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

10/26/2015S. Poornachandra ( )2 Objective Denoising of biomedical signals with better performance

10/26/2015S. Poornachandra ( )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

10/26/2015S. Poornachandra ( )4 Statistical Estimations Mean Variance Risk

10/26/2015S. Poornachandra ( )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: Length of ECG data considered: 5000

10/26/2015S. Poornachandra ( )6 Other biosignals used.... EEG PCG Pulse Waveform

10/26/2015S. Poornachandra ( )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 =

10/26/2015S. Poornachandra ( )8 Time-domain Advantages Simple Easy to implement Lower computational complexity Disadvantages Slow convergence when the input is highly colored

10/26/2015S. Poornachandra ( )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

10/26/2015S. Poornachandra ( )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

10/26/2015S. Poornachandra ( )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

10/26/2015S. Poornachandra ( )12 DWT – Demystified d 3 : Level 3 DWT Coeff. Length: 512 B: 0 ~  g[n]h[n] g[n]h[n] g[n]h[n] 2 d 1 : Level 1 DWT Coeff. Length: 256 B: 0 ~  /2 Hz Length: 256 B:  /2 ~  Hz Length: 128 B: 0 ~  /4 Hz Length: 128 B:  /4 ~  /2 Hz d 2 : Level 2 DWT Coeff. …a 3 …. Length: 64 B: 0 ~  /8 Hz Length: 64 B:  /8 ~  /4 Hz |H(j  )|   /2 -  /2 |G(j  )|   --  /2 -  /2 a2a2 a1a1 Level 3 approximation Coefficients

10/26/2015S. Poornachandra ( )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.

10/26/2015S. Poornachandra ( )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.

10/26/2015S. Poornachandra ( )15 Pioneers …  Donoho and Johnstone (1994) – Soft Shrinkage  Coifman and Donoho (1995) – Cycle SpinningCycle Spinning  Nason (1996) – Cross Validation ShrinkageCross Validation  Bruce and Gao (1997) –Garrote Shrinkage

10/26/2015S. Poornachandra ( )16 Shrinkage functions

10/26/2015S. Poornachandra ( )17 Shrinkage Algorithm Apply DWT to the vector y and obtain the empirical wavelet coefficients c j,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.

10/26/2015S. Poornachandra ( )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.

10/26/2015S. Poornachandra ( )19 Median Absolute Deviation Prof. Donoho proposed Where, is the estimate of noise variance Median Absolute Deviation MAD(v)=[|v 1 -v med |, …, |v 1 -v med |] med

10/26/2015S. Poornachandra ( )20 Alpha-trim Filter The alpha-trim filter is a special type of L-filter, A particular choice of a j 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.

10/26/2015S. Poornachandra ( )21 Threshold at each subband The Threshold values at each subband for 20% noise level is given in tablessubband SNR (dB) PRD (%) ECG Signal

10/26/2015S. Poornachandra ( )22 Wavelet level analysis

10/26/2015S. Poornachandra ( )23 Wavelet level analysis

10/26/2015S. Poornachandra ( )24 Hybrid Model …. Analysis Filter a3a3 d2d2 d3d3 d1d1 Hard shrinkage X shrinkage X shrinkage X shrinkage

10/26/2015S. Poornachandra ( )25 Basic shrinkage (ECG)

10/26/2015S. Poornachandra ( )26 Basic shrinkage (PCG)

10/26/2015S. Poornachandra ( )27 BSWTAF-I (Scale-Domain Analysis) ATI Model Analysis Filter Adaptive Filter Shrinkage Function Synthesis Filter

10/26/2015S. Poornachandra ( )28 BSWTAF-II (Scale-Domain Analysis) TAI Model Analysis Filter Shrinkage Function Adaptive Filter Synthesis Filter

10/26/2015S. Poornachandra ( )29 ASWTAF Model (Time-Domain Analysis) TIA Model Analysis Filter Shrinkage Function Adaptive Filter Synthesis Filter

10/26/2015S. Poornachandra ( )30 ECG Simulation….

10/26/2015S. Poornachandra ( )31 ECG Simulation….

10/26/2015S. Poornachandra ( )32 EEG Simulation….

10/26/2015S. Poornachandra ( )33 EEG Simulation….

10/26/2015S. Poornachandra ( )34 PCG Simulation….

10/26/2015S. Poornachandra ( )35 PCG Simulation….

10/26/2015S. Poornachandra ( )36 Shrinkage Distribution

10/26/2015S. Poornachandra ( )37 Hyper Shrinkage Function Where

10/26/2015S. Poornachandra ( )38 Modified-hyper shrinkage function k is the scaling function

10/26/2015S. Poornachandra ( )39 Subband Adaptive shrinkage function

10/26/2015S. Poornachandra ( )40 ECG Denoising - Noise level is 20%

10/26/2015S. Poornachandra ( )41 ECG Denoising - Noise level is 20%

10/26/2015S. Poornachandra ( )42 EEG Denoising - Noise level is 20%

10/26/2015S. Poornachandra ( )43 EEG Denoising - Noise level is 20%

10/26/2015S. Poornachandra ( )44 PCG Denoising - Noise level is 20%

10/26/2015S. Poornachandra ( )45 PCG Denoising - Noise level is 20%

10/26/2015S. Poornachandra ( )46 Objective… Reduce the minimum mean square error (MMSE) between original ECG f and denoised ECG. y = [y 1, y 2,..., y N ]   N Then y i = f(x i ) + n i, i = 1, 2,..,N The risk function,

