detection, classification, or estimation-and filtering problems using only compressive measurements and without ever reconstructing the signals involved. We provide theoretical bounds along with experimental results.

A Fast Alternating Direction Method for TVL1-L2 Signal Reconstruction From Partial Fourier Data

Abstract: Recent compressive sensing results show that it is possible to accurately reconstruct certain compressible signals from relatively few linear measurements via solving nonsmooth convex optimization problems. In this paper, we propose the use of the alternating direction method - a classic approach for optimization problems with separable variables (D. Gabay and B. Mercier, ?A dual algorithm for the solution of nonlinear variational problems via finite-element approximations,? Computer and Mathematics with Applications, vol. 2, pp. 17-40, 1976; R. Glowinski and A. Marrocco, ?Sur lapproximation par elements finis dordre un, et la resolution par penalisation-dualite dune classe de problemes de Dirichlet nonlineaires,? Rev. Francaise dAut. Inf. Rech. Oper., vol. R-2, pp. 41-76, 1975) - for signal reconstruction from partial Fourier (i.e., incomplete frequency) measurements. Signals are reconstructed as minimizers of the sum of three terms corresponding to total variation, ?1-norm of a certain transform, and least squares data fitting. Our algorithm, called RecPF and published online, runs very fast (typically in a few seconds on a laptop) because it requires a small number of iterations, each involving simple shrinkages and two fast Fourier transforms (or alternatively discrete cosine transforms when measurements are in the corresponding domain). RecPF was compared with two state-of-the-art algorithms on recovering magnetic resonance images, and the results show that it is highly efficient, stable, and robust.

Normalized Iterative Hard Thresholding: Guaranteed Stability and Performance

Abstract: Sparse signal models are used in many signal processing applications. The task of estimating the sparsest coefficient vector in these models is a combinatorial problem and efficient, often suboptimal strategies have to be used. Fortunately, under certain conditions on the model, several algorithms could be shown to efficiently calculate near-optimal solutions. In this paper, we study one of these methods, the so-called Iterative Hard Thresholding algorithm. While this method has strong theoretical performance guarantees whenever certain theoretical properties hold, empirical studies show that the algorithm's performance degrades significantly, whenever the conditions fail. What is more, in this regime, the algorithm also often fails to converge. As we are here interested in the application of the method to real world problems, in which it is not known in general, whether the theoretical conditions are satisfied or not, we suggest a simple modification that guarantees the convergence of the method, even in this regime. With this modification, empirical evidence suggests that the algorithm is faster than many other state-of-the-art approaches while showing similar performance. What is more, the modified algorithm retains theoretical performance guarantees similar to the original algorithm.

Iterative Reweighted $\ell_1$ and $\ell_2$ Methods for Finding Sparse Solutions

Abstract: A variety of practical methods have recently been introduced for finding maximally sparse representations from overcomplete dictionaries, a central computational task in compressive sensing applications as well as numerous others. Many of the underlying algorithms rely on iterative reweighting schemes that produce more focal estimates as optimization progresses. Two such variants are iterative reweighted l1 and l2 minimization; however, some properties related to convergence and sparse estimation, as well as possible generalizations, are still not clearly understood or fully exploited. In this paper, we make the distinction between separable and non-separable iterative reweighting algorithms. The vast majority of existing methods are separable, meaning the weighting of a given coefficient at each iteration is only a function of that individual coefficient from the previous iteration (as opposed to dependency on all coefficients). We examine two such separable reweighting schemes: an l2 method from Chartrand and Yin (2008) and an l1 approach from Cande's (2008), elaborating on convergence results and explicit connections between them. We then explore an interesting non-separable alternative that can be implemented via either l2 or l1 reweighting and maintains several desirable properties relevant to sparse recovery despite a highly non-convex underlying cost function. For example, in the context of canonical sparse estimation problems, we prove uniform superiority of this method over the minimum l1 solution in that, 1) it can never do worse when implemented with reweighted l1, and 2) for any dictionary and sparsity profile, there will always exist cases where it does better. These results challenge the prevailing reliance on strictly convex (and separable) penalty functions for finding sparse solutions. We then derive a new non-separable variant with similar properties that exhibits further performance improvements in empirical tests. Finally, we address natural extensions to group sparsity problems and non-negative sparse coding.

