1 citations · 1 across the 4 of their papers we have counts for
6 papers
ESPRIT versus ESPIRA for reconstruction of short cosine sums and its application
Nadiia Derevianko, Gerlind Plonka, Raha Razavi
In this paper we introduce two new algorithms for stable approximation with and recovery of short cosine sums. The used signal model contains cosine terms with arbitrary real posit…
Exact Reconstruction of Extended Exponential Sums using Rational Approximation of their Fourier Coefficients
Nadiia Derevianko, Gerlind Plonka
In this paper we derive a new recovery procedure for the reconstruction of extended exponential sums of the form $y(t) = \sum_{j=1}^{M} \left( \sum_{m=0}^{n_j} \, γ_{j,m} \, t^{m}…
Exact Reconstruction of Sparse Non-Harmonic Signals from Fourier Coefficients
Markus Petz, Gerlind Plonka, Nadiia Derevianko
In this paper, we derive a new reconstruction method for real non-harmonic Fourier sums, i.e., real signals which can be represented as sparse exponential sums of the form $f(t) =…
Optimal Rank-1 Hankel Approximation of Matrices: Frobenius Norm, Spectral Norm, and Cadzow's Algorithm
Hanna Knirsch, Markus Petz, Gerlind Plonka
We characterize optimal rank-1 matrix approximations with Hankel or Toeplitz structure with regard to two different norms, the Frobenius norm and the spectral norm, in a new way. M…
Modifications of Prony's Method for the Recovery and Sparse Approximation of Generalized Exponential Sums
Ingeborg Keller, Gerlind Plonka
In this survey we describe some modifications of Prony's method. In particular, we consider the recovery of general expansions into eigenfunctions of linear differential operators…
A Tree-based Dictionary Learning Framework
Renato Budinich, Gerlind Plonka
We propose a new outline for adaptive dictionary learning methods for sparse encoding based on a hierarchical clustering of the training data. Through recursive application of a cl…