Distributed interpolatory algorithms for set membership estimation

This work addresses the distributed estimation problem in a set membership framework. The agents of a network collect measurements which are affected by bounded errors, thus implying that the unknown parameters to be estimated belong to a suitable feasible set. Two distributed algorithms are considered, based on projections of the estimate of each agent onto its local feasible set. The main contribution of the paper is to show that such algorithms are asymptotic interpolatory estimators, i.e. they converge to an element of the global feasible set, under the assumption that the feasible set associated to each measurement is convex. The proposed techniques are demonstrated on a distributed linear regression estimation problem

On the Convergence of Alternating Direction Lagrangian Methods for Nonconvex Structured Optimization Problems

Nonconvex and structured optimization problems arise in many engineering applications that demand scalable and distributed solution methods. The study of the convergence properties of these methods is in general difficult due to the nonconvexity of the problem. In this paper, two distributed solution methods that combine the fast convergence properties of augmented Lagrangian-based methods with the separability properties of alternating optimization are investigated. The first method is adapted from the classic quadratic penalty function method and is called the Alternating Direction Penalty Method (ADPM). Unlike the original quadratic penalty function method, in which single-step optimizations are adopted, ADPM uses an alternating optimization, which in turn makes it scalable. The second method is the well-known Alternating Direction Method of Multipliers (ADMM). It is shown that ADPM for nonconvex problems asymptotically converges to a primal feasible point under mild conditions and an additional condition ensuring that it asymptotically reaches the standard first order necessary conditions for local optimality are introduced. In the case of the ADMM, novel sufficient conditions under which the algorithm asymptotically reaches the standard first order necessary conditions are established. Based on this, complete convergence of ADMM for a class of low dimensional problems are characterized. Finally, the results are illustrated by applying ADPM and ADMM to a nonconvex localization problem in wireless sensor networks.Comment: 13 pages, 6 figure

MScMS-II: an innovative IR-based indoor coordinate measuring system for large-scale metrology applications

According to the current great interest concerning large-scale metrology applications in many different fields of manufacturing industry, technologies and techniques for dimensional measurement have recently shown a substantial improvement. Ease-of-use, logistic and economic issues, as well as metrological performance are assuming a more and more important role among system requirements. This paper describes the architecture and the working principles of a novel infrared (IR) optical-based system, designed to perform low-cost and easy indoor coordinate measurements of large-size objects. The system consists of a distributed network-based layout, whose modularity allows fitting differently sized and shaped working volumes by adequately increasing the number of sensing units. Differently from existing spatially distributed metrological instruments, the remote sensor devices are intended to provide embedded data elaboration capabilities, in order to share the overall computational load. The overall system functionalities, including distributed layout configuration, network self-calibration, 3D point localization, and measurement data elaboration, are discussed. A preliminary metrological characterization of system performance, based on experimental testing, is also presente

Decentralized MPC based Obstacle Avoidance for Multi-Robot Target Tracking Scenarios

In this work, we consider the problem of decentralized multi-robot target tracking and obstacle avoidance in dynamic environments. Each robot executes a local motion planning algorithm which is based on model predictive control (MPC). The planner is designed as a quadratic program, subject to constraints on robot dynamics and obstacle avoidance. Repulsive potential field functions are employed to avoid obstacles. The novelty of our approach lies in embedding these non-linear potential field functions as constraints within a convex optimization framework. Our method convexifies non-convex constraints and dependencies, by replacing them as pre-computed external input forces in robot dynamics. The proposed algorithm additionally incorporates different methods to avoid field local minima problems associated with using potential field functions in planning. The motion planner does not enforce predefined trajectories or any formation geometry on the robots and is a comprehensive solution for cooperative obstacle avoidance in the context of multi-robot target tracking. We perform simulation studies in different environmental scenarios to showcase the convergence and efficacy of the proposed algorithm. Video of simulation studies: \url{https://youtu.be/umkdm82Tt0M

The Integration of Positron Emission Tomography With Magnetic Resonance Imaging

A number of laboratories and companies are currently exploring the development of integrated imaging systems for magnetic resonance imaging (MRI) and positron emission tomography (PET). Scanners for both preclinical and human research applications are being pursued. In contrast to the widely distributed and now quite mature PET/computed tomography technology, most PET/MRI designs allow for simultaneous rather than sequential acquisition of PET and MRI data. While this offers the possibility of novel imaging strategies, it also creates considerable challenges for acquiring artifact-free images from both modalities. This paper discusses the motivation for developing combined PET/MRI technology, outlines the obstacles in realizing such an integrated instrument, and presents recent progress in the development of both the instrumentation and of novel imaging agents for combined PET/MRI studies. The performance of the first-generation PET/MRI systems is described. Finally, a range of possible biomedical applications for PET/MRI are outlined

Gen-2 Hand-Held Optical Imager towards Cancer Imaging: Reflectance and Transillumination Phantom Studies

Hand-held near-infrared (NIR) optical imagers are developed by various researchers towards non-invasive clinical breast imaging. Unlike these existing imagers that can perform only reflectance imaging, a generation-2 (Gen-2) hand-held optical imager has been recently developed to perform both reflectance and transillumination imaging. The unique forked design of the hand-held probe head(s) allows for reflectance imaging (as in ultrasound) and transillumination or compressed imaging (as in X-ray mammography). Phantom studies were performed to demonstrate two-dimensional (2D) target detection via reflectance and transillumination imaging at various target depths (1–5 cm deep) and using simultaneous multiple point illumination approach. It was observed that 0.45 cc targets were detected up to 5 cm deep during transillumination, but limited to 2.5 cm deep during reflectance imaging. Additionally, implementing appropriate data post-processing techniques along with a polynomial fitting approach, to plot 2D surface contours of the detected signal, yields distinct target detectability and localization. The ability of the gen-2 imager to perform both reflectance and transillumination imaging allows its direct comparison to ultrasound and X-ray mammography results, respectively, in future clinical breast imaging studies