Compressed Synthetic Aperture Radar

Abstract: In this paper, we introduce a new synthetic aperture radar (SAR) imaging modality which can provide a high-resolution map of the spatial distribution of targets and terrain using a significantly reduced number of needed transmitted and/or received electromagnetic waveforms. This new imaging scheme, requires no new hardware components and allows the aperture to be compressed. It also presents many new applications and advantages which include strong resistance to countermesasures and interception, imaging much wider swaths and reduced on-board storage requirements.

General Deviants: An Analysis of Perturbations in Compressed Sensing

Abstract: We analyze the Basis Pursuit recovery of signals with general perturbations. Previous studies have only considered partially perturbed observations Ax + e. Here, x is a signal which we wish to recover, A is a full-rank matrix with more columns than rows, and e is simple additive noise. Our model also incorporates perturbations E to the matrix A which result in multiplicative noise. This completely perturbed framework extends the prior work of Candes, Romberg, and Tao on stable signal recovery from incomplete and inaccurate measurements. Our results show that, under suitable conditions, the stability of the recovered signal is limited by the noise level in the observation. Moreover, this accuracy is within a constant multiple of the best-case reconstruction using the technique of least squares. In the absence of additive noise, numerical simulations essentially confirm that this error is a linear function of the relative perturbation.

Signal Processing for Passive Radar Using OFDM Waveforms

Abstract: Passive radar is a concept where illuminators of opportunity are used in a multistatic radar setup. New digital signals, like digital audio/video broadcast (DAB/DVB), are excellent candidates for this scheme, as they are widely available, can be easily decoded to acquire the noise-free signal, and employ orthogonal frequency division multiplex (OFDM). Multicarrier transmission schemes like OFDM use block channel equalization in the frequency domain, efficiently implemented as a fast Fourier transform, and these channel estimates can directly be used to identify targets based on Fourier analysis across subsequent blocks. In this paper, we derive the exact matched filter formulation for passive radar using OFDM waveforms. We then show that the current approach using Fourier analysis across block channel estimates is equivalent to the matched filter, based on a piecewise constant assumption on the Doppler-induced phase rotation in the time domain. We next present high-resolution algorithms based on the same assumption: first we implement MUSIC as a 2-D spectral estimator using spatial smoothing; then we use the new concept of compressed sensing to identify targets. We compare the new algorithms and the current approach using numerical simulation and experimental data recorded from a DAB network in Germany.

The Use of Mobile Devices in Aiding Dietary Assessment and Evaluation

Abstract: There is a growing concern about chronic diseases and other health problems related to diet including obesity and cancer. The need to accurately measure diet (what foods a person consumes) becomes imperative. Dietary intake provides valuable insights for mounting intervention programs for prevention of chronic diseases. Measuring accurate dietary intake is considered to be an open research problem in the nutrition and health fields. In this paper, we describe a novel mobile telephone food record that will provide an accurate account of daily food and nutrient intake. Our approach includes the use of image analysis tools for identification and quantification of food that is consumed at a meal. Images obtained before and after foods are eaten are used to estimate the amount and type of food consumed. The mobile device provides a unique vehicle for collecting dietary information that reduces the burden on respondents that are obtained using more classical approaches for dietary assessment. We describe our approach to image analysis that includes the segmentation of food items, features used to identify foods, a method for automatic portion estimation, and our overall system architecture for collecting the food intake information.

