In this letter, Laplace distribution is used to model the prior for the direction of arrival (DoA) of sources. In order to incorporate the real and imaginary part of the received signal, we propose a method that pairwise estimates the hyperparameters for parts of the signal coefficients. In addition, we propose a multitask algorithm to extend the application of our method to the situation where multiple measurements are available. Nonuniform linear arrays are used to demonstrate the validity and advantages of the proposed method including its improved efficiency and accuracy compared with the state-of-art DoA estimation methods.

We present a novel egocentric visual localization algorithm for an indoor navigation system, called PERCEPT -V, which is designed to assist the blind and visually impaired users traveling independently in an unfamiliar indoor space. Through the integration of a background extraction module based on Robust Principle Component Analysis (RPCA) into the localization algorithm, we successfully improve the resilience of camera localization to the presence of crowds in the observed scene. Experiments using datasets of videos containing various levels of crowd activity show that the proposed algorithm can increase prominently the reliability of localization performance.

High spectral resolution brings hyperspectral images with large amounts of information, which makes these images more useful in many applications than images obtained from traditional multispectral scanners with low spectral resolution. However, the high data dimensionality of hyperspectral images increases the burden on data computation, storage, and transmission; fortunately, the high redundancy in the spectral domain allows for significant dimensionality reduction. Band selection provides a simple dimensionality reduction scheme by discarding bands that are highly redundant, thereby preserving the structure of the data set. This paper proposes a new criterion for pointwise-ranking-based band selection that uses a nonhomogeneous hidden Markov chain (NHMC) model for redundant wavelet coefficients of each hyperspectral signature. The model provides a binary multiscale label that encodes semantic features that are useful to discriminate spectral types. A band ranking score considers the average correlation among the average NHMC labels for each band. We also test richer discrete-valued label vectors that provide a more finely grained quantization of spectral fluctuations. In addition, since band selection methods based on band ranking often ignore correlations in selected bands, we study the effect of redundancy elimination, applied on the selected features, on the performance of an example classification problem. Our experimental results also include an optional redundancy elimination step and test their effect on classification performance that is based on the selected bands. The experimental results also include a comparison with several relevant supervised band selection techniques.

This paper proposes a new hyperspectral unmixing method for nonlinearly mixed hyperspectral data using a semantic representation in a semisupervised fashion, assuming the availability of a spectral reference library. Existing semisupervised unmixing algorithms select members from an endmember library that are present at each of the pixels; most such methods assume a linear mixing model. However, those methods will fail in the presence of nonlinear mixing among the observed spectra. To address this issue, we develop an endmember selection method using a recently proposed semantic spectral representation obtained via nonhomogeneous hidden Markov chain model for a wavelet transform of the spectra. The semantic representation can encode spectrally discriminative features for any observed spectrum, and therefore, our proposed method can perform endmember selection without any assumption on the mixing model. The experimental results show that in the presence of sufficiently nonlinear mixing, our proposed method outperforms dictionary-based sparse unmixing approaches based on linear models.

This paper proposes an out-of-sample extension framework for a global manifold learning algorithm (Isomap) that uses temporal information in out-of-sample points in order to make the embedding more robust to noise and artifacts. Given a set of noise-free training data and its embedding, the proposed framework extends the embedding for a noisy time series. This is achieved by adding a spatio-temporal compactness term to the optimization objective of the embedding. To the best of our knowledge, this is the first method for out-of-sample extension of manifold embeddings that leverages timing information available for the extension set. Experimental results demonstrate that our out-of-sample extension algorithm renders a more robust and accurate embedding of sequentially ordered image data in the presence of various noise and artifacts when compared with other timing-aware embeddings. Additionally, we show that an out-of-sample extension framework based on the proposed algorithm outperforms the state of the art in eye-gaze estimation.

