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Wavelet Based Subband Shrinkage Models and their Applications in Denoising of Biomedical Signals

Wavelet Based Subband Shrinkage Models and their Applications in Denoising of Biomedical Signals. By Dr. S. Poornachandra Dean IQAC SNS College of Engineering. Objective. Denoising of biomedical signals with better performance. Types of noises. The muscle artifacts Respirator muscles

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Wavelet Based Subband Shrinkage Models and their Applications in Denoising of Biomedical Signals

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  1. Wavelet Based Subband Shrinkage Models and their Applications in Denoising of Biomedical Signals By Dr. S. Poornachandra Dean IQAC SNS College of Engineering

  2. Objective • Denoising of biomedical signals with better performance S. Poornachandra (2001399722)

  3. Types of noises • The muscle artifacts • Respirator muscles • Cardiac muscle • Moving artifacts • Electro-magnetic radiations • Power line frequency noise • Instrument noise • Interference of other physiological signals S. Poornachandra (2001399722)

  4. Statistical Estimations • Mean • Variance • Risk S. Poornachandra (2001399722)

  5. ECG Specification • The practical ECG was downloaded from the PhysioBank • Sampling rate is 360Hz • Resolution is 11 Bits/Samples • Bit rate is 3960 bps • Length of ECG data: 650000 • Length of ECG data considered: 5000 S. Poornachandra (2001399722)

  6. Other biosignals used. . . . • EEG • PCG • Pulse Waveform S. Poornachandra (2001399722)

  7. Parameters for Analysis • Signal to Noise Ratio (SNR) • = • Percentage Root Mean-Squared Difference(PRD) • = • SNR Improvements • = Input SNR – Output SNR • RMS Error • = RMS (Recovered Signal – Original Signal) • PSNR • = S. Poornachandra (2001399722)

  8. Time-domain • Advantages • Simple • Easy to implement • Lower computational complexity • Disadvantages • Slow convergence when the input is highly colored S. Poornachandra (2001399722)

  9. Need for Transform-domain • Advantages • Better convergence • Parallism • Disadvantages • Complexity increases as order of the filter increases • Exhibit slow convergence • High minimum mean square error • Remedy • Subbanding – reduced coefficients at each subband S. Poornachandra (2001399722)

  10. Advantages of Wavelet • Works on non-stationary data • Time-frequency aspect gives information about frequency composition of a signal at a particular time • Short signal pieces also have significance S. Poornachandra (2001399722)

  11. Wavelets Defined . . . . . • “The wavelet transform is a tool that cuts up data, functions or operators into different frequency components and then studies each component with a resolution matched to its scales” • Dr. Ingrid Daubechies, Lucent, Princeton U S. Poornachandra (2001399722)

  12. |H(j)| Length: 512 B: 0 ~  g[n] h[n]  /2 -/2 Length: 256 B: 0 ~ /2 Hz Length: 256 B: /2 ~  Hz a1 |G(j)| d1: Level 1 DWT Coeff. g[n] h[n] Length: 128 B: 0 ~  /4 Hz  Length: 128 B: /4 ~ /2 Hz -/2 /2 -  a2 d2: Level 2 DWT Coeff. g[n] h[n] 2 2 2 2 2 2 Length: 64 B: 0 ~ /8 Hz Length: 64 B: /8 ~ /4 Hz …a3…. Level 3 approximation Coefficients DWT – Demystified d3: Level 3 DWT Coeff. S. Poornachandra (2001399722)

  13. Shrinkage ? • A shrinkage method compares empirical wavelet coefficient with a threshold and is set to zero if its magnitude is less than the threshold value. S. Poornachandra (2001399722)

  14. Condition & Characteristics of Shrinkage • The magnitude of signal component must be larger than existing noise component • It does not introduce artifacts • The wavelet transform localizes the most important spatial and frequential features of a regular signal in a limited number of wavelet coefficients. • Observations suggest that small coefficients should be replace by zero, because they are dominated by noise and carry only a small amount of information. S. Poornachandra (2001399722)

  15. Pioneers … • Donoho and Johnstone (1994) – Soft Shrinkage • Coifman and Donoho (1995) – Cycle Spinning • Nason (1996) – Cross Validation Shrinkage • Bruce and Gao (1997) –Garrote Shrinkage S. Poornachandra (2001399722)

  16. Shrinkage functions S. Poornachandra (2001399722)

  17. Shrinkage Algorithm Apply DWT to the vector y and obtain the empirical wavelet coefficients cj,k at scale j, where j = 1, 2, . . , J. Estimated coefficients are obtained based on the threshold = [1, 2, . . . . j]T. Apply shrinkage to the empirical wavelet coefficients at each scale j. The estimate of the function can be obtained by taking inverse DWT. S. Poornachandra (2001399722)

