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Multi-resolution Analysis

Multi-resolution Analysis. TFDs, Wavelets Etc. PCG applications. Heart Sound Introduction. Recording PCG. S2 signal. Occurs because of blood flow and closure of Aortic and Pulmonary valves. Is composed of two sub signals A2 – created because of Aortic valve closure

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Multi-resolution Analysis

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  1. Multi-resolution Analysis TFDs, Wavelets Etc.PCG applications

  2. Heart Sound Introduction

  3. Recording PCG

  4. S2 signal • Occurs because of blood flow and closure of Aortic and Pulmonary valves. • Is composed of two sub signals • A2 – created because of Aortic valve closure • P2 - created because of Pulmonary valve closure • A2 is characterized with lower frequencies than P2 and is usually precedes it in time.

  5. FT – Fourier Transform • Fourier Transform returns the frequency components of the signal globaly. • For example: • S2 signalfiltered in[20,120]

  6. FT – Fourier Transform • The corresponding FT: • What does this give us? • No Temporal info!

  7. Short Time FT for changing signals • FT windowed: Window size 64 Window size 128 Window size 256

  8. Short Time FT for changing signals • Uncertainty Principle • Each window N samples. • N/2 coefficients signifying 0-fs/2 frequencies. • Space between coefficients

  9. Multi-Resolution Analysis Chirplet Transform Wavelet Transform Wigner-Ville Distribution

  10. Wavelet Transform - Intro • Basis functions are compact in time and frequency. • Basis function are created basic function called “Mother Wavelet”

  11. Wavelet Transform - Intro • Basis function are created from mother wavelet through scaling and shifting

  12. Wavelet Transform CTW Discrete

  13. Wavelet Transform – PCG applications • Obaidat M.S., J. Med. Eng. Tech., 1993Used wavelet transform for HS analysis:

  14. Wavelet Transform – PCG applications • Reed T.R et al. Proceeding Signal and Image Processing -2005Used Wavelet decomposition and reconstruction for PCA feature extraction and segmentation to Diastolic and systolic parts

  15. Wavelet Transform – PCG applications • Liang, H.   Hartimo, I.   Signal Process. & Comput. Technol. Lab., Helsinki Univ. of Technol., EspooUsed Wavelet Decomposition and Reconstruction of PCG as input to an ANN for study of murmurs. • There are several other works doing the same for detection of different HS conditions

  16. Wavelet Transform - Applications • Image Analysis: • Feature Extraction • Wavelet and Fractal connection – Self similarity

  17. S-Transform • CTW with mother wavelet: • Properties: • Not Orthogonal • Directly invertible into the Fourier Transform Spectrum

  18. S-Transform – PCG Application • G Livanos*, N Ranganatha, J Jiang, Computers in Cardiology 2000.Showed that S-Transform can perform best for the needs of a user who needs a simple and clear display of intensity, frequency and timing, in comparison to Morlet wavelet and STFT.

  19. Wigner-Ville Distribution • Mathematical definition: • Valuable: • because of preserving FT essence: • Is always pure real

  20. Wigner-Ville Distribution • Problematic: • Cross components unlimited

  21. Wigner-Ville Distribution – PCG Applications • Xu, Durand et al, IEEE transactions on biomedical engineering 2000, used WVD to extract A2 and P2 from S2 signals and used this to estimate A2-P2 interval

  22. Wigner-Ville Distribution – PCG Applications • Seedahamed S.M. et al, Biomedical Signal Processing and control (Feb 2006).Use WVD to estimate IF (instantaneous frequency).

  23. Instead of wavelet basis function that can be scaled and shifted Chirplet Transform uses basis functions that derive for chirps where the phase changes too. Chirplet Transform

  24. Chirplet Transform - Applications • O’Neill J.C. et al gave and algorithm to create sparse representation of signal using max likelihood estimation of chirplets

  25. Chirplet Transform - Applications

  26. My work • Currently trying to use TFDs and wavelet transform to extract interval time of A2-P2. • Currently working on using S-Transform for basis for a feature extraction algorithm

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