Optimally Tuned Iterative Reconstruction Algorithms for Compressed Sensing

Abstract: We conducted an extensive computational experiment, lasting multiple CPU-years, to optimally select parameters for two important classes of algorithms for finding sparse solutions of underdetermined systems of linear equations. We make the optimally tuned implementations available at sparselab.stanford.edu; they run ?out of the box? with no user tuning: it is not necessary to select thresholds or know the likely degree of sparsity. Our class of algorithms includes iterative hard and soft thresholding with or without relaxation, as well as CoSaMP, subspace pursuit and some natural extensions. As a result, our optimally tuned algorithms dominate such proposals. Our notion of optimality is defined in terms of phase transitions, i.e., we maximize the number of nonzeros at which the algorithm can successfully operate. We show that the phase transition is a well-defined quantity with our suite of random underdetermined linear systems. Our tuning gives the highest transition possible within each class of algorithms. We verify by extensive computation the robustness of our recommendations to the amplitude distribution of the nonzero coefficients as well as the matrix ensemble defining the underdetermined system. Our findings include the following. 1) For all algorithms, the worst amplitude distribution for nonzeros is generally the constant-amplitude random-sign distribution, where all nonzeros are the same amplitude. 2) Various random matrix ensembles give the same phase transitions; random partial isometries may give different transitions and require different tuning. 3) Optimally tuned subspace pursuit dominates optimally tuned CoSaMP, particularly so when the system is almost square.

MIMO Radar Using Compressive Sampling

Abstract: A multiple-input multiple-output (MIMO) radar system is proposed for obtaining angle and Doppler information on potential targets. Transmitters and receivers are nodes of a small scale wireless network and are assumed to be randomly scattered on a disk. The transmit nodes transmit uncorrelated waveforms. Each receive node applies compressive sampling to the received signal to obtain a small number of samples, which the node subsequently forwards to a fusion center. Assuming that the targets are sparsely located in the angle-Doppler space, based on the samples forwarded by the receive nodes the fusion center formulates an l 1 -optimization problem, the solution of which yields target angle and Doppler information. The proposed approach achieves the superior resolution of MIMO radar with far fewer samples than required by other approaches. This implies power savings during the communication phase between the receive nodes and the fusion center. Performance in the presence of a jammer is analyzed for the case of slowly moving targets. Issues related to forming the basis matrix that spans the angle-Doppler space, and for selecting a grid for that space are discussed. Extensive simulation results are provided to demonstrate the performance of the proposed approach at difference jammer and noise levels.

Construction of a Large Class of Deterministic Sensing Matrices That Satisfy a Statistical Isometry Property

Abstract: Compressed Sensing aims to capture attributes of k-sparse signals using very few measurements. In the standard compressed sensing paradigm, the N × C measurement matrix ? is required to act as a near isometry on the set of all k-sparse signals (restricted isometry property or RIP). Although it is known that certain probabilistic processes generate N × C matrices that satisfy RIP with high probability, there is no practical algorithm for verifying whether a given sensing matrix ? has this property, crucial for the feasibility of the standard recovery algorithms. In contrast, this paper provides simple criteria that guarantee that a deterministic sensing matrix satisfying these criteria acts as a near isometry on an overwhelming majority of k-sparse signals; in particular, most such signals have a unique representation in the measurement domain. Probability still plays a critical role, but it enters the signal model rather than the construction of the sensing matrix. An essential element in our construction is that we require the columns of the sensing matrix to form a group under pointwise multiplication. The construction allows recovery methods for which the expected performance is sub-linear in C, and only quadratic in N, as compared to the super-linear complexity in C of the Basis Pursuit or Matching Pursuit algorithms; the focus on expected performance is more typical of mainstream signal processing than the worst case analysis that prevails in standard compressed sensing. Our framework encompasses many families of deterministic sensing matrices, including those formed from discrete chirps, Delsarte-Goethals codes, and extended BCH codes.

