TSP Article

We consider the problem of stochastic optimization with nonlinear constraints, where the decision variable is not vector-valued but instead a function belonging to a reproducing Kernel Hilbert Space (RKHS). Currently, there exist solutions to only special cases of this problem.

The theoretical basis for conventional acquisition of bandlimited signals typically relies on uniform time sampling and assumes infinite-precision amplitude values. In this paper, we explore signal representation and recovery based on uniform amplitude sampling with assumed infinite precision timing information. 

Distributed estimation fusion is concerned with the combination of local estimates from multiple distributed sensors to produce a fused result. In this paper, we characterize local estimates as posterior probability densities, and assume that they all belong to a parametric family. Our starting point is to consider this family as a Riemannian manifold by introducing the Fisher information metric.

Linear regression models contaminated by Gaussian noise (inlier) and possibly unbounded sparse outliers are common in many signal processing applications. Sparse recovery inspired robust regression (SRIRR) techniques are shown to deliver high-quality estimation performance in such regression models. Unfortunately, most SRIRR techniques assume a priori knowledge of noise statistics like inlier noise variance or outlier statistics like number of outliers.

Recently, many sparse arrays have been proposed to increase the number of degrees of freedom for direction of arrival (DoA) estimation especially for circular signals. Though many practical signals are noncircular, still the properties of noncircularity are hardly exploited in the design of sparse linear arrays. A new array geometry for noncircular signals, which significantly increases the aperture of the virtual array, has been proposed in this paper. 

Various signal processing applications can be expressed as large-scale optimization problems with a composite objective structure, where the Lipschitz constant of the smooth part gradient is either not known, or its local values may only be a fraction of the global value. The smooth part may be strongly convex as well. The algorithms capable of addressing this problem class in its entirety are black-box accelerated first-order methods, related to either Nesterov's Fast Gradient Method or the Accelerated Multistep Gradient Scheme, which were developed and analyzed using the estimate sequence mathematical framework.