Arun Venkitaraman

Greedy Sparse Learning Over Network

In this paper, we develop a greedy algorithm for solving the problem of sparse learning over a right stochastic network in a distributed manner. The nodes iteratively estimate the sparse signal by exchanging a weighted version of their individual intermediate estimates over the network. We provide a restricted-isometry-property (RIP)-based theoretical performance guarantee in the presence of additive noise. In the absence of noise, we show that under certain conditions on the RIP-constant of measurement matrix at each node of the network, the individual node estimates collectively converge to the true sparse signal. Furthermore, we provide an upper bound on the number of iterations required by the greedy algorithm to converge. Through simulations, we also show that the practical performance of the proposed algorithm is better than other state-of-the-art distributed greedy algorithms found in the literature.

Motion-based segmentation of chest and abdomen region of neonates from videos

Respiration rate (RR) is one of the important vital signs used for clinical monitoring of neonates in intensive care units. Due to the fragile skin of the neonates, it is preferable to have monitoring systems with minimal contact with the neonate. Recently, several methods have been proposed for contact-free monitoring of vital signs using a video camera. Detection of the chest-and-abdomen region of the neonate is crucial to determining the respiration rate accurately. We propose a technique for automatic selection of the region of interest (ROI) in neonates using motion. Our approach is based on the observation that points on the chest-and-abdomen region, and hence, the corresponding optic flow vectors, exhibit coherency in the motion caused by breathing. The motion induced due to the movement of the neonate (e.g., hands and legs) is not coherent and hence does not exhibit the characteristics of respiratory motion. We evaluate the proposed technique using several videos of neonates and demonstrate that it picks up the ROI accurately in spite of the movement of the neonate. We compare its performance with that of the standard motion history image (MHI) framework, using different metrics. Results indicate that our method can be profitably employed in RR studies.

Graph linear prediction results in smaller error than standard linear prediction

Linear prediction is a popular strategy employed in the analysis and representation of signals. In this paper, we propose a new linear prediction approach by considering the standard linear prediction in the context of graph signal processing, which has gained significant attention recently. We view the signal to be defined on the nodes of a graph with an adjacency matrix constructed using the coefficients of the standard linear predictor (SLP). We prove theoretically that the graph based linear prediction approach results in an equal or better performance compared with the SLP in terms of the prediction gain. We illustrate the proposed concepts by application to real speech signals.

On Hilbert Transform, Analytic Signal, and Modulation Analysis for Signals over Graphs

We propose Hilbert transform and analytic signal construction for signals over graphs. This is motivated by the popularity of Hilbert transform, analytic signal, and modulation analysis in conventi ...

Distributed greedy sparse learning over doubly stochastic networks

In this paper, we develop a greedy algorithm for sparse learning over a doubly stochastic network. In the proposed algorithm, nodes of the network perform sparse learning by exchanging their individual intermediate variables. The algorithm is iterative in nature. We provide a restricted isometry property (RIP)-based theoretical guarantee both on the performance of the algorithm and the number of iterations required for convergence. Using simulations, we show that the proposed algorithm provides good performance.

A connectedness constraint for learning sparse graphs

Graphs are naturally sparse objects that are used to study many problems involving networks, for example, distributed learning and graph signal processing. In some cases, the graph is not given, but must be learned from the problem and available data. Often it is desirable to learn sparse graphs. However, making a graph highly sparse can split the graph into several disconnected components, leading to several separate networks. The main difficulty is that connectedness is often treated as a combinatorial property, making it hard to enforce in e.g. convex optimization problems. In this article, we show how connectedness of undirected graphs can be formulated as an analytical property and can be enforced as a convex constraint. We especially show how the constraint relates to the distributed consensus problem and graph Laplacian learning. Using simulated and real data, we perform experiments to learn sparse and connected graphs from data.