Real time detection of harmonic structure: A case for topological signal analysis

The goal of this study is to find evidence of cyclicity or periodicity in data with low computational complexity and high accuracy. Using delay embeddings, we transform the timedomain signal into a point cloud, whose topology reflects the periodic behavior of the signal. Persistent homology is employed to determine the underlying manifold of the point cloud, and the Euler characteristic provides for a fast computation of topology of the resulting manifold. We apply the introduced approach to breathing sound signals for wheeze detection. Our experiments substantiate the capabilities of the proposed method.

[1]  Y.-L. Chen,et al.  Detecting Recompression of JPEG Images via Periodicity Analysis of Compression Artifacts for Tampering Detection , 2011, IEEE Transactions on Information Forensics and Security.

[2]  Herbert Edelsbrunner,et al.  Computational Topology - an Introduction , 2009 .

[3]  Robert L. Wilkins,et al.  Fundamentals of lung and heart sounds , 2015 .

[4]  Hong Yan,et al.  Autoregressive and Iterative Hidden Markov Models for Periodicity Detection and Solenoid Structure Recognition in Protein Sequences , 2013, IEEE Journal of Biomedical and Health Informatics.

[5]  Springhouse.  Comprar Auscultation Skills: Breath and Heart Sounds 4/e | Springhouse | 9781605474540 | Lippincott Williams & Wilkins , 2009 .

[6]  Trevor Gibbs.  Auscultation Skills: Breath and Heart Sounds , 2000, BMJ : British Medical Journal.

[7]  Sridhar Krishnan,et al.  Adventitious Sounds Identification and Extraction Using Temporal–Spectral Dominance-Based Features , 2011, IEEE Transactions on Biomedical Engineering.

[8]  Jamal Tuqan,et al.  A DSP Approach for Finding the Codon Bias in DNA Sequences , 2008, IEEE Journal of Selected Topics in Signal Processing.

[9]  Ariel Salomon,et al.  Use of temporal information: detection of periodicity, aperiodicity, and pitch in speech , 2005, IEEE Transactions on Speech and Audio Processing.

[10]  Grantham Pang,et al.  Regularity Analysis for Patterned Texture Inspection , 2009, IEEE Transactions on Automation Science and Engineering.

[11]  Vin de Silva,et al.  On the Local Behavior of Spaces of Natural Images , 2007, International Journal of Computer Vision.

[12]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[13]  Hamid Krim,et al.  Persistent Homology of Delay Embeddings and its Application to Wheeze Detection , 2014, IEEE Signal Processing Letters.

[14]  Leontios J. Hadjileontiadis,et al.  Analysis of Wheezes Using Wavelet Higher Order Spectral Features , 2010, IEEE Transactions on Biomedical Engineering.

[15]  Leontios J. Hadjileontiadis,et al.  Wheeze detection based on time-frequency analysis of breath sounds , 2007, Comput. Biol. Medicine.

[16]  Herbert Edelsbrunner,et al.  Topological Persistence and Simplification , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[17]  Korbinian Strimmer,et al.  Identifying periodically expressed transcripts in microarray time series data , 2008, Bioinform..

[18]  Antoni Homs-Corbera,et al.  Time-frequency detection and analysis of wheezes during forced exhalation , 2004, IEEE Transactions on Biomedical Engineering.

[19]  Gunnar E. Carlsson,et al.  Topological estimation using witness complexes , 2004, PBG.