114 3.7 Performance of the joint threshold and quantization strategy. is taken from lead II of the mitarecord 117. 178 4.2 Carrying out the WEDD measure when the signal with noise and distortion in the iso-.
Introduction
In two-stage May schemes, fixed numbers of bits are assigned to wavelet coefficients that can produce severe signal distortion and thus reduce the coding efficiency of the compression algorithm. Since a vector consists of wavelet coefficients with different dynamic ranges, it is not efficient to allocate a fixed number of bits to represent the wavelet coefficients due to the different characteristics of different ECG signals.
Overview of Cardiovascular Signals
The Electrocardiogram
The appearance of the ST segment changes dramatically in the presence of ischemia or during myocardial infarction. QT interval: The QT interval is measured from the beginning of the QRS complex to the end of the T wave.
The Phonocardiogram
Cardiac Data Acquisition
The main goal of any such technique is to obtain maximum data compression without sacrificing clinically relevant information. The main goal of any such method is to obtain maximum data compression without introducing clinically significant distortions.
Classical Data Compression System
Signal Irrelevancy and Redundancy
In medical practice, ECG signals are recorded for a longer time for the diagnosis of cardiovascular diseases. Multi-channel ECG signals have three types of correlations [5, 6]: the intra-beat, the inter-beat and the inter-channel/lead.
Coding Efficiency
Intrabeat correlation represents the correlation between consecutive samples in an ECG cycle. Beat-to-beat correlation represents the correlation between consecutive beats in a single-channel ECG signal.
Distortion or Quality Measures
MSE is the L2 norm of the arithmetic difference between the original and the compressed signal. Some local measures of error are maximum amplitude error (MAX) or maximum error (PE), normalized MAX (NMAX), and standard error (StdErr).
Classification of ECG Compression Methods
Time Domain Compression Methods
- Statistical Coding Techniques
- Redundancy Reduction Techniques
- Adaptive Sampling Techniques
- Parameter Extraction Compression Techniques
This algorithm calculates the statistical parameters (mean value (μ), standard deviation (σ) and third moment (M)) of the ECG signal used online. The algorithm applies the SAPA algorithm to the high-frequency parts of the ECG signal (i.e. the QRS complex) and the cubic splines approximation to the lower-frequency segments (i.e. the S-Q segment).
Frequency Domain Compression Methods
The experimental results of some transform-based ECG signal compression methods are presented here. Ramakrishnan and Saha [119] presented a compression technique for single-channel ECG based on the automatic QRS detection, period and amplitude normalization (PAN) and vector quantization of the PAN beats.
Wavelet Transform Based ECG Compression Methods
When signal plus noise information is compressed, most of the noise in the original recordings is filtered out during compression. A detailed overview of wavelet-based ECG compression methods is presented in the next chapter.
Two-Dimensional ECG Compression Methods
The performance of the 2D compression method may deteriorate if the quasi-periodicity is not satisfied. The effect of noise removal, i.e. the amount of noise removed by compression filtering, may not be the same for all test record conditions.
Quality Controlled ECG Compression Methods
The authors concluded that the compression performance of the ALQ-TRE method is better than that of the filter bank [121] and SPIHT [145] based methods. This can lead to confusion when assessing the quality of the compressed signal.
Phonocardiogram Signal Compression Methods
The use of the PRD measure in evaluating ECG compression methods has no practical value [74]. In threshold-based methods, the wavelet coefficients of the original signal are compared to some thresholds based on target criteria such as retained energy (RE), distortion rate, and compression ratio (CR).
Objective of the Thesis
Wavelet Energy Based Diagnostic Distortion Measure
The proposed measure is a weighted percentage root mean square difference between the wave subband coefficients of the original and compressed signals with weights equal to the relative wave subband energy of the corresponding subbands. The WEDD measure appears to be a correct representation of the amount of signal distortion at all subbands and correlates well with subjective rating compared to the PRD and WWPRD measures.
Quality Controlled Compression of Cardiovascular Signals
Organization of the Thesis
This chapter reviews the electrocardiogram compression methods and distortion measures used for evaluating the compressed signal quality. Many ECG compression methods are reported that exploit one or more of the correlations present in the signal.
Wavelet Transform
Discrete Wavelet Transform
Daubechies proved that a necessary and sufficient condition for a stable reconstruction is that the energy of the wave coefficients must lie between two positive limits. The advantages of dyadic DWT are (1) reducing the complexity and redundancy of CWT and (2) preserving most of the nice properties of CWT, such as linearity, shift covariance, scale covariance, and scaling property.
Multiresolution Analysis
The advantages of the dyadic DWT are (1) reducing the complexity and redundancy of the CWT, and (2) maintaining most of the good properties of the CWT such as linearity, displacement covariance, scale covariance, and scaling property [183, 184] . The wavelet function ψ(t) has a companion, the scaling function φ(t), which also forms an orthonormal basis set of L2(ℜ),φj,k(t) =2−j/2 φ(2−jt− k).
Wavelet Filter Banks for ECG Signal Decomposition
The high-frequency information of the signal is contained in D1(n), and the lower components are observed in D5(n). In the next section, we discuss the coding schemes reported for the wavelet coefficients of the ECG signal.
One-Dimensional Wavelet Based ECG Compression Methods
- Tree Based Methods
- Vector Quantization Based Methods
- Linear Prediction and Template Matching Based Methods
- Threshold Based Methods
- Quantization Approaches for Wavelet Coefficients
Therefore, we present different quantization approaches applied to the wavelet coefficients of ECG signals. Quantization step sizes are given relative to the nominal dynamic range of the coefficients.
