RUI: Development of Nonorthogonal Fusion Frames and Reflective Sensing with Applications

San Francisco State University, San Francisco CA

Investigators

Abstract

Li DMS-1010058 The investigator develops a new (non-orthogonal) fusion frame, a notion of reflective sensing, and their applications. They are derived from the need for sparse fusion frame operators for efficient data fusion applications in general distributed systems. Theme 1 of the project defines a new non-orthogonal fusion frame. Preliminary studies show that the matrix representation of the new fusion frame operator can be diagonal over the same example where the existing fusion frame operator is completely sparse-less. Because the fusion operation ultimately involves the inverse of the fusion frame operator, and because subspace transformations are generally unavailable in practical data fusion applications, such a new fusion frame with sparse or diagonal fusion operator becomes crucial. Theme 2 studies a notion of multi-fusion frames based on multiple non-orthogonal projections onto one subspace. Nearly surprisingly, the new multi-fusion frame operator defined on one proper subspace can be easily positive and invertible. A number of theoretical issues are to be understood. Rooted in studies of themes 1 and 2, theme 3 outlines a notion of reflective sensing and multiple reflective sensing. Their theory and applications in side-measured tomography and multi-path wireless signal receiving are examined. It is relevant to point out that the implementation of non-orthogonal projection operators is naturally achievable, based on earlier work by the investigator on pseudoframes for subspaces. The project relates to signal processing applications. Signal processing generally refers to making the signal easy to handle or of better quality. It is everywhere seen in our modern society. In this project, the principal novelties introduced to signal processing are the new notion of non-orthogonal fusion frames and ideas of performing data fusion from, e.g., wireless signals received from multiple paths. Fusion frame is a notion developed specifically for various data fusion applications. Data fusion means combining data measured by different devices or by different means in order to obtain refined data. The advantage of non-orthogonal fusion frames lies in the fact that they greatly improve efficiency of the data fusion procedure in practical sensor networks, particularly when the amount of data is large. The project aims to develop effective methods of combining data detected in an array of sensors where information overlay (among sensors) is abundant and unpredictable. With extremely complicated information overlaps, exact and efficient data combination is made possible by non-orthogonal fusion frames. In particular, the project explores image fusion to provide a combined image of much greater precision or resolution without ad-hoc procedures present in conventional techniques. Data fusion problems arise in many applications, ranging from commercial imaging to geographic survey, mapping, wireless communication, multi-sensor/camera surveillance systems, and a great number of sensor network applications.