Cross-correlation is a popular signal processing technique used in numerous location tracking systems for obtaining reliablerangeinformation. However, its efficient design and practical implementation has not yet been achieved on mote platforms that are typical in wireless sensor network due to resource constrains. In this paper, we proposeStructS-XCorr: cross-correlation via structured sparse representation, a new computing framework for ranging based on$\ell _1$-norm minimization[1]and structured sparsity. The key idea is to compress the ranging signal samples on the mote by efficient random projections and transfer them to a central device; where a convex optimization process estimates the range by exploiting the sparse signal structure in the proposedcorrelationdictionary. Through theoretical validation, extensive empirical studies and experiments on anend-to-endacoustic ranging system implemented on resource limited off-the-shelf sensor nodes, we show that the proposed framework can achieve up totwo orders of magnitudebetter performance compared to other approaches such as working on DCT domain and downsampling. Compared to the standard cross-correlation, it is able to obtain range estimates with a bias of 2-6 cm with 30 percent and approximately 100 cm with 5 percent compressed measurements. Its structured sparsity model is able to improve the ranging accuracy by 40 percent under challenging recovery conditions (such as high compression factor and low signal-to-noise ratio) by overcoming limitations due to dictionary coherence.

We consider the problem of selecting an optimal mask for an image manifold, i.e., choosing a subset of the pixels of the image that preserves the manifold's geometric structure present in the original data. Such masking implements a form of compressive sensing through emerging imaging sensor platforms for which the power expense grows with the number of pixels acquired. Our goal is for the manifold learned from masked images to resemble its full image counterpart as closely as possible. More precisely, we show that one can indeed accurately learn an image manifold without having to consider a large majority of the image pixels. In doing so, we consider two masking methods that preserve the local and global geometric structure of the manifold, respectively. In each case, the process of finding the optimal masking pattern can be cast as a binary integer program, which is computationally expensive but can be approximated by a fast greedy algorithm. Numerical experiments show that the relevant manifold structure is preserved through the data-dependent masking process, even for modest mask sizes.

We consider the problem of selecting a subset of the dimensions of an image manifold that best preserves the underlying local structure in the original data. We have previously shown that masks which preserve the data neighborhood graph are well suited to global manifold learning algorithms. However, local manifold learning algorithms leverage a geometric structure beyond that captured by this neighborhood graph. In this paper, we present a mask selection algorithm that further preserves this additional structure by designing an extended data neighborhood graph that connects all neighbors of each data point, forming local cliques. Numerical experiments show the improvements achieved by employing the extended graph in the mask selection process.

The literature on compressive parameter estimation has been mostly focused on the use of sparsity dictionaries that encode a sampling of the parameter space; these dictionaries, however, suffer from coherence issues that must be controlled for successful estimation. We propose the use of statistical parameter estimation methods within the approximate message passing (AMP) algorithm for signal recovery. Our proposed work leverages the recently highlighted connection between statistical denoising methods and the thresholding step commonly used during recovery. As an example, we consider line spectral estimation by leveraging the well-known Root MUSIC algorithm. Numerical experiments show significant improvements in estimation performance.

The linear model, in which a set of observations is assumed to be given by a linear combination of columns of a matrix (often termed a dictionary), has long been the mainstay of the statistics and signal processing literature. One particular challenge for inference under linear models is understanding the conditions on the dictionary under which reliable inference is possible. This challenge has attracted renewed attention in recent years, since many modern inference problems (e.g, high-dimensional statistics and compressed sensing) deal with the underdetermined setting, in which the number of observations is much smaller than the number of columns in the dictionary. This paper makes several contributions for this setting when the set of observations is given by a linear combination of a small number of groups of columns of the dictionary, termed the block-sparse case. First, it specifies conditions on the dictionary under which most block submatrices of the dictionary (often termed block subdictionaries) are well conditioned. This result is fundamentally different from prior work on block-sparse inference because: 1) it provides conditions that can be explicitly computed in polynomial time; 2) the given conditions translate into near-optimal scaling of the number of columns of the block subdictionaries as a function of the number of observations for a large class of dictionaries; and 3) it suggests that the spectral norm, rather than the column/block coherences of the dictionary, fundamentally limits the scaling of dimensions of the well-conditioned block subdictionaries. Second, in order to help understand the significance of this result in the context of block-sparse inference, this paper investigates the problems of block-sparse recovery and block-sparse regression in underdetermined settings. In both of these problems, this paper utilizes its result concerning conditioning of block subdictionaries and establishes that near-optimal block-sparse recovery and block-sparse regression is possible for a large class of dictionaries as long as the dictionary satisfies easily computable conditions and the coefficients describing the linear combination of groups of columns can be modeled through a mild statistical prior. Third, the paper reports extensive numerical experiments that highlight the effects of different measures of the dictionary in block-sparse inference problems.

