arXiv subjects

Sundeep Prabhakar Chepuri

Publications and source records attributed to Sundeep Prabhakar Chepuri.

At least 55 records · Page 3Linked to original sources

arXiv2019

Learning product graphs from multidomain signals

In this paper, we focus on learning the underlying product graph structure from multidomain training data. We assume that the product graph is formed from a Cartesian graph product of two smaller factor graphs. We then pose the product graph learning problem as the factor graph Laplacian matrix estimation problem. To estimate the factor graph Laplacian matrices, we assume that the data is smooth with respect to the underlying product graph. When the training data is noise free or complete, learning factor graphs can be formulated as a convex optimization problem, which has an explicit solution based on the water-filling algorithm. The developed framework is illustrated using numerical experiments on synthetic data as well as real data related to air quality monitoring in India.

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arXiv2019

Sampling And Reconstruction Of Diffusive Fields On Graphs

In this paper, the focus is on the reconstruction of a diffusive field and the localization of the underlying driving sources on arbitrary graphs by observing a significantly smaller subset of vertices of the graph uniformly in time. Specifically, we focus on the heat diffusion equation driven by an initial field and an external time-invariant input. When the underlying driving sources are modeled as an initial field or external input, the sources (hence the diffusive field) can be recovered from the subsampled observations without imposing any band-limiting or sparsity constraints. When the diffusion is induced by both the initial field and external input, then the field and sources can be recovered from the subsampled observations, however, by imposing band-limiting constraints on either the initial field or external input. For heat diffusion on graphs, we can compensate for the unobserved vertices with the temporal samples at the observed vertices. If the observations are noiseless, then the recovery is exact. Nonetheless, the developed least squares estimators perform reasonably well with noisy observations. We apply the developed theory for localizing and recovering hot spots on a rectangular metal plate with a cavity.

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arXiv2019

Analog Beamforming for Active Imaging using Sparse Arrays

This paper studies analog beamforming in active sensing applications, such as millimeter-wave radar or ultrasound imaging. Analog beamforming architectures employ a single RF-IF chain connected to all array elements via inexpensive phase shifters. This can drastically lower costs compared to fully-digital beamformers having a dedicated RF-IF chain for each sensor. However, controlling only the element phases may lead to elevated side-lobe levels and degraded image quality. We address this issue by image addition, which synthesizes a high resolution image by adding together several lower resolution component images. Image addition also facilitates the use of sparse arrays, which can further reduce array costs. To limit the image acquisition time, we formulate an optimization problem for minimizing the number of component images, subject to achieving a desired point spread function. We propose a gradient descent algorithm for finding a locally optimal solution to this problem. We also derive an upper bound on the number of component images needed for achieving the traditional fully-digital beamformer solution.

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arXiv2019

Sensor Placement and Resource Allocation for Energy Harvesting IoT Networks

The paper studies optimal sensor selection for source estimation in energy harvesting Internet of Things (IoT) networks. Specifically, the focus is on the selection of the sensor locations which minimizes the estimation error at a fusion center, and to optimally allocate power and bandwidth for each selected sensor subject to a prescribed spectral and energy budget. To do so, measurement accuracy, communication link quality, and the amount of energy harvested are all taken into account. The sensor selection is studied under both analog and digital transmission schemes from the selected sensors to the fusion center. In the digital transmission case, an information theoretic approach is used to model the transmission rate, observation quantization, and encoding. We numerically prove that with a sufficient system bandwidth, the digital system outperforms the analog system with a possibly different sensor selection. Two source models are studied in this paper: static source estimation for a vector of correlated sources and dynamic state estimation for a scalar source. The design problem of interest is a Boolean non convex optimization problem, which is solved by relaxing the Boolean constraints. We propose a randomized rounding algorithm which generalizes the existing algorithm. The proposed randomized rounding algorithm takes the joint sensor location, power and bandwidth selection into account to efficiently round the obtained relaxed solution.

