Related papers: Truly Sub-Nyquist Generalized Eigenvalue Method wi…
We introduce a simple, general, and convergent scheme to compute generalized eigenfunctions of self-adjoint operators with continuous spectra on rigged Hilbert spaces. Our approach does not require prior knowledge about the eigenfunctions,…
Cognitive Radio (CR) networks presents a paradigm shift aiming to alleviate the spectrum scarcity problem exasperated by the increasing demand on this limited resource. It promotes dynamic spectrum access, cooperation among heterogeneous…
Fast-sampled models are essential for control design, e.g., to address intersample behavior. The aim of this paper is to develop a non-parametric identification technique for fast-sampled models of systems that have relevant dynamics and…
Compressed sensing is a technique to sample compressible signals below the Nyquist rate, whilst still allowing near optimal reconstruction of the signal. In this paper we present a theoretical analysis of the iterative hard thresholding…
Compressive sensing is a methodology for the reconstruction of sparse or compressible signals using far fewer samples than required by the Nyquist criterion. However, many of the results in compressive sensing concern random sampling…
Reconstructing an infinite-dimensional signal from a finite set of measurements is a fundamental problem in approximation theory and signal processing. While the generalized sampling (GS) framework provides a robust methodology for…
In this paper, we study a generalized finite element method for solving second-order elliptic partial differential equations with rough coefficients. The method uses local approximation spaces computed by solving eigenvalue problems on…
Wideband spectrum sensing (WSS) is an essential technology for cognitive radio. However, the sampling rate is still a bottleneck of WSS. Several sub-Nyquist sensing methods have been proposed. These technologies deteriorate in the low…
In the past few years, new approaches to radar signal processing have been introduced which allow the radar to perform signal detection and parameter estimation from much fewer measurements than that required by Nyquist sampling. These…
Reconstructing continuous signals from a small number of discrete samples is a fundamental problem across science and engineering. In practice, we are often interested in signals with 'simple' Fourier structure, such as bandlimited,…
Computing eigenvalues of very large matrices is a critical task in many machine learning applications, including the evaluation of log-determinants, the trace of matrix functions, and other important metrics. As datasets continue to grow in…
We consider the problem of how to compute eigenvalues of a self-adjoint operator when a direct application of the Galerkin (finite-section) method is unreliable. The last two decades have seen the development of the so-called quadratic…
The purpose of this paper is to report on recent approaches to reconstruction problems based on analog, or in other words, infinite-dimensional, image and signal models. We describe three main contributions to this problem. First, linear…
Spectral dimensionality reduction methods enable linear separations of complex data with high-dimensional features in a reduced space. However, these methods do not always give the desired results due to irregularities or uncertainties of…
We present a novel technique to overcome the limitations of the applicability of Principal Component Analysis to typical real-life data sets, especially astronomical spectra. Our new approach addresses the issues of outliers, missing…
The average spectrum method is a promising approach for the analytic continuation of imaginary time or frequency data to the real axis. It determines the analytic continuation of noisy data from a functional average over all admissible…
To obtain the best resolution for any measurement there is an ever-present challenge to achieve maximal differentiation between signal and noise over as fine of sampling dimensions as possible. In diffraction science these issues are…
Efficient estimation of wideband spectrum is of great importance for applications such as cognitive radio. Recently, sub-Nyquist sampling schemes based on compressed sensing have been proposed to greatly reduce the sampling rate. However,…
This work deals with approximate solution of generalized eigenvalue problem with coefficient matrix that is an affine function of d-parameters. The coefficient matrix is assumed to be symmetric positive definite and spectrally equivalent to…
We describe an approach based on compressive-sampling which allows for a considerable reduction in the acquisition time in Fourier-transform spectroscopy. In this approach, an N-point Fourier spectrum is resolved from much less than N…