This paper studies conditions for high-dimensional inference when the set of observations is given by a linear combination of a small number of groups of columns of a design matrix, termed the “block-sparse” case. In this regard, it first specifies conditions on the design matrix under which most of its block submatrices are well conditioned. It then leverages this result for average-case analysis of high-dimensional block-sparse recovery and regression. In contrast to earlier works, the results of this paper are fundamentally different because (i) they provide conditions on arbitrary designs that can be explicitly computed in polynomial time, (ii) the provided conditions translate into near-optimal scaling of the number of observations with the number of active blocks of the design matrix, and (iii) they suggest that the spectral norm, rather than the column/block coherences, of the design matrix fundamentally limits the performance of computational methods in high-dimensional settings.

We consider the application of non-homogeneous hidden Markov chain (NHMC) models to the problem of hyperspectral signature classification. It has been previously shown that the NHMC model enables the detection of several semantic structural features of hyperspectral signatures. However, there are some aspects of the spectral data that are not fully captured by the proposed NHMC models such as the relatively smooth but fluctuating regions and the fluctuation orientations. In order to address these limitations, we propose an improved NHMC model based on Daubechies-1 wavelets in conjunction with an increased the model complexity. Experimental results show that the revised approach outperforms existing approaches relevant in classification tasks.

Existing approaches to compressive sensing of frequency-sparse signals focuses on signal recovery rather than spectral estimation. Furthermore, the recovery performance is limited by the coherence of the required sparsity dictionaries and by the discretization of the frequency parameter space. In this paper, we introduce a greedy recovery algorithm that leverages a band-exclusion function and a polar interpolation function to address these two issues in spectral compressive sensing. Our algorithm is geared towards line spectral estimation from compressive measurements and outperforms most existing approaches in fidelity and tolerance to noise.

Motivated by the compelling application of interference mitigation at wideband receivers in wireless communication and sensing systems, we consider the recovery of a frequency-sparse signal from samples of small magnitude. The standard ℓ1-norm minimization results in an inadequate signal-dependent recovery performance, and hence we introduce three techniques to improve the quality of recovery. The performance of each of these three techniques is characterized through numerical simulations, from which we conclude that each of the proposed techniques show the promise of substantially improving recovery performance.

In compressive sensing, a small collection of linear projections of a sparse signal contains enough information to permit signal recovery. Distributed compressive sensing extends this framework by defining ensemble sparsity models, allowing a correlated ensemble of sparse signals to be jointly recovered from a collection of separately acquired compressive measurements. In this paper, we introduce a framework for modeling sparse signal ensembles that quantifies the intra- and intersignal dependences within and among the signals. This framework is based on a novel bipartite graph representation that links the sparse signal coefficients with the measurements obtained for each signal. Using our framework, we provide fundamental bounds on the number of noiseless measurements that each sensor must collect to ensure that the signals are jointly recoverable.

Melanoma detection relies on visual inspection of skin samples under the microscope via a qualitative set of indicators, causing large discordance among pathologists. New developments in pump-probe imaging enable the extraction of melanin intensity levels from skin samples and provide baseline qualitative figures for melanoma detection and classification. However, such basic figures do not capture the diverse types of cellular structure that distinguish different stages of melanoma. In this paper, we propose an initial approach for feature extraction for classification purposes via Hidden Markov Tree models trained on skin sample melanin intensity images. Our experimental results show that the proposed features provide a mathematical microscope that is able to better discriminate cellular structure, enabling successful classification of skin samples that are mislabeled when the baseline melanin intensity qualitative figures are used.

The role of random measurement in compressive sensing is analogous to the role of random codes in coding theory. In coding theory, decoders that can correct beyond the minimum distance of a code allow random codes to achieve the Shannon limit. In compressed sensing, the counterpart of minimum distance is the spark of the measurement matrix, i.e., the size of the smallest set of linearly dependent columns. This paper constructs a family of measurement matrices where the columns are formed by exponentiating codewords from a classical binary error-correcting code of block length M. The columns can be partitioned into mutually unbiased bases, and the spark of the corresponding measurement matrix is shown to be O(√M) by identifying a configuration of columns that plays a role similar to that of the Dirac comb in classical Fourier analysis. Further, an explicit basis for the null space of these measurement matrices is given in terms of indicator functions of binary self-dual codes. Reliable reconstruction of k-sparse inputs is shown for k of order M/log(M) which is best possible and far beyond the worst case lower bound provided by the spark.