Compressive Estimation of Doubly Selective Channels in Multicarrier Systems: Leakage Effects and Sparsity-Enhancing Processing

Abstract: We consider the application of compressed sensing (CS) to the estimation of doubly selective channels within pulse-shaping multicarrier systems (which include orthogonal frequency-division multiplexing (OFDM) systems as a special case). By exploiting sparsity in the delay-Doppler domain, CS-based channel estimation allows for an increase in spectral efficiency through a reduction of the number of pilot symbols. For combating leakage effects that limit the delay-Doppler sparsity, we propose a sparsity-enhancing basis expansion and a method for optimizing the basis with or without prior statistical information about the channel. We also present an alternative CS-based channel estimator for (potentially) strongly time-frequency dispersive channels, which is capable of estimating the ?off-diagonal? channel coefficients characterizing intersymbol and intercarrier interference (ISI/ICI). For this estimator, we propose a basis construction combining Fourier (exponential) and prolate spheroidal sequences. Simulation results assess the performance gains achieved by the proposed sparsity-enhancing processing techniques and by explicit estimation of ISI/ICI channel coefficients.

Iterative Adaptive Approaches to MIMO Radar Imaging

Abstract: Multiple-input multiple-output (MIMO) radar can achieve superior performance through waveform diversity over conventional phased-array radar systems. When a MIMO radar transmits orthogonal waveforms, the reflected signals from scatterers are linearly independent of each other. Therefore, adaptive receive filters, such as Capon and amplitude and phase estimation (APES) filters, can be directly employed in MIMO radar applications. High levels of noise and strong clutter, however, significantly worsen detection performance of the data-dependent beamformers due to a shortage of snapshots. The iterative adaptive approach (IAA), a nonparametric and user parameter-free weighted least-squares algorithm, was recently shown to offer improved resolution and interference rejection performance in several passive and active sensing applications. In this paper, we show how IAA can be extended to MIMO radar imaging, in both the negligible and nonnegligible intrapulse Doppler cases, and we also establish some theoretical convergence properties of IAA. In addition, we propose a regularized IAA algorithm, referred to as IAA-R, which can perform better than IAA by accounting for unrepresented additive noise terms in the signal model. Numerical examples are presented to demonstrate the superior performance of MIMO radar over single-input multiple-output (SIMO) radar, and further highlight the improved performance achieved with the proposed IAA-R method for target imaging.

Target Velocity Estimation and Antenna Placement for MIMO Radar With Widely Separated Antennas

Abstract: This paper studies the velocity estimation performance for multiple-input multiple-output (MIMO) radar with widely spaced antennas. We derive the Cramer-Rao bound (CRB) for velocity estimation and study the optimized system/configuration design based on CRB. General results are presented for an extended target with reflectivity varying with look angle. Then detailed analysis is provided for a simplified case, assuming an isotropic scatterer. For given transmitted signals, optimal antenna placement is analyzed in the sense of minimizing the CRB of the velocity estimation error. We show that when all antennas are located at approximately the same distance from the target, symmetrical placement is optimal and the relative position of transmitters and receivers can be arbitrary under the orthogonal received signal assumption. In this case, it is also shown that for MIMO radar with optimal placement, velocity estimation accuracy can be improved by increasing either the signal time duration or the product of the number of transmit and receive antennas.

Combining Long Short-Term Memory and Dynamic Bayesian Networks for Incremental Emotion-Sensitive Artificial Listening

Abstract: The automatic estimation of human affect from the speech signal is an important step towards making virtual agents more natural and human-like. In this paper, we present a novel technique for incremental recognition of the user's emotional state as it is applied in a sensitive artificial listener (SAL) system designed for socially competent human-machine communication. Our method is capable of using acoustic, linguistic, as well as long-range contextual information in order to continuously predict the current quadrant in a two-dimensional emotional space spanned by the dimensions valence and activation. The main system components are a hierarchical dynamic Bayesian network (DBN) for detecting linguistic keyword features and long short-term memory (LSTM) recurrent neural networks which model phoneme context and emotional history to predict the affective state of the user. Experimental evaluations on the SAL corpus of non-prototypical real-life emotional speech data consider a number of variants of our recognition framework: continuous emotion estimation from low-level feature frames is evaluated as a new alternative to the common approach of computing statistical functionals of given speech turns. Further performance gains are achieved by discriminatively training LSTM networks and by using bidirectional context information, leading to a quadrant prediction F1-measure of up to 51.3 %, which is only 7.6 % below the average inter-labeler consistency.