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arXiv2018

Sampling and Reconstruction of Signals on Product Graphs

In this paper, we consider the problem of subsampling and reconstruction of signals that reside on the vertices of a product graph, such as sensor network time series, genomic signals, or product ratings in a social network. Specifically, we leverage the product structure of the underlying domain and sample nodes from the graph factors. The proposed scheme is particularly useful for processing signals on large-scale product graphs. The sampling sets are designed using a low-complexity greedy algorithm and can be proven to be near-optimal. To illustrate the developed theory, numerical experiments based on real datasets are provided for sampling 3D dynamic point clouds and for active learning in recommender systems.

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arXiv2018

Sparse Sampling for Inverse Problems with Tensors

We consider the problem of designing sparse sampling strategies for multidomain signals, which can be represented using tensors that admit a known multilinear decomposition. We leverage the multidomain structure of tensor signals and propose to acquire samples using a Kronecker-structured sensing function, thereby circumventing the curse of dimensionality. For designing such sensing functions, we develop low-complexity greedy algorithms based on submodular optimization methods to compute near-optimal sampling sets. We present several numerical examples, ranging from multi-antenna communications to graph signal processing, to validate the developed theory.

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arXiv2018

Sparse Antenna and Pulse Placement for Colocated MIMO Radar

Multiple input multiple output (MIMO) radar is known for its superiority over conventional radar due to its antenna and waveform diversity. Although higher angular resolution, improved parameter identifiability, and better target detection are achieved, the hardware costs (due to multiple transmitters and multiple receivers) and high energy consumption (multiple pulses) limit the usage of MIMO radars in large scale networks. On one hand, higher angle and velocity estimation accuracy is required, but on the other hand, a lower number of antennas/pulses is desirable. To achieve such a compromise, in this work, the Cram'er-Rao lower bound (CRLB) for the angle and velocity estimator is employed as a performance metric to design the antenna and pulse placement. It is shown that the CRLB derived for two targets is a more appropriate criterion in comparison with the single-target CRLB since the two-target CRLB takes into account both the mainlobe width and sidelobe level of the ambiguity function. In this paper, several algorithms for antenna and pulse selection based on convex and submodular optimization are proposed. Numerical experiments are provided to illustrate the developed theory.

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arXiv2017

Near-Optimal Sparse Sensing for Gaussian Detection with Correlated Observations

Detection of a signal under noise is a classical signal processing problem. When monitoring spatial phenomena under a fixed budget, i.e., either physical, economical or computational constraints, the selection of a subset of available sensors, referred to as sparse sensing, that meets both the budget and performance requirements is highly desirable. Unfortunately, the subset selection problem for detection under dependent observations is combinatorial in nature and suboptimal subset selection algorithms must be employed. In this work, different from the widely used convex relaxation of the problem, we leverage submodularity, the diminishing returns property, to provide practical near optimal algorithms suitable for large-scale subset selection. This is achieved by means of low-complexity greedy algorithms, which incur a reduced computational complexity compared to their convex counterparts.

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arXiv2017

Microphone Subset Selection for MVDR Beamformer Based Noise Reduction

In large-scale wireless acoustic sensor networks (WASNs), many of the sensors will only have a marginal contribution to a certain estimation task. Involving all sensors increases the energy budget unnecessarily and decreases the lifetime of the WASN. Using microphone subset selection, also termed as sensor selection, the most informative sensors can be chosen from a set of candidate sensors to achieve a prescribed inference performance. In this paper, we consider microphone subset selection for minimum variance distortionless response (MVDR) beamformer based noise reduction. The best subset of sensors is determined by minimizing the transmission cost while constraining the output noise power (or signal-to-noise ratio). Assuming the statistical information on correlation matrices of the sensor measurements is available, the sensor selection problem for this model-driven scheme is first solved by utilizing convex optimization techniques. In addition, to avoid estimating the statistics related to all the candidate sensors beforehand, we also propose a data-driven approach to select the best subset using a greedy strategy. The performance of the greedy algorithm converges to that of the model-driven method, while it displays advantages in dynamic scenarios as well as on computational complexity. Compared to a sparse MVDR or radius-based beamformer, experiments show that the proposed methods can guarantee the desired performance with significantly less transmission costs.

