Dennis Sundman

Projection-Based and Look-Ahead Strategies for Atom Selection

In this paper, we improve iterative greedy search algorithms in which atoms are selected serially over iterations, i.e., one-by-one over iterations. For serial atom selection, we devise two new schemes to select an atom from a set of potential atoms in each iteration. The two new schemes lead to two new algorithms. For both the algorithms, in each iteration, the set of potential atoms is found using a standard matched filter. In case of the first scheme, we propose an orthogonal projection strategy that selects an atom from the set of potential atoms. Then, for the second scheme, we propose a look-ahead strategy such that the selection of an atom in the current iteration has an effect on the future iterations. The use of look-ahead strategy requires a higher computational resource. To achieve a tradeoff between performance and complexity, we use the two new schemes in cascade and develop a third new algorithm. Through experimental evaluations, we compare the pro posed algorithms with existing greedy search and convex relaxation algorithms.

Distributed greedy pursuit algorithms

For compressed sensing over arbitrarily connected networks, we consider the problem of estimating underlying sparse signals in a distributed manner. We introduce a new signal model that helps to describe inter-signal correlation among connected nodes. Based on this signal model along with a brief survey of existing greedy algorithms, we develop distributed greedy algorithms with low communication overhead. Incorporating appropriate modifications, we design two new distributed algorithms where the local algorithms are based on appropriately modified existing orthogonal matching pursuit and subspace pursuit. Further, by combining advantages of these two local algorithms, we design a new greedy algorithm that is well suited for a distributed scenario. By extensive simulations we demonstrate that the new algorithms in a sparsely connected network provide good performance, close to the performance of a centralized greedy solution.

A greedy pursuit algorithm for distributed compressed sensing

We develop a greedy pursuit algorithm for solving the distributed compressed sensing problem in a connected network. This algorithm is based on subspace pursuit and uses the mixed support-set signal model. Through experimental evaluation, we show that the distributed algorithm performs significantly better than the standalone (disconnected) solution and close to a centralized (fully connected to a central point) solution.

Look ahead orthogonal matching pursuit

For compressive sensing, we endeavor to improve the recovery performance of the existing orthogonal matching pursuit (OMP) algorithm. To achieve a better estimate of the underlying support set progressively through iterations, we use a look ahead strategy. The choice of an atom in the current iteration is performed by checking its effect on the future iterations (look ahead strategy). Through experimental evaluations, the effect of look ahead strategy is shown to provide a significant improvement in performance.

On the use of compressive sampling for wide-band spectrum sensing

In a scenario where a cognitive radio unit wishes to transmit, it needs to know over which frequency bands it can operate. It can obtain this knowledge by estimating the power spectral density from a Nyquist-rate sampled signal. For wide-band signals sampling at the Nyquist rate is a major challenge and may be unfeasible. In this paper we accurately detect spectrum holes in sub-Nyquist frequencies without assuming wide sense stationarity in the compressed sampled signal. A novel extension to further reduce the sub-Nyquist samples is then presented by introducing a memory based compressed sensing that relies on the spectrum to be slowly varying.

Look ahead parallel pursuit

We endeavor to improve compressed sensing reconstruction performance of parallel pursuit algorithms. In an iteration, standard parallel pursuit algorithms use a support-set expansion by a fixed number of coefficients, leading to restricted performance. To achive a better performance, we develop a look ahead strategy that adaptively chooses the best number of coefficients. We develop a new algorithm which we call look ahead parallel pursuit, where a look ahead strategy is invoked on a minimal residual norm criterion. The new algorithm provides a trade-off between performance and complexity.

Methods for Distributed Compressed Sensing

Compressed sensing is a thriving research field covering a class of problems where a large sparse signal is reconstructed from a few random measurements. In the presence of several sensor nodes measuring correlated sparse signals, improvements in terms of recovery quality or the requirement for a fewer number of local measurements can be expected if the nodes cooperate. In this paper, we provide an overview of the current literature regarding distributed compressed sensing; in particular, we discuss aspects of network topologies, signal models and recovery algorithms.

Robust matching pursuit for recovery of Gaussian sparse signal

For compressive sensing (CS) recovery of Gaussian sparse signal, we explore the framework of Bayesian linear models to achieve a robust reconstruction performance in the presence of measurement noise. Using a priori statistical knowledge, we develop a minimum mean square error (MMSE) estimation based iterative greedy search algorithm. Through experimental evaluations, we show that the new algorithm provides a robust CS reconstruction performance compared to an existing least square based algorithm.

Design and Analysis of a Greedy Pursuit for Distributed Compressed Sensing

We consider a distributed compressed sensing scenario where many sensors measure correlated sparse signals and the sensors are connected through a network. Correlation between sparse signals is modeled by a partial common support-set. For such a scenario, the main objective of this paper is to develop a greedy pursuit algorithm. We develop a distributed parallel pursuit (dipp) algorithm based on exchange of information about estimated support-sets at sensors. The exchange of information helps to improve estimation of the partial common support-set, that in turn helps to gradually improve estimation of support-sets in all sensors, leading to a better quality reconstruction performance. We provide restricted isometry property (RIP) based theoretical analysis on the algorithms convergence and reconstruction performance. Under certain theoretical requirements (i.e., under certain assumptions) on the quality of information exchange over the network and RIP parameters of sensor nodes, we show that the dipp algorithm converges to a performance level that depends on a scaled additive measurement noise power (convergence in theory) where the scaling coefficient is a function of RIP parameters and information processing quality parameters. Using simulations, we show practical reconstruction performance of dipp vis-a-vis amount of undersampling, signal-to-measurement-noise ratios and network-connectivity conditions.

Distributed predictive subspace pursuit

In a compressed sensing setup with jointly sparse, correlated data, we develop a distributed greedy algorithm called distributed predictive subspace pursuit. Based on estimates from neighboring sensor nodes, this algorithm operates iteratively in two steps: first forming a prediction of the signal and then solving the compressed sensing problem with an iterative linear minimum mean squared estimator. Through simulations we show that the algorithm provides better performance than current state-of-the-art algorithms.