Fundamental Limit of Sample Generalized Eigenvalue Based Detection of Signals in Noise Using Relatively Few Signal-Bearing and Noise-Only Samples

Abstract: The detection problem in statistical signal processing can be succinctly formulated: given m (possibly) signal bearing, n -dimensional signal-plus-noise snapshot vectors (samples) and N statistically independent n-dimensional noise-only snapshot vectors, can one reliably infer the presence of a signal? This problem arises in the context of applications as diverse as radar, sonar, wireless communications, bioinformatics, and machine learning and is the critical first step in the subsequent signal parameter estimation phase. The signal detection problem can be naturally posed in terms of the sample generalized eigenvalues. The sample generalized eigenvalues correspond to the eigenvalues of the matrix formed by ?whitening? the signal-plus-noise sample covariance matrix with the noise-only sample covariance matrix. In this paper, we prove a fundamental asymptotic limit of sample generalized eigenvalue-based detection of signals in arbitrarily colored noise when there are relatively few signal bearing and noise-only samples. Specifically, we show why when the (eigen) signal-to-noise ratio (SNR) is below a critical value, that is a simple function of n , m, and N, then reliable signal detection, in an asymptotic sense, is not possible. If, however, the eigen-SNR is above this critical value then a simple, new random matrix theory-based algorithm, which we present here, will reliably detect the signal even at SNRs close to the critical value. Numerical simulations highlight the accuracy of our analytical prediction, permit us to extend our heuristic definition of the effective number of identifiable signals in colored noise and display the dramatic improvement in performance relative to the classical estimator by Zhao We discuss implications of our result for the detection of weak and/or closely spaced signals in sensor array processing, abrupt change detection in sensor networks, and clustering methodologies in machine learning.

A Stochastic Gradient Approach on Compressive Sensing Signal Reconstruction Based on Adaptive Filtering Framework

Abstract: Based on the methodological similarity between sparse signal reconstruction and system identification, a new approach for sparse signal reconstruction in compressive sensing (CS) is proposed in this paper. This approach employs a stochastic gradient-based adaptive filtering framework, which is commonly used in system identification, to solve the sparse signal reconstruction problem. Two typical algorithms for this problem: l 0-least mean square ( l 0-LMS) algorithm and l 0-exponentially forgetting window LMS (l 0-EFWLMS) algorithm are hence introduced here. Both the algorithms utilize a zero attraction method, which has been implemented by minimizing a continuous approximation of l 0 norm of the studied signal. To improve the performances of these proposed algorithms, an l 0-zero attraction projection (l 0 -ZAP) algorithm is also adopted, which has effectively accelerated their convergence rates, making them much faster than the other existing algorithms for this problem. Advantages of the proposed approach, such as its robustness against noise, etc., are demonstrated by numerical experiments.

Transmit Subaperturing for MIMO Radars With Co-Located Antennas

Abstract: We present a transmit subaperturing (TS) approach for multiple-input multiple-output (MIMO) radars with co-located antennas. The proposed scheme divides the transmit array elements into multiple groups, each group forms a directional beam and modulates a distinct waveform, and all beams are steerable and point to the same direction. The resulting system is referred to as a TS-MIMO radar. A TS-MIMO radar is a tunable system that offers a continuum of operating modes from the phased-array radar, which achieves the maximum directional gain but the least interference rejection ability, to the omnidirectional transmission based MIMO radar, which can handle the largest number of interference sources but offers no directional gain. Tuning of the TS-MIMO system can be easily made by changing the configuration of the transmit subapertures, which provides a direct tradeoff between the directional gain and interference rejection power of the system. The performance of the TS-MIMO radar is examined in terms of the output signal-to-interference-plus-noise ratio (SINR) of an adaptive beamformer in an interference and training limited environment, where we show analytically how the output SINR is affected by several key design parameters, including the size/number of the subapertures and the number of training signals. Our results are verified by computer simulation and comparisons are made among various operating modes of the proposed TS-MIMO system.