  18. Threshold methods • The rigrsure uses for the soft shrinkage estimator, which is a shrinkage solution rule based on Stein’s Unbiased Risk Estimate (SURE). • The sqtwolog threshold uses a fixed form threshold yielding minimax performance multiplied by a small factor proportional to log(length(x)). • The heursure threshold is the hybridization of both rigrsure and sqtwolog threshold. • The minimax threshold uses a fixed threshold chosen to yield minimax performance for MSE against an ideal procedure. S. Poornachandra (2001399722)

  19. Median Absolute Deviation • Prof. Donoho proposed • Where, is the estimate of noise variance • Median Absolute Deviation • MAD(v)=[|v1-vmed|, … , |v1-vmed|]med S. Poornachandra (2001399722)

  20. Alpha-trim Filter • The alpha-trim filter is a special type of L-filter, • A particular choice of aj coefficient yields a alpha-trim filter • where T is the largest integer which is less than or equal to αM, 0 ≤ α ≤ 0.5. When α = zero, the α-trim filter becomes the running mean filter; When α = 0.5, the α-trim filter becomes the median filter. S. Poornachandra (2001399722)

  21. Threshold at each subband • The Threshold values at each subband for 20% noise level is given in tables • SNR (dB) • PRD (%) • ECG Signal S. Poornachandra (2001399722)

  22. Wavelet level analysis S. Poornachandra (2001399722)

  23. Wavelet level analysis S. Poornachandra (2001399722)

  24. d1 X shrinkage d2 X shrinkage d3 X shrinkage a3 Hard shrinkage Hybrid Model …. • Analysis Filter S. Poornachandra (2001399722)

  25. Basic shrinkage (ECG) S. Poornachandra (2001399722)

  26. Basic shrinkage (PCG) S. Poornachandra (2001399722)

  27. Analysis Filter Adaptive Filter Shrinkage Function Synthesis Filter BSWTAF-I (Scale-Domain Analysis) • ATI Model S. Poornachandra (2001399722)

  28. Analysis Filter Shrinkage Function Adaptive Filter Synthesis Filter BSWTAF-II (Scale-Domain Analysis) • TAI Model S. Poornachandra (2001399722)

  29. Analysis Filter Shrinkage Function Synthesis Filter Adaptive Filter ASWTAF Model (Time-Domain Analysis) • TIA Model S. Poornachandra (2001399722)

  30. ECG Simulation…. S. Poornachandra (2001399722)

  31. ECG Simulation…. S. Poornachandra (2001399722)

  32. EEG Simulation…. S. Poornachandra (2001399722)

  33. EEG Simulation…. S. Poornachandra (2001399722)

  34. PCG Simulation…. S. Poornachandra (2001399722)

  35. PCG Simulation…. S. Poornachandra (2001399722)

  36. Shrinkage Distribution S. Poornachandra (2001399722)

  37. Hyper Shrinkage Function • Where S. Poornachandra (2001399722)

  38. Modified-hyper shrinkage function • k is the scaling function S. Poornachandra (2001399722)

  39. Subband Adaptive shrinkage function S. Poornachandra (2001399722)

  40. ECG Denoising - Noise level is 20% S. Poornachandra (2001399722)

  41. ECG Denoising - Noise level is 20% S. Poornachandra (2001399722)

  42. EEG Denoising - Noise level is 20% S. Poornachandra (2001399722)

  43. EEG Denoising - Noise level is 20% S. Poornachandra (2001399722)

  44. PCG Denoising - Noise level is 20% S. Poornachandra (2001399722)

  45. PCG Denoising - Noise level is 20% S. Poornachandra (2001399722)

  46. Objective… Reduce the minimum mean square error (MMSE) between original ECG f and denoised ECG . y = [y1, y2, . . . , yN] N Then yi = f(xi) + ni, i = 1, 2, . . ,N The risk function, S. Poornachandra (2001399722)

  47. Estimation of Mean, Variance and Risk S. Poornachandra (2001399722)

  48. Mean estimationfor Hyper Shrinkage • Let X ~ N(θ,1),  and be the probability distribution and the density function for standard Gaussian random variable respectively, then the Mean estimation is given by S. Poornachandra (2001399722)

  49. Variance estimationfor Hyper Shrinkage • The Variance estimation is given by S. Poornachandra (2001399722)

  50. Risk estimationfor Hyper Shrinkage • The Risk estimation is given by S. Poornachandra (2001399722)

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