Stochastic Lyapunov analysis for consensus algorithms with noisy measurements

Abstract — This paper studies the coordination and consensus of networked agents in an uncertain environment. We consider a group of agents on an undirected graph with fixed topology, but differing from most existing work, each agent has only noisy measurements of its neighbors ’ states. Traditional consensus algorithms in general cannot deal with such a scenario. For consensus seeking, we introduce stochastic approximation type algorithms with a decreasing step size. We present a stochastic Lyaponuv analysis based upon the total mean potential associated with the agents. Subsequently, the so-called direction of invariance is introduced, which combined with the decay property of the stochastic Lyapunov function leads to mean square convergence of the consensus algorithm. I

Stochastic consensus over noisy networks with Markovian and arbitrary switches

This paper considers stochastic consensus problems over lossy wireless networks. We first propose a measurement model with a random link gain, additive noise, and Markovian lossy signal reception, which captures uncertain operational conditions of practical networks. For consensus seeking, we apply stochastic approximation and derive a Markovian mode dependent recursive algorithm. Mean square and almost sure (i.e., probability one) convergence analysis is developed via a state space decomposition approach when the coefficient matrix in the algorithm satisfies a zero row and column sum condition.Subsequently,we consider a model with arbitrary random switching and a common stochastic Lyapunov function technique is used to prove convergence. Finally,our method is applied to models with heterogeneous quantizers and packet losses, and convergence results are proved

Sparsity driven ultrasound imaging

An image formation framework for ultrasound imaging from synthetic transducer arrays based on sparsity-driven regularization functionals using single-frequency Fourier domain data is proposed. The framework involves the use of a physics-based forward model of the ultrasound observation process, the formulation of image formation as the solution of an associated optimization problem, and the solution of that problem through efficient numerical algorithms. The sparsity-driven, model-based approach estimates a complex-valued reflectivity field and preserves physical features in the scene while suppressing spurious artifacts. It also provides robust reconstructions in the case of sparse and reduced observation apertures. The effectiveness of the proposed imaging strategy is demonstrated using experimental data

Optical Coherence Tomography Findings in Idiopathic Macular Holes

Purpose. To describe the characteristics of idiopathic macular holes (MH) on optical coherence tomography (OCT) and correlate OCT with clinical assessment. Design. Cross-sectional chart review and OCT assessment. Participants. Sixty-seven eyes with a clinically diagnosed idiopathic MH with available OCT data. Methods. A retrospective chart review and OCT assessment. Results. Based on OCT grading, 40 eyes had a full-thickness macular hole (FTMH) and 21 eyes had a lamellar macular hole (LMH). Clinical exam and OCT assessment agreed in 53 (87%) eyes when assessing the extent of MH. Six eyes (14.6%) in the FTMH group, and 3 eyes in the LMH group (14.3%) had persistent vitreomacular traction. Thirty-seven eyes (92.5%) in the FTMH group and 11 eyes (52.4%) in the LMH group had associated intraretinal cysts. Two eyes (5.0%) in the FTMH group and zero eyes in the LMH group had subretinal fluid. Intraretinal cysts were found to be more frequently associated with FTMH than with LMH (P < 0.001). Conclusion. This paper described OCT findings in a group of patients with clinically diagnosed MH. A high level of correlation between clinical assessment and OCT findings of LMH and FTMH was observed, and intraretinal cysts were often present in FTMH