Diarization of Telephone Conversations Using Factor Analysis

Abstract: We report on work on speaker diarization of telephone conversations which was begun at the Robust Speaker Recognition Workshop held at Johns Hopkins University in 2008. Three diarization systems were developed and experiments were conducted using the summed-channel telephone data from the 2008 NIST speaker recognition evaluation. The systems are a Baseline agglomerative clustering system, a Streaming system which uses speaker factors for speaker change point detection and traditional methods for speaker clustering, and a Variational Bayes system designed to exploit a large number of speaker factors as in state of the art speaker recognition systems. The Variational Bayes system proved to be the most effective, achieving a diarization error rate of 1.0% on the summed-channel data. This represents an 85% reduction in errors compared with the Baseline agglomerative clustering system. An interesting aspect of the Variational Bayes approach is that it implicitly performs speaker clustering in a way which avoids making premature hard decisions. This type of soft speaker clustering can be incorporated into other diarization systems (although causality has to be sacrificed in the case of the Streaming system). With this modification, the Baseline system achieved a diarization error rate of 3.5% (a 50% reduction in errors).

Sequential Compressed Sensing

Abstract: Compressed sensing allows perfect recovery of sparse signals (or signals sparse in some basis) using only a small number of random measurements. Existing results in compressed sensing literature have focused on characterizing the achievable performance by bounding the number of samples required for a given level of signal sparsity. However, using these bounds to minimize the number of samples requires a priori knowledge of the sparsity of the unknown signal, or the decay structure for near-sparse signals. Furthermore, there are some popular recovery methods for which no such bounds are known. In this paper, we investigate an alternative scenario where observations are available in sequence. For any recovery method, this means that there is now a sequence of candidate reconstructions. We propose a method to estimate the reconstruction error directly from the samples themselves, for every candidate in this sequence. This estimate is universal in the sense that it is based only on the measurement ensemble, and not on the recovery method or any assumed level of sparsity of the unknown signal. With these estimates, one can now stop observations as soon as there is reasonable certainty of either exact or sufficiently accurate reconstruction. They also provide a way to obtain ?run-time? guarantees for recovery methods that otherwise lack a priori performance bounds. We investigate both continuous (e.g., Gaussian) and discrete (e.g., Bernoulli) random measurement ensembles, both for exactly sparse and general near-sparse signals, and with both noisy and noiseless measurements.

Robust Sampling and Reconstruction Methods for Sparse Signals in the Presence of Impulsive Noise

Abstract: Recent results in compressed sensing show that a sparse or compressible signal can be reconstructed from a few incoherent measurements. 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 current reconstruction algorithms, fail to recover a close approximation of the signal. In this paper, we propose robust methods for sampling and reconstructing sparse signals in the presence of impulsive noise. To solve the problem of impulsive noise embedded in the underlying signal prior the measurement process, we propose a robust nonlinear measurement operator based on the weighed myriad estimator. In addition, we introduce a geometric optimization problem based on L 1 minimization employing a Lorentzian norm constraint on the residual error to recover sparse signals from noisy measurements. Analysis of the proposed methods show that in impulsive environments when the noise posses infinite variance we have a finite reconstruction error and furthermore these methods yield successful reconstruction of the desired signal. Simulations demonstrate that the proposed methods significantly outperform commonly employed compressed sensing sampling and reconstruction techniques in impulsive environments, while providing comparable performance in less demanding, light-tailed environments.