10/26/2015S. Poornachandra ( )47 Estimation of Mean, Variance and Risk

10/26/2015S. Poornachandra ( )48 Mean estimation for 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

10/26/2015S. Poornachandra ( )49 Variance estimation for Hyper Shrinkage The Variance estimation is given by

10/26/2015S. Poornachandra ( )50 Risk estimation for Hyper Shrinkage The Risk estimation is given by

10/26/2015S. Poornachandra ( )51 Mean estimation for Subband Adaptive Shrinkage The Mean estimation is given by

10/26/2015S. Poornachandra ( )52 Variance estimation for Subband Adaptive Shrinkage The Variance estimation is given by

10/26/2015S. Poornachandra ( )53 Powerline Frequency Interference Cancellation

10/26/2015S. Poornachandra ( )54 50 Hz Noise Cancellation in ECG

10/26/2015S. Poornachandra ( )55 50 Hz Noise Cancellation ECG

10/26/2015S. Poornachandra ( )56 50 Hz Noise Cancellation ECG

10/26/2015S. Poornachandra ( )57 50 Hz Noise Cancellation in EEG

10/26/2015S. Poornachandra ( )58 50 Hz Noise Cancellation in EEG

10/26/2015S. Poornachandra ( )59 50 Hz Noise Cancellation in EEG

10/26/2015S. Poornachandra ( )60 50 Hz Noise Cancellation in PCG

10/26/2015S. Poornachandra ( )61 50 Hz Noise Cancellation in PCG

10/26/2015S. Poornachandra ( )62 50 Hz Noise Cancellation in PCG

10/26/2015S. Poornachandra ( )63 Journal publication arise from this work  Poornachandra S. and N. Kumaravel, “A Wavelet coefficient smoothened RLS-Adaptive denoising model for ECG”, Journal of Biomedical Sciences Instrumentation, vol. 39, ISA vol. 437, pp , April  Poornachandra S. and N. Kumaravel, “Hyper-trim shrinkage for denoising of ECG signal”, ELSEVIER Journal of Digital Signal Processing, Vol. 15, Issue-3, pp , May  Poornachandra S. and N. Kumaravel, “Wavelet based Adaptive Denoising Models for Biological Signals”, Journal of Institute of Engineers, Vol. 86, Nov  Poornachandra S. and N. Kumaravel, “Subband-Adaptive Shrinkage for Denoising of ECG Signals”, EURASIP Journal on Applied Signal Processing (Available online).

10/26/2015S. Poornachandra ( )64 Journal publication arise from this work  Poornachandra S. and N. Kumaravel, “Wavelet Thresholding by  -Trim Mean Filter”, Journal of Institute of Engineers, Vol. 87, January 2007  Poornachandra S. and N. Kumaravel, “Statistical Estimation for Hyper Shrinkage”, ELSEVIER Journal of Digital Signal Processing, (Available online).  Poornachandra S. and N. Kumaravel, “A Novel method for the Elimination of Power Line Frequency in ECG Signal using Hyper Shrinkage Function”, ELSEVIER Journal of Digital Signal Processing, (In Press).  Poornachandra S. and N. Kumaravel, “Hyper Shrinkage for Denoising of ECG Signal with Adaptive Filter”, ELSEVIER Journal of Digital Signal Processing, (Under Review).

10/26/2015S. Poornachandra ( )65 Conference publication  Poornachandra S. and Dr N. Kumaravel, “A new wavelet co-efficient smoothened Adaptive filtering for bio-signal”, Proc. of ICBME, 4 th –7 th December 2002, Singapore.  Poornachandra S. and Dr N. Kumaravel “Wavelet coefficient smoothened LMS-adaptive denoising model for electro-cardio graph”, Proc. of NCC, 31 st -2 nd Jan-Feb 2003, Chennai, India.  Poornachandra S., Dr N. Kumaravel et al., “A modified Wavelet model with RLS-adaptive for denoising Gaussian Noise from ECG signal”, Proc. of NSIP, 8 th –11 th June 2003, Grudo-Triesta, Italy.

10/26/2015S. Poornachandra ( )66 Conference publication  Poornachandra S., Dr N. Kumaravel et al., “Denoising of ECG by  -Trim thresholding of Wavelet coefficients”, Proc. of NCC, 31 st -2 nd Jan-Feb 2004, Bangalore, India.  Poornachandra S., Dr. N. Kumaravel et al, “WaveShrink using Modified Hyper-Shrinkage Function” Proc. of IEEE- EMBC, 1 st – 4 th September 2005, Shanghai, China.(best session paper award)  Poornachandra S., Dr. N. Kumaravel et al, “A Novel method for the elimination of powerline frequency in ECG signals using modified-hyper shrinkage”, Proc. of IFMBE, ICBME2005, 7 th – 10 th December 2005, Singapore.

10/26/2015S. Poornachandra ( )67 Conclusion….. In real time bio-signal acquisition, the noise level is always less than the signal level. Hence shrinkage is the better choice for denoising This thesis suggested that shrinkage can also be used to eliminate powerline frequency from bio-signals. This thesis proposed following shrinkage function that are better than the existing ones and its mathematical models Hyper shrinkage Modified shrinkage Subband-Adaptive shrinkage

10/26/2015S. Poornachandra ( )68 Suggested for future work 1. Image processing applications 2. VLSI implementation 3. Better shrinkage models can be proposed 4. Communication signal processing 5. Iterative shrinkage 6. Fussy shrinkage

10/26/2015S. Poornachandra ( )69 Bias and Variance