Compressive sensing (CS) is an emerging approach for the acquisition of signals having a sparse or compressible representation in some basis. While the CS literature has mostly focused on problems involving 1-D signals and 2-D images, many important applications involve multidimensional signals; the construction of sparsifying bases and measurement systems for such signals is complicated by their higher dimensionality. In this paper, we propose the use of Kronecker product matrices in CS for two purposes. First, such matrices can act as sparsifying bases that jointly model the structure present in all of the signal dimensions. Second, such matrices can represent the measurement protocols used in distributed settings. Our formulation enables the derivation of analytical bounds for the sparse approximation of multidimensional signals and CS recovery performance, as well as a means of evaluating novel distributed measurement schemes.

The aim of compressed sensing is to recover attributes of sparse signals using very few measurements. Given an overall bit budget for quantization, this paper demonstrates that there is value to redundant measurement. The measurement matrices considered here are required to have the property that signal recovery is still possible even after dropping certain subsets of D measurements. It introduces the concept of a measurement matrix that is weakly democratic in the sense that the amount of information about the signal carried by each of the designated D-subsets is the same. Examples of deterministic measurement matrices that are weakly democratic are constructed by exponentiating codewords from the binary second order Reed Muller code. The value in rejecting D measurements that are on average larger, is to be able to provide a finer grid for vector quantization of the remaining measurements, even after discounting the original budget by the bits used to identify the reject set. Simulation results demonstrate that redundancy improves recovery SNR, sometimes by a wide margin. Optimum performance occurs when a significant fraction of measurements are rejected.

Compressive sensing (CS) is an emerging approach for acquisition of signals having a sparse or compressible representation in some basis. While CS literature has mostly focused on problems involving 1-D and 2-D signals, many important applications involve signals that are multidimensional. We propose the use of Kronecker product matrices in CS for two purposes. First, we can use such matrices as sparsifying bases that jointly model the different types of structure present in the signal. Second, the measurement matrices used in distributed measurement settings can be easily expressed as Kronecker products. This new formulation enables the derivation of analytical bounds for sparse approximation and CS recovery of multidimensional signals.

This paper develops a new class of algorithms for signal recovery in the distributed compressive sensing (DCS) framework. DCS exploits both intra-signal and inter-signal correlations through the concept of joint sparsity to further reduce the number of measurements required for recovery. DCS is well-suited for sensor network applications due to its universality, computational asymmetry, tolerance to quantization and noise, and robustness to measurement loss. In this paper we propose recovery algorithms for the sparse common and innovation joint sparsity model. Our approach leads to a class of efficient algorithms, the Texas Hold 'Em algorithms, which are scalable both in terms of communication bandwidth and computational complexity.

The emergence of low-cost sensing architectures for diverse modalities has made it possible to deploy sensor networks that capture a single event from a large number of vantage points and using multiple modalities. In many scenarios, these networks acquire large amounts of very high-dimensional data. For example, even a relatively small network of cameras can generate massive amounts of high-dimensional image and video data. One way to cope with this data deluge is to exploit low-dimensional data models. Manifold models provide a particularly powerful theoretical and algorithmic framework for capturing the structure of data governed by a small number of parameters, as is often the case in a sensor network. However, these models do not typically take into account dependencies among multiple sensors. We thus propose a new joint manifold framework for data ensembles that exploits such dependencies. We show that joint manifold structure can lead to improved performance for a variety of signal processing algorithms for applications including classification and manifold learning. Additionally, recent results concerning random projections of manifolds enable us to formulate a scalable and universal dimensionality reduction scheme that efficiently fuses the data from all sensors.