Signaling Strategies for the Hybrid MIMO Phased-Array Radar

Abstract: The hybrid MIMO phased array radar (HMPAR) is a notional concept for a multisensor radar architecture that combines elements of traditional phased-array radar with the emerging technology of multiple-input multiple output (MIMO) radar. A HMPAR comprises a large number, MP, of T/R elements, organized into M subarrays of P elements each. Within each subarray, passive element-level phase shifting is used to steer transmit and receive beams in some desired fashion. Each of the M subarrays are in turn driven by independently amplified phase-coded signals which could be quasi-orthogonal, phase-coherent, or partially correlated. Such a radar system could be used in an airborne platform for concurrent search, detect, and track missions. This paper considers various signaling strategies which could be employed in the notional HMPAR architecture to achieve various objectives quantified by transmit beampatterns and space-time ambiguity functions. First, we propose a method to generate multiple correlated signals for uniform linear and rectangular arrays that achieve arbitrary rectangular transmit beampatterns in one and two dimensions, while maintaining desirable temporal properties. Examples of the range of transmit beampatterns possible with this technique are illustrated for an array of MP=900 elements, arranged using different values of M and P. Then the space-time, or MIMO, ambiguity function that is appropriate for the HMPAR radar system is derived. Examples of ambiguity functions for our signals using a one-dimensional HMPAR architecture are given, demonstrating that one can achieve phased-array-like resolution on receive, for arbitrary transmit beampatterns.

MIMO Radar Detection in Non-Gaussian and Heterogeneous Clutter

Abstract: In this paper, the generalized likelihood ratio test-linear quadratic (GLRT-LQ) has been extended to the multiple-input multiple-output (MIMO) case where all transmit-receive subarrays are considered jointly as a system such that only one detection threshold is used. The GLRT-LQ detector has been derived based on the spherically invariant random vector (SIRV) model and is constant false alarm rate (CFAR) with respect to the clutter power fluctuations (also known as the texture). The new MIMO detector is then shown to be texture-CFAR as well. The theoretical performance of this new detector is first analytically derived and then validated using Monte Carlo simulations. Its detection performance is then compared to that of the well-known Optimum Gaussian Detector (OGD) under Gaussian and non-Gaussian clutter. Next, the adaptive version of the detector is investigated. The covariance matrix is estimated using the Fixed Point (FP) algorithm which enables the detector to remain texture- and matrix-CFAR. The effects of the estimation of the covariance matrix on the detection performance are also investigated.

Compressive Sensing for Missing Data Imputation in Noise Robust Speech Recognition

Abstract: An effective way to increase the noise robustness of automatic speech recognition is to label noisy speech features as either reliable or unreliable (missing), and to replace (impute) the missing ones by clean speech estimates. Conventional imputation techniques employ parametric models and impute the missing features on a frame-by-frame basis. At low signal-to-noise ratios (SNRs), these techniques fail, because too many time frames may contain few, if any, reliable features. In this paper, we introduce a novel non-parametric, exemplar-based method for reconstructing clean speech from noisy observations, based on techniques from the field of Compressive Sensing. The method, dubbed sparse imputation, can impute missing features using larger time windows such as entire words. Using an overcomplete dictionary of clean speech exemplars, the method finds the sparsest combination of exemplars that jointly approximate the reliable features of a noisy utterance. That linear combination of clean speech exemplars is used to replace the missing features. Recognition experiments on noisy isolated digits show that sparse imputation outperforms conventional imputation techniques at SNR = -5 dB when using an ideal `oracle' mask. With error-prone estimated masks sparse imputation performs slightly worse than the best conventional technique.

