Related papers: Sensing with Optimal Matrices
We derive, similar to Lau and Riha, a matrix formulation of a general best approximation theorem of Singer for the special case of spectral approximations of a given matrix from a given subspace. Using our matrix formulation we describe the…
In this work, we address the exact D-optimal experimental design problem by proposing an efficient algorithm that rapidly identifies the support of its continuous relaxation. Our method leverages a column generation framework to solve such…
The subspace method is one of the mainstream system identification method of linear systems, and its basic idea is to estimate the system parameter matrices by projecting them into a subspace related to input and output. However, most of…
The increasing recognition of the association between adverse human health conditions and many environmental substances as well as processes has led to the need to monitor them. An important problem that arises in environmental statistics…
We study the low rank approximation problem of any given matrix $A$ over $\mathbb{R}^{n\times m}$ and $\mathbb{C}^{n\times m}$ in entry-wise $\ell_p$ loss, that is, finding a rank-$k$ matrix $X$ such that $\|A-X\|_p$ is minimized. Unlike…
Much of the work in the literature on optimal discrimination designs assumes that the models of interest are fully specified, apart from unknown parameters in some models. Recent work allows errors in the models to be non-normally…
We study the problem of selecting most informative subset of a large observation set to enable accurate estimation of unknown parameters. This problem arises in a variety of settings in machine learning and signal processing including…
Compressed sensing is a promising technique that attempts to faithfully recover sparse signal with as few linear and nonadaptive measurements as possible. Its performance is largely determined by the characteristic of sensing matrix.…
We present a framework which incorporates three aspects of the estimation problem, namely, sparse sensor configuration, optimal precision, and robustness in the presence of model uncertainty. The problem is formulated in the…
In this paper, we investigate the joint optimal sensing and distributed Medium Access Control (MAC) protocol design problem for cognitive radio (CR) networks. We consider both scenarios with single and multiple channels. For each scenario,…
This paper introduces a framework to study discrete optimization problems which are parametric in the following sense: their constraint matrices correspond to matrices over the ring $\mathbb{Z}[x]$ of polynomials in one variable. We…
We investigate two new optimization problems -- minimizing a submodular function subject to a submodular lower bound constraint (submodular cover) and maximizing a submodular function subject to a submodular upper bound constraint…
Among the major difficulties that one may encounter when estimating parameters in a nonlinear regression model are the nonuniqueness of the estimator, its instability with respect to small perturbations of the observations and the presence…
In this paper we compute families of reduced order models that match a prescribed set of moments of a highly dimensional linear time-invariant system. First, we fully parametrize the models in the interpolation points and in the free…
Maximum distance separable convolutional codes are the codes that present best performance in error correction among all convolutional codes with certain rate and degree. In this paper, we show that taking the constant matrix coefficients…
We study the problem of optimizing nonlinear objective functions over matroids presented by oracles or explicitly. Such functions can be interpreted as the balancing of multi-criteria optimization. We provide a combinatorial polynomial time…
The problem of designing bit-to-pattern mappings and power allocation schemes for orthogonal frequency-division multiplexing (OFDM) systems that employ subcarrier index modulation (IM) is considered. We assume the binary source conveys a…
We call a matrix completely mixable if the entries in its columns can be permuted so that all row sums are equal. If it is not completely mixable, we want to determine the smallest maximal and largest minimal row sum attainable. These…
We study the problem of solving a linear sensing system when the observations are unlabeled. Specifically we seek a solution to a linear system of equations y = Ax when the order of the observations in the vector y is unknown. Focusing on…
The condition number of solutions to full rank linear least-squares problem are shown to be given by an optimization problem that involves nuclear norms of rank 2 matrices. The condition number is with respect to the least-squares…