Compressive sensing (CS) is an alternative to Shannon/Nyquist sampling for the acquisition of sparse or compressible signals that can be well approximated by just K ¿ N elements from an N -dimensional basis. Instead of taking periodic samples, CS measures inner products with M < N random vectors and then recovers the signal via a sparsity-seeking optimization or greedy algorithm. Standard CS dictates that robust signal recovery is possible from M = O(K log(N/K)) measurements. It is possible to substantially decrease M without sacrificing robustness by leveraging more realistic signal models that go beyond simple sparsity and compressibility by including structural dependencies between the values and locations of the signal coefficients. This paper introduces a model-based CS theory that parallels the conventional theory and provides concrete guidelines on how to create model-based recovery algorithms with provable performance guarantees. A highlight is the introduction of a new class of structured compressible signals along with a new sufficient condition for robust structured compressible signal recovery that we dub the restricted amplification property, which is the natural counterpart to the restricted isometry property of conventional CS. Two examples integrate two relevant signal models-wavelet trees and block sparsity-into two state-of-the-art CS recovery algorithms and prove that they offer robust recovery from just M = O(K) measurements. Extensive numerical simulations demonstrate the validity and applicability of our new theory and algorithms.

Wideband analog signals push contemporary analog-to-digital conversion (ADC) systems to their performance limits. In many applications, however, sampling at the Nyquist rate is inefficient because the signals of interest contain only a small number of significant frequencies relative to the band limit, although the locations of the frequencies may not be known a priori. For this type of sparse signal, other sampling strategies are possible. This paper describes a new type of data acquisition system, called a random demodulator, that is constructed from robust, readily available components. Let K denote the total number of frequencies in the signal, and let W denote its band limit in hertz. Simulations suggest that the random demodulator requires just O(K log(W/K)) samples per second to stably reconstruct the signal. This sampling rate is exponentially lower than the Nyquist rate of W hertz. In contrast to Nyquist sampling, one must use nonlinear methods, such as convex programming, to recover the signal from the samples taken by the random demodulator. This paper provides a detailed theoretical analysis of the system's performance that supports the empirical observations.

Compressive sensing aims to recover a sparse or compressible signal from a small set of projections onto random vectors; conventional solutions involve linear programming or greedy algorithms that can be computationally expensive. Moreover, these recovery techniques are generic and assume no particular structure in the signal aside from sparsity. In this paper, we propose a new algorithm that enables fast recovery of piecewise smooth signals, a large and useful class of signals whose sparse wavelet expansions feature a distinct "connected tree" structure. Our algorithm fuses recent results on iterative reweighted pound1-norm minimization with the wavelet Hidden Markov Tree model. The resulting optimization-based solver outperforms the standard compressive recovery algorithms as well as previously proposed wavelet-based recovery algorithms. As a bonus, the algorithm reduces the number of measurements necessary to achieve low-distortion reconstruction.

Compressive Sensing (CS) combines sampling and compression into a single sub-Nyquist linear measurement process for sparse and compressible signals. In this paper, we extend the theory of CS to include signals that are concisely represented in terms of a graphical model. In particular, we use Markov Random Fields (MRFs) to represent sparse signals whose nonzero coefficients are clustered. Our new model-based reconstruction algorithm, dubbed Lattice Matching Pursuit (LaMP), stably recovers MRF-modeled signals using many fewer measurements and computations than the current state-of-the-art algorithms.

We propose a framework for exploiting dimension-reducing random projections in detection and classification problems. Our approach is based on the generalized likelihood ratio test; in the case of image classification, it exploits the fact that a set of images of a fixed scene under varying articulation parameters forms a low-dimensional, nonlinear manifold. Exploiting recent results showing that random projections stably embed a smooth manifold in a lower-dimensional space, we develop the multiscale smashed filter as a compressive analog of the familiar matched filter classifier. In a practical target classification problem using a single-pixel camera that directly acquires compressive image projections, we achieve high classification rates using many fewer measurements than the dimensionality of the images.

The new theory of compressive sensing enables direct analog-to-information conversion of compressible signals at sub-Nyquist acquisition rates. The authors develop new theory, algorithms, performance bounds, and a prototype implementation for an analog-to-information converter based on random demodulation. The architecture is particularly apropos for wideband signals that are sparse in the time-frequency plane. End-to-end simulations of a complete transistor-level implementation prove the concept under the effect of circuit nonidealities.

