Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Applications of Singular Entropy to Signals and Singular Smoothness to Images

Oscar Romero, Néstor Thome

TL;DR

The paper develops a novel algebraic–statistical framework combining SVD and GSVD with metrics such as Energy Gap Variation, Singular Energy, Singular Entropy, and Singular Smoothness to tackle two problems: (i) robust separation of maternal and fetal ECG signals, and (ii) detection of natural anomalies in landscape images. Energy Gap Variation and its generalized form guide thresholding for component separation, while Singular Smoothness provides a brightness-independent measure of information density for images. Numerical experiments on ECG data and landscape imagery demonstrate improved separation and efficient anomaly highlighting, with GSVD offering enhanced discriminative power at higher computational cost. The approach offers a principled, extensible toolbox for signal/ image analysis in noisy, real-world datasets.

Abstract

This paper explores signal and image analysis by using the Singular Value Decomposition (SVD) and its extension, the Generalized Singular Value Decomposition (GSVD). A key strength of SVD lies in its ability to separate information into orthogonal subspaces. While SVD is a well-established tool in ECG analysis, particularly for source separation, this work proposes a refined method for selecting a threshold to distinguish between maternal and fetal components more effectively. In the first part of the paper, the focus is onmedical signal analysis,where the concepts of Energy Gap Variation (EGV) and Singular Energy are introduced to isolate fetal and maternal ECG signals, improving the known ones. Furthermore, the approach is significantly enhanced by the application of GSVD, which provides additional discriminative power for more accurate signal separation. The second part introduces a novel technique called Singular Smoothness, developed for image analysis. This method incorporates Singular Entropy and the Frobenius normto evaluate information density, and is applied to the detection of natural anomalies such asmountain fractures and burned forest regions. Numerical experiments are presented to demonstrate the effectiveness of the proposed approaches.

Applications of Singular Entropy to Signals and Singular Smoothness to Images

TL;DR

The paper develops a novel algebraic–statistical framework combining SVD and GSVD with metrics such as Energy Gap Variation, Singular Energy, Singular Entropy, and Singular Smoothness to tackle two problems: (i) robust separation of maternal and fetal ECG signals, and (ii) detection of natural anomalies in landscape images. Energy Gap Variation and its generalized form guide thresholding for component separation, while Singular Smoothness provides a brightness-independent measure of information density for images. Numerical experiments on ECG data and landscape imagery demonstrate improved separation and efficient anomaly highlighting, with GSVD offering enhanced discriminative power at higher computational cost. The approach offers a principled, extensible toolbox for signal/ image analysis in noisy, real-world datasets.

Abstract

This paper explores signal and image analysis by using the Singular Value Decomposition (SVD) and its extension, the Generalized Singular Value Decomposition (GSVD). A key strength of SVD lies in its ability to separate information into orthogonal subspaces. While SVD is a well-established tool in ECG analysis, particularly for source separation, this work proposes a refined method for selecting a threshold to distinguish between maternal and fetal components more effectively. In the first part of the paper, the focus is onmedical signal analysis,where the concepts of Energy Gap Variation (EGV) and Singular Energy are introduced to isolate fetal and maternal ECG signals, improving the known ones. Furthermore, the approach is significantly enhanced by the application of GSVD, which provides additional discriminative power for more accurate signal separation. The second part introduces a novel technique called Singular Smoothness, developed for image analysis. This method incorporates Singular Entropy and the Frobenius normto evaluate information density, and is applied to the detection of natural anomalies such asmountain fractures and burned forest regions. Numerical experiments are presented to demonstrate the effectiveness of the proposed approaches.

Paper Structure

This paper contains 8 sections, 32 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. ECG's analysis from a cutoff point
  4. Landscape study
  5. Results of the numerical experiments
  6. ECG
  7. Landscape
  8. Conclusions

Figures (6)

  • Figure 1: Energy gap variation and ECG-MECG-FECG.
  • Figure 2: GSVD energy gap variation and ECG-MECG-FECG.
  • Figure 3: Cutoff point computation time: SVD and GSVD methods.
  • Figure 4: Forest and burn severity. (a) Original forest. (b) Burn severity map.
  • Figure 5: Forest and burn severity. (a) Original forest. (b) Burn severity map.
  • ...and 1 more figures