Eigenvalue-based time delay estimation of repetitive biomedical signals

Abstract

The time delay estimation problem associated with an ensemble of misaligned, repetitive signals is revisited. Each observed signal is assumed to be composed of an unknown, deterministic signal corrupted by Gaussian, white noise. This paper shows that maximum likelihood (ML) time delay estimation can be viewed as the maximiza

Unipolar Electrogram Eigenvalue Distribution Analysis for the Identification of Atrial Fibrosis

“…f . Four u-EGMs scenarios for non-aligned (NA) and aligned (A) u-EGMs at non-fibrotic (NF) and fibrotic (F) areas are considered and their approximate theoretical eigenvalues are derived according to the procedure presented in [10]. Table 1 shows the eigenvalues λ k and EIGDR for the four scenarios.…”

Machine Learning Approach and Waves Synchronization Improvement for the Localization of Atrial Flutter Circuit Based on the 12-Leads ECG

“…, M (1) where s(n) is an unknown, deterministic signal, with energy E s and energy of its first derivative E s , θ i is random, zero mean, integer valued time delay with variance σ 2 θ , and v i (n) is a zero-mean, white noise with variance σ 2 v , uncorrelated with θ i . It is shown in [5] that the estimation of the θ i 's can be carried out by maximizing an eigenvalue-based criteria. The eigenvalues λ i are then computed from the intra-signal correlation matrix.…”

“…This alignment, also addressed as a time delay estimation problem, has been considered in [5] as a problem of eigenvalues maximization in a context of one-dimensional multiple observations. In the context of 12-leads ECG system, the multiple delayed F-waves should be considered as a 12-dimensional alignment.…”

“…In the context of 12-leads ECG system, the multiple delayed F-waves should be considered as a 12-dimensional alignment. Then, results from [5] is easily extended in this work to the N-dimensional space in order to improve the accuracy of the delays estimation. The subsequent synchronous averaging provides reduced noise F-waves where features captured from visual inspection are in that case computerized.…”

Time delay estimation using wavelet denoising maximum likelihood method for underwater reverberant environment

“…For many decades, time delay estimation (TDE) has been of substantial research interest in many fields such as radar [1, 2], sonar [3–5], seismology, geophysics, bio‐medicine [6–8], and localising and tracking sources. In general, electromagnetic waves are used in source identification, localisation, and tracking.…”