The recently introduced theory of compressed sensing (CS) enables the reconstruction or approximation of sparse or compressible signals from a small set of incoherent projections; often the number of projections can be much smaller than the number of Nyquist rate samples. In this paper, we show that the CS framework is information scalable to a wide range of statistical inference tasks. In particular, we demonstrate how CS principles can solve signal detection problems given incoherent measurements without ever reconstructing the signals involved. We specifically study the case of signal detection in strong inference and noise and propose an incoherent detection and estimation algorithm (IDEA) based on matching pursuit. The number of measurements and computations necessary for successful detection using IDEA is significantly lower than that necessary for successful reconstruction. Simulations show that IDEA is very resilient to strong interference, additive noise, and measurement quantization. When combined with random measurements, IDEA is applicable to a wide range of different signal classes

We propose and study a new technique for efficiently acquiring and reconstructing signals based on convolution with a fixed FIR filter having random taps. The method is designed for sparse and compressible signals, i.e., ones that are well approximated by a short linear combination of vectors from an orthonormal basis. Signal reconstruction involves a nonlinear orthogonal matching pursuit algorithm that we implement efficiently by exploiting the nonadaptive, time-invariant structure of the measurement process. While simpler and more efficient than other random acquisition techniques like compressed sensing, random filtering is sufficiently generic to summarize many types of compressible signals and generalizes to streaming and continuous-time signals. Extensive numerical experiments demonstrate its efficacy for acquiring and reconstructing signals sparse in the time, frequency, and wavelet domains, as well as piecewise smooth signals and Poisson processes

Compressive sensing is an emerging field based on the rev elation that a small group of non-adaptive linear projections of a compressible signal contains enough information for reconstruction and processing. In this paper, we propose algorithms and hardware to support a new theory of compressive imaging. Our approach is based on a new digital image/video camera that directly acquires random projections of the signal without first collecting the pixels/voxels. Our camera architecture employs a digital micromirror array to perform optical calculations of linear projections of an image onto pseudorandom binary patterns. Its hallmarks include the ability to obtain an image with a single detection element while measuring the image/video fewer times than the number of pixels this can significantly reduce the computation required for video acquisition/encoding. Because our system relies on a single photon detector, it can also be adapted to image at wavelengths that are currently impossible with conventional CCD and CMOS imagers. We are currently testing a proto type design for the camera and include experimental results.

This paper develops a new framework for distributed coding and compression in sensor networks based on distributed compressed sensing (DCS). DCS exploits both intra-signal and inter-signal correlations through the concept of joint sparsity; just a few measurements of a jointly sparse signal ensemble contain enough information for reconstruction. DCS is well-suited for sensor network applications, thanks to its simplicity, universality, computational asymmetry, tolerance to quantization and noise, robustness to measurement loss, and scalability. It also requires absolutely no inter-sensor collaboration. We apply our framework to several real world datasets to validate the framework.

Compressed sensing is an emerging field based on the revelation that a small group of linear projections of a sparse signal contains enough information for reconstruc- tion. In this paper we introduce a new theory for distributed compressed sensing (DCS) that enables new distributed coding algorithms for multi-signal ensembles that exploit both intra- and inter-signal correlation structures. The DCS theory rests on a new concept that we term the joint sparsity of a signal ensemble. We study three simple models for jointly sparse signals, propose algorithms for joint recov- ery of multiple signals from incoherent projections, and characterize theoretically and empirically the number of measurements per sensor required for accurate re- construction. In some sense DCS is a framework for distributed compression of sources with memory, which has remained a challenging problem in information theory for some time. DCS is immediately applicable to a range of problems in sensor networks and arrays.

Decision fusion is a decentralized decision making process where local decisions are combined to reach a global decision. In this work, we propose a complementary optimal decision fusion (CODF) method to the target detection task that arises in wireless ad hoc sensor network signal processing. We conduct extensive comparative study using real world sensor signal data, and observe superior performance of CODF when compared with state-of-the-art decision fusion methods. In addition to distributed sensor network applications, the proposed CODF algorithm can be applied to numerous multi-modality, multi-agent, multi-media signal processing problems.

Decision fusion is a decentralized decision making process where local decisions are combined to reach a global decision. In this work, we propose a complementary optimal decision fusion (CODF) method to the target detection task that arises in wireless ad hoc sensor network signal processing. We conduct extensive comparative study using standard datasets, and observe superior performance of CODF when compared with state-of-the-art decision fusion methods. In addition to distributed sensor network applications, the proposed CODF algorithm can be applied to numerous multi-modality, multi-agent, multi-media signal processing problems.