Rational, Replacement, and Local Invariants of a Group Action

The paper presents a new algorithmic construction of a finite generating set of rational invariants for the rational action of an algebraic group on the affine space. The construction provides an algebraic counterpart of the moving frame method in differential geometry. The generating set of rational invariants appears as the coefficients of a Groebner basis, reduction with respect to which allows to express a rational invariant in terms of the generators. The replacement invariants, introduced in the paper, are tuples of algebraic functions of the rational invariants. Any invariant, whether rational, algebraic or local, can be can be rewritten terms of replacement invariants by a simple substitution.Comment: 37 page

How to find real-world applications for compressive sensing

The potential of compressive sensing (CS) has spurred great interest in the research community and is a fast growing area of research. However, research translating CS theory into practical hardware and demonstrating clear and significant benefits with this hardware over current, conventional imaging techniques has been limited. This article helps researchers to find those niche applications where the CS approach provides substantial gain over conventional approaches by articulating lessons learned in finding one such application; sea skimming missile detection. As a proof of concept, it is demonstrated that a simplified CS missile detection architecture and algorithm provides comparable results to the conventional imaging approach but using a smaller FPA. The primary message is that all of the excitement surrounding CS is necessary and appropriate for encouraging our creativity but we all must also take off our "rose colored glasses" and critically judge our ideas, methods and results relative to conventional imaging approaches.Comment: 10 page

Algebraic List-decoding of Subspace Codes

Subspace codes were introduced in order to correct errors and erasures for randomized network coding, in the case where network topology is unknown (the noncoherent case). Subspace codes are indeed collections of subspaces of a certain vector space over a finite field. The Koetter-Kschischang construction of subspace codes are similar to Reed-Solomon codes in that codewords are obtained by evaluating certain (linearized) polynomials. In this paper, we consider the problem of list-decoding the Koetter-Kschischang subspace codes. In a sense, we are able to achieve for these codes what Sudan was able to achieve for Reed-Solomon codes. In order to do so, we have to modify and generalize the original Koetter-Kschischang construction in many important respects. The end result is this: for any integer $L$, our list-$L$ decoder guarantees successful recovery of the message subspace provided that the normalized dimension of the error is at most $L - \frac{L(L+1)}{2}R$ where $R$ is the normalized packet rate. Just as in the case of Sudan's list-decoding algorithm, this exceeds the previously best known error-correction radius $1-R$, demonstrated by Koetter and Kschischang, for low rates $R$

Gait recognition with shifted energy image and structural feature extraction

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2012 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.In this paper, we present a novel and efficient gait recognition system. The proposed system uses two novel gait representations, i.e., the shifted energy image and the gait structural profile, which have increased robustness to some classes of structural variations. Furthermore, we introduce a novel method for the simulation of walking conditions and the generation of artificial subjects that are used for the application of linear discriminant analysis. In the decision stage, the two representations are fused. Thorough experimental evaluation, conducted using one traditional and two new databases, demonstrates the advantages of the proposed system in comparison with current state-of-the-art systems

Nonlinear Inversion from Partial EIT Data: Computational Experiments

Electrical impedance tomography (EIT) is a non-invasive imaging method in which an unknown physical body is probed with electric currents applied on the boundary, and the internal conductivity distribution is recovered from the measured boundary voltage data. The reconstruction task is a nonlinear and ill-posed inverse problem, whose solution calls for special regularized algorithms, such as D-bar methods which are based on complex geometrical optics solutions (CGOs). In many applications of EIT, such as monitoring the heart and lungs of unconscious intensive care patients or locating the focus of an epileptic seizure, data acquisition on the entire boundary of the body is impractical, restricting the boundary area available for EIT measurements. An extension of the D-bar method to the case when data is collected only on a subset of the boundary is studied by computational simulation. The approach is based on solving a boundary integral equation for the traces of the CGOs using localized basis functions (Haar wavelets). The numerical evidence suggests that the D-bar method can be applied to partial-boundary data in dimension two and that the traces of the partial data CGOs approximate the full data CGO solutions on the available portion of the boundary, for the necessary small $k$ frequencies.Comment: 24 pages, 12 figure