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arXiv2017

Graph Sampling for Covariance Estimation

In this paper the focus is on subsampling as well as reconstructing the second-order statistics of signals residing on nodes of arbitrary undirected graphs. Second-order stationary graph signals may be obtained by graph filtering zero-mean white noise and they admit a well-defined power spectrum whose shape is determined by the frequency response of the graph filter. Estimating the graph power spectrum forms an important component of stationary graph signal processing and related inference tasks such as Wiener prediction or inpainting on graphs. The central result of this paper is that by sampling a significantly smaller subset of vertices and using simple least squares, we can reconstruct the second-order statistics of the graph signal from the subsampled observations, and more importantly, without any spectral priors. To this end, both a nonparametric approach as well as parametric approaches including moving average and autoregressive models for the graph power spectrum are considered. The results specialize for undirected circulant graphs in that the graph nodes leading to the best compression rates are given by the so-called minimal sparse rulers. A near-optimal greedy algorithm is developed to design the subsampling scheme for the non-parametric and the moving average models, whereas a particular subsampling scheme that allows linear estimation for the autoregressive model is proposed. Numerical experiments on synthetic as well as real datasets related to climatology and processing handwritten digits are provided to demonstrate the developed theory.

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arXiv2016

Learning Sparse Graphs Under Smoothness Prior

In this paper, we are interested in learning the underlying graph structure behind training data. Solving this basic problem is essential to carry out any graph signal processing or machine learning task. To realize this, we assume that the data is smooth with respect to the graph topology, and we parameterize the graph topology using an edge sampling function. That is, the graph Laplacian is expressed in terms of a sparse edge selection vector, which provides an explicit handle to control the sparsity level of the graph. We solve the sparse graph learning problem given some training data in both the noiseless and noisy settings. Given the true smooth data, the posed sparse graph learning problem can be solved optimally and is based on simple rank ordering. Given the noisy data, we show that the joint sparse graph learning and denoising problem can be simplified to designing only the sparse edge selection vector, which can be solved using convex optimization.

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arXiv2016

Sensor Selection for Estimation with Correlated Measurement Noise

In this paper, we consider the problem of sensor selection for parameter estimation with correlated measurement noise. We seek optimal sensor activations by formulating an optimization problem, in which the estimation error, given by the trace of the inverse of the Bayesian Fisher information matrix, is minimized subject to energy constraints. Fisher information has been widely used as an effective sensor selection criterion. However, existing information-based sensor selection methods are limited to the case of uncorrelated noise or weakly correlated noise due to the use of approximate metrics. By contrast, here we derive the closed form of the Fisher information matrix with respect to sensor selection variables that is valid for any arbitrary noise correlation regime, and develop both a convex relaxation approach and a greedy algorithm to find near-optimal solutions. We further extend our framework of sensor selection to solve the problem of sensor scheduling, where a greedy algorithm is proposed to determine non-myopic (multi-time step ahead) sensor schedules. Lastly, numerical results are provided to illustrate the effectiveness of our approach, and to reveal the effect of noise correlation on estimation performance.

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arXiv2016

Subsampling for Graph Power Spectrum Estimation

In this paper we focus on subsampling stationary random processes that reside on the vertices of undirected graphs. Second-order stationary graph signals are obtained by filtering white noise and they admit a well-defined power spectrum. Estimating the graph power spectrum forms a central component of stationary graph signal processing and related inference tasks. We show that by sampling a significantly smaller subset of vertices and using simple least squares, we can reconstruct the power spectrum of the graph signal from the subsampled observations, without any spectral priors. In addition, a near-optimal greedy algorithm is developed to design the subsampling scheme.

