Mohammadreza Soltani

A fast iterative algorithm for demixing sparse signals from nonlinear observations

In this paper, we propose an iterative algorithm based on hard thresholding for demixing a pair of signals from nonlinear observations of their superposition. We focus on the under-determined case where the number of available observations is far less than the ambient dimension of the signals. We derive nearly-tight upper bounds on the sample complexity of the algorithm to achieve stable recovery of the component signals. Moreover, we show that the algorithm enjoys a linear convergence rate. We provide a range of simulations to illustrate the performance of the algorithm both on synthetic and real data.

Demixing sparse signals from nonlinear observations

Signal demixing is of special importance in several applications ranging from astronomy to computer vision. The goal in demixing is to recover a set of signals from their linear superposition. In this paper, we study the more challenging scenario where only a limited number of nonlinear measurements of the signal superposition are available. Our contribution is a simple, fast algorithm that recovers the component signals from the nonlinear measurements. We support our algorithm with a rigorous theoretical analysis, and provide upper bounds on the estimation error as well as the sample complexity of demixing the components (up to a scalar ambiguity). We also provide a range of simulation results, and observe that the method outperforms a previous algorithm based on convex relaxation.

Data fusion utilization for optimizing large-scale Wireless Sensor Networks

Wireless Sensor Networks (WSN) continue their tremendous growth acceleration. WSNs have found their way into a wide range of domains, from military and transportation applications to medical and environmental monitoring. Some of these applications can include a very large number of nodes, which poses significant challenges to network lifetime, data transmission, and overall reliability. Recently, data fusion approaches are gaining traction in WSNs for improving reported data accuracy and help predict future events. They are used to improve the reliability of delivered information. While this addresses data accuracy, it does not address the inefficiencies caused by very large nodes and high data redundancy. Data aggregation is a simple way of streamlining data flow, but does not fully address the issue. The large WSN size causes congestion and increases the traffic load in the network; plus, decreasing the performance of the WSN and potentially disrupting its operation altogether. In this paper, we therefore explore Kalman Filters (KF) based data fusion as a technique to reduce the number of active sensor nodes in a very large WSN to conserve network resources while preserving the required data reliability and accuracy. Our results show that there is great potential for improving WSN operations utilizing our proposed approach.

Utilization of convex optimization for data fusion-driven sensor management in WSNs

In large-scale Wireless Sensor Networks (WSNs), one of the most important challenges is manageability of the network. With the increase in sensor nodes, data forwarding, route selection, network reliability and data accuracy are vital characteristics of WSNs that suffer from the growth in scale. In this paper, we propose a data fusion based approach to drastically improve network lifetime, reduce excessive network load, and improve overall WSN performance. Our proposed approach utilizes employment of data fusion to intelligently select a subset of nodes with information needed for the data fusion, while removing all redundant nodes without impacting the fused data quality. We also introduce two methods for reducing the number of sensor nodes in a generic estimation problem using data fusion for reliability improvement of the sensed data in the presence of noise. The first method is based on observation similarity, while the second method leverages convex optimization. Our results show that our proposed methods can greatly improve large-scale WSN operation efficiency.

Stable recovery of sparse vectors from random sinusoidal feature maps

Random sinusoidal features are a popular approach for speeding up kernel-based inference in large datasets. Prior to the inference stage, the approach suggests performing dimensionality reduction by first multiplying each data vector by a random Gaussian matrix, and then computing an element-wise sinusoid. Theoretical analysis shows that collecting a sufficient number of such features can be reliably used for subsequent inference in kernel classification and regression. In this work, we demonstrate that with a mild increase in the dimension of the embedding, it is also possible to reconstruct the data vector from such random sinusoidal features, provided that the underlying data is sparse enough. In particular, we propose a numerically stable algorithm for reconstructing the data vector given the nonlinear features, and analyze its sample complexity. Our algorithm can be extended to other types of structured inverse problems, such as demixing a pair of sparse (but incoherent) vectors. We support the efficacy of our approach via numerical experiments.