An inverse factorization algorithm for linear prediction

AbstractA new inverse factorization technique is presented for solving linear prediction problems arising in signal processing. The algorithm is similar to a scheme of Qiao in that is uses the rectangular Toeplitz structure of the data to recursively compute the prediction error and to solve the problem when the optimum filter order has been found. The novelty of the scheme presented here is the use of an inverse factorization scheme due to Pan and Plemmons for solving the linear prediction problem with low computational complexity and without the need for solving triangular systems. We also provide a linear systolic array for solving these problems

Computing finite semigroups

Using a variant of Schreier's Theorem, and the theory of Green's relations, we show how to reduce the computation of an arbitrary subsemigroup of a finite regular semigroup to that of certain associated subgroups. Examples of semigroups to which these results apply include many important classes: transformation semigroups, partial permutation semigroups and inverse semigroups, partition monoids, matrix semigroups, and subsemigroups of finite regular Rees matrix and 0-matrix semigroups over groups. For any subsemigroup of such a semigroup, it is possible to, among other things, efficiently compute its size and Green's relations, test membership, factorize elements over the generators, find the semigroup generated by the given subsemigroup and any collection of additional elements, calculate the partial order of the D-classes, test regularity, and determine the idempotents. This is achieved by representing the given subsemigroup without exhaustively enumerating its elements. It is also possible to compute the Green's classes of an element of such a subsemigroup without determining the global structure of the semigroup.PreprintPostprintPeer reviewe

Satellite-matrix-switched, time-division-multiple-access network simulator

A versatile experimental Ka-band network simulator has been implemented at the NASA Lewis Research Center to demonstrate and evaluate a satellite-matrix-switched, time-division-multiple-access (SMS-TDMA) network and to evaluate future digital ground terminals and radiofrequency (RF) components. The simulator was implemented by using proof-of-concept RF components developed under NASA contracts and digital ground terminal and link simulation hardware developed at Lewis. This simulator provides many unique capabilities such as satellite range delay and variation simulation and rain fade simulation. All network parameters (e.g., signal-to-noise ratio, satellite range variation rate, burst density, and rain fade) are controlled and monitored by a central computer. The simulator is presently configured as a three-ground-terminal SMS-TDMA network

Synthetic boundary conditions for image deblurring

AbstractIn this paper we introduce a new boundary condition that can be used when reconstructing an image from observed blurred and noisy data. Our approach uses information from the observed image to enforce boundary conditions that continue image features such as edges and texture across the boundary. Because of its similarity to methods used in texture synthesis, we call our approach synthetic boundary conditions. We provide an efficient algorithm for implementing the new boundary condition, and provide a linear algebraic framework for the approach that puts it in the context of more classical and well known image boundary conditions, including zero, periodic, reflective, and anti-reflective. Extensive numerical experiments show that our new synthetic boundary conditions provide a more accurate approximation of the true image scene outside the image boundary, and thus allow for better reconstructions of the unknown, true image scene

LSEMINK: A Modified Newton-Krylov Method for Log-Sum-Exp Minimization

This paper introduces LSEMINK, an effective modified Newton-Krylov algorithm geared toward minimizing the log-sum-exp function for a linear model. Problems of this kind arise commonly, for example, in geometric programming and multinomial logistic regression. Although the log-sum-exp function is smooth and convex, standard line search Newton-type methods can become inefficient because the quadratic approximation of the objective function can be unbounded from below. To circumvent this, LSEMINK modifies the Hessian by adding a shift in the row space of the linear model. We show that the shift renders the quadratic approximation to be bounded from below and that the overall scheme converges to a global minimizer under mild assumptions. Our convergence proof also shows that all iterates are in the row space of the linear model, which can be attractive when the model parameters do not have an intuitive meaning, as is common in machine learning. Since LSEMINK uses a Krylov subspace method to compute the search direction, it only requires matrix-vector products with the linear model, which is critical for large-scale problems. Our numerical experiments on image classification and geometric programming illustrate that LSEMINK considerably reduces the time-to-solution and increases the scalability compared to geometric programming and natural gradient descent approaches. It has significantly faster initial convergence than standard Newton-Krylov methods, which is particularly attractive in applications like machine learning. In addition, LSEMINK is more robust to ill-conditioning arising from the nonsmoothness of the problem. We share our MATLAB implementation at https://github.com/KelvinKan/LSEMINK

Wide-Range Optical CMOS-Based Diagnostics

Colorimetric, chemiluminescence and refractive index based diagnostics are some of the most important sensing techniques in biomedical science and clinical medicine. Conventionally laboratories and medical clinics rely on bulky and dedicated equipment for each diagnostic technique independently. In this paper, we present CMOS sensor based solutions, comprising a single photon avalanche detector array and photodiode array. The CMOS platform offers low cost integration and wide range of light-based diagnostic techniques, leading to development of point-of-care devices