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arXiv2014

Sparsity-Promoting Sensor Selection for Non-linear Measurement Models

Sensor selection is an important design problem in large-scale sensor networks. Sensor selection can be interpreted as the problem of selecting the best subset of sensors that guarantees a certain estimation performance. We focus on observations that are related to a general non-linear model. The proposed framework is valid as long as the observations are independent, and its likelihood satisfies the regularity conditions. We use several functions of the Cramér-Rao bound (CRB) as a performance measure. We formulate the sensor selection problem as the design of a selection vector, which in its original form is a nonconvex l0-(quasi) norm optimization problem. We present relaxed sensor selection solvers that can be efficiently solved in polynomial time. We also propose a projected subgradient algorithm that is attractive for large-scale problems and also show how the algorithm can be easily distributed. The proposed framework is illustrated with a number of examples related to sensor placement design for localization.

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arXiv2013

60 GHz Wireless Link Within Metal Enclosures: Channel Measurements and System Analysis

Wireless channel measurement results for 60 GHz within a closed metal cabinet are provided. A metal cabinet is chosen to emulate the environment within a mechatronic system, which have metal enclosures in general. A frequency domain sounding technique is used to measure the wireless channel for different volumes of the metal enclosure, considering both line-of-sight (LOS) and non-line-of-sight (NLOS) scenarios. Large-scale and small-scale characteristics of the wireless channel are extracted in order to build a comprehensive channel model. In contrast to conventional indoor channels at 60 GHz, the channel in the metal enclosure is highly reflective resulting in a rich scattering environment with a significantly large root-mean-square (RMS) delay spread. Based on the obtained measurement results, the bit error rate (BER) performance is evaluated for a wideband orthogonal frequency division multiplexing (OFDM) system.

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arXiv2013

Rigid Body Localization Using Sensor Networks: Position and Orientation Estimation

In this paper, we propose a novel framework called rigid body localization for joint position and orientation estimation of a rigid body. We consider a setup in which a few sensors are mounted on a rigid body. The absolute position of the sensors on the rigid body, or the absolute position of the rigid body itself is not known. However, we know how the sensors are mounted on the rigid body, i.e., the sensor topology is known. Using range-only measurements between the sensors and a few anchors (nodes with known absolute positions), and without using any inertial measurements (e.g., accelerometers), we estimate the position and orientation of the rigid body. For this purpose, the absolute position of the sensors is expressed as an affine function of the Stiefel manifold. In other words, we represent the orientation as a rotation matrix, and absolute position as a translation vector. We propose a least-squares (LS), simplified unitarily constrained LS (SUC-LS), and optimal unitarily constrained least-squares (OUC-LS) estimator, where the latter is based on Newton's method. As a benchmark, we derive a unitarily constrained Cramér-Rao bound (UC-CRB). The known topology of the sensors can sometimes be perturbed during fabrication. To take these perturbations into account, a simplified unitarily constrained total-least-squares (SUC-TLS), and an optimal unitarily constrained total-least-squares (OUC-TLS) estimator are also proposed.

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arXiv2013

Position and Orientation Estimation of a Rigid Body: Rigid Body Localization

Rigid body localization refers to a problem of estimating the position of a rigid body along with its orientation using anchors. We consider a setup in which a few sensors are mounted on a rigid body. The absolute position of the rigid body is not known, but, the relative position of the sensors or the topology of the sensors on the rigid body is known. We express the absolute position of the sensors as an affine function of the Stiefel manifold and propose a simple least-squares (LS) estimator as well as a constrained total least-squares (CTLS) estimator to jointly estimate the orientation and the position of the rigid body. To account for the perturbations of the sensors, we also propose a constrained total least-squares (CTLS) estimator. Analytical closed-form solutions for the proposed estimators are provided. Simulations are used to corroborate and analyze the performance of the proposed estimators.

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arXiv2013

Sparsity-Exploiting Anchor Placement for Localization in Sensor Networks

We consider the anchor placement problem in localization based on one-way ranging, in which either the sensor or the anchors send the ranging signals. The number of anchors deployed over a geographical area is generally sparse, and we show that the anchor placement can be formulated as the design of a sparse selection vector. Interestingly, the case in which the anchors send the ranging signals, results in a joint ranging energy optimization and anchor placement problem. We make abstraction of the localization algorithm and instead use the Cramér-Rao lower bound (CRB) as the performance constraint. The anchor placement problem is formulated as an elegant convex optimization problem which can be solved efficiently.

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