A Multimodal Approach to Blind Source Separation of Moving Sources

Abstract: A novel multimodal approach is proposed to solve the problem of blind source separation (BSS) of moving sources. The challenge of BSS for moving sources is that the mixing filters are time varying; thus, the unmixing filters should also be time varying, which are difficult to calculate in real time. In the proposed approach, the visual modality is utilized to facilitate the separation for both stationary and moving sources. The movement of the sources is detected by a 3-D tracker based on video cameras. Positions and velocities of the sources are obtained from the 3-D tracker based on a Markov Chain Monte Carlo particle filter (MCMC-PF), which results in high sampling efficiency. The full BSS solution is formed by integrating a frequency domain blind source separation algorithm and beamforming: if the sources are identified as stationary for a certain minimum period, a frequency domain BSS algorithm is implemented with an initialization derived from the positions of the source signals. Once the sources are moving, a beamforming algorithm which requires no prior statistical knowledge is used to perform real time speech enhancement and provide separation of the sources. Experimental results confirm that by utilizing the visual modality, the proposed algorithm not only improves the performance of the BSS algorithm and mitigates the permutation problem for stationary sources, but also provides a good BSS performance for moving sources in a low reverberant environment.

Low-Complexity Variable Frame Rate Analysis for Speech Recognition and Voice Activity Detection

Abstract: Frame-based speech processing inherently assumes a stationary behavior of speech signals in a short period of time. Over a long time, the characteristics of the signals can change significantly and frames are not equally important, underscoring the need for frame selection. In this paper, we present a low-complexity and effective frame selection approach based on a posteriori signal-to-noise ratio (SNR) weighted energy distance: The use of an energy distance, instead of, e.g., a standard cepstral distance, makes the approach computationally efficient and enables fine granularity search, and the use of a posteriori SNR weighting emphasizes the reliable regions in noisy speech signals. It is experimentally found that the approach is able to assign a higher frame rate to fast changing events such as consonants, a lower frame rate to steady regions like vowels and no frames to silence, even for very low SNR signals. The resulting variable frame rate analysis method is applied to three speech processing tasks that are essential to natural interaction with intelligent environments. First, it is used for improving speech recognition performance in noisy environments. Second, the method is used for scalable source coding schemes in distributed speech recognition where the target bit rate is met by adjusting the frame rate. Third, it is applied to voice activity detection. Very encouraging results are obtained for all three speech processing tasks.

Imaging of Moving Targets With Multi-Static SAR Using an Overcomplete Dictionary

Abstract: This paper presents a method for imaging of moving targets using multi-static radar by treating the problem as one of joint spatial reflectivity signal inversion with respect to an overcomplete dictionary of target velocities. Existing approaches to dealing with moving targets in SAR solve the nonlinear problem of target scattering and motion estimation typically through decoupled matched filtering. In contrast, by using an overcomplete dictionary approach we effectively linearize the forward model and solve the moving target problem as a larger, unified regularized inversion problem subject to sparsity constraints. This unified framework allows estimation of scatter motion and reflectivity to be done in an optimal and global way. We show examples of the potential of the new method for sensing configurations with transmitters and receivers randomly dispersed in a multi-static geometry within a narrow forward cone around the scene of interest.

Dynamic Updating for $\ell_{1}$ Minimization

Abstract: The theory of compressive sensing (CS) has shown us that under certain conditions, a sparse signal can be recovered from a small number of linear incoherent measurements. An effective class of reconstruction algorithms involve solving a convex optimization program that balances the l1 norm of the solution against a data fidelity term. Tremendous progress has been made in recent years on algorithms for solving these l1 minimization programs. These algorithms, however, are for the most part static: they focus on finding the solution for a fixed set of measurements. In this paper, we present a suite of dynamic algorithms for solving l1 minimization programs for streaming sets of measurements. We consider cases where the underlying signal changes slightly between measurements, and where new measurements of a fixed signal are sequentially added to the system. We develop algorithms to quickly update the solution of several different types of l1 optimization problems whenever these changes occur, thus avoiding having to solve a new optimization problem from scratch. Our proposed schemes are based on homotopy continuation, which breaks down the solution update in a systematic and efficient way into a small number of linear steps. Each step consists of a low-rank update and a small number of matrix-vector multiplications - very much like recursive least squares. Our investigation also includes dynamic updating schemes for l1 decoding problems, where an arbitrary signal is to be recovered from redundant coded measurements which have been corrupted by sparse errors.