Quality Assessment Approaches for the Distorted ECG Signal
Non-Diagnostic Distortion Measures
- Global Error Criteria
- Local Error Criteria
KKK is defined as 2.26) where µ0 and µr are respectively the average values of the original signal and the compressed or reconstructed signal. The correlation measure is used to find the shape similarity between the original and reconstructed local wavelets [192].
Diagnostic Distortion Measures
- Weighted PRD Criterion
- Weighted Diagnostic Distortion Criterion
- Average Absolute Error Criterion
- Wavelet based Weighted PRD Criterion
The diagnostic distortion measure is implemented by comparing the PQRST complex functions of the original signal with the compressed one. Some of the diagnostic functions are Pamp, QRS+amp, QRS−amp,Tamp,Pdur,QRSdur,Tdur,PRInt,STint and STslope.
Evaluation of Distortion Measures
- Performance of PRD Criteria
- Performance of MAX Criteria
- Performance of Average Absolute Error Criterion
- Performance of Wavelet based Weighted PRD Criterion
- Comparison of the Distortion Measures
It can be observed that the duration of the P wave is prolonged in the compressed signal. Some of the diagnostic features are Pamp,QRS+amp,QRS−amp,Tamp,Pdur,QRSdur,Tdur,PRint and STint.
Evaluation of ECG Compression Methods
- Effects of Preprocessing (Mean Removal and Amplitude Normalization)
- Effects of Quantization on the Desired RE or EPE Criterion
- Effects of Quantization on the Desired PWCZ Criterion
- Effects of Quantization on the Desired PRD Criterion
- Scalar Quantization Approaches for Wavelet Coefficients
- Quality Controlled Coding Methods Based on PRD and WWPRD Criteria
A higher number of bits will result in better preservation of the target energy in the compressed signal. Experiments show that the performance of the quantizers depends on the distribution of the wavelet coefficients of the ECG signal.
Motivation for the Present Research Work
Most threshold-based schemes are based on a two-stage design, where the wavelet coefficients are first tightly bounded, and then the non-zero wavelet coefficients are quantized using fixed USQ schemes. Most of the energy in the ECG signal is concentrated in the low-frequency range, and in each subband of the wavelet transform, the energy distribution is concentrated in a small number of wavelet coefficients.
Construction of Adaptive Subband Coding Scheme
Preprocessing: Blocking and Mean Removal
But the mean value and the noise do not contribute any medical significance during clinical evaluation of the ECG signal. The effect of the use of noisy ECG signals will be discussed using different noisy recordings taken from themita database.
Wavelet-Multiresolution Signal Decomposition
- Wavelet Filters and Decomposition Level
- Wavelet Subbands: Approximation and Detail
- Statistical Distribution of the Wavelet Coefficients
- Energy Based Classification of Wavelet Coefficients
The amplitude distributions of the wavelet coefficients of the subbands are different due to the different characteristics of the ECG morphology. Histograms of wavelet coefficients in subbands of test signals are shown in fig.
Wavelet Thresholding and Threshold Selection
- Criterion for Threshold Selection
- Wavelet Thresholding Rule
- Threshold Finding Algorithm and Results of Wavelet Thresholding Phase 112
- Limitation of the Quantization Approaches
- Background and Problem Statement
- Adaptive TCZNUMQ Scheme for Wavelet Coefficients
- Results of Adaptive TCZNUMQ Scheme
In addition, some rolling coefficients lying in the quantizer zero zone area can be rounded to zero. The quantization error of the wavelet coefficients lies in the width of the outer zone, which is limited by.
Modified Index Coding Scheme for Significance Map
- Performance of the Modified Index Coding Scheme
We compare the performance of the proposed encoder for the importance map derived from frames. The overall performance of the proposed MIC is compared with the HT8BSM encoding for binary significance mapping (BSM).
Rate- and Distortion-Driven Subband Coding Algorithms
Determination of Coding Parameters
- Effects of Energy Packing Efficiency
- Selection of Quantization Bit
- Selection of Data Length and Block Length
The performance of the proposed algorithms with different block lengths for a data length of M = 65536 samples is shown in Fig. The results show that the performance of the proposed algorithm is better for large block length.
The TDL Driven ECG Compression Algorithm
- Variation of Mean
- Variation of Noise Level
- Time Varying PQRST Complex Morphologies
But the performance of the proposed algorithm is worse than the WT+AVQ algorithm with a target PRD1 value of 6% for myth records 101, 111, and 208. For example, for a PRD1 value of 3%, the minimum and maximum CDR values are 407 bps and 1067 bps, respectively.
The TDR Driven ECG Compression Algorithm
From the experimental results, it can be observed that the number of iterations depends on the variable, N,band CDR. Experimental results show that the number of iterations required to achieve the desired CDR value decreases with increasing.
Comparison with Other ECG Compression Algorithms
Quality Assessment of Compressed Signal by Visual Inspection
It is shown that the CRs of the proposed TDR algorithm are very close to the CR targets. The correct diagnosis of SPIHT and the proposed algorithm is 100% when the target CR is below 4.
Computational Complexity
The performance of the proposed TDR algorithm can be improved if a block length of 2048 or 4096 samples is used for compression at the cost of increased complexity. It can be observed that the performance of the proposed data rate based wavelet thresholding ECG signal compression algorithm is better than other ECG encoders.
Evaluation of the Proposed Algorithm for Real Time Application
For ECG data 117 and 232 from the database, the compression performances of the proposed algorithms and WPFDEC [121] are shown in Table 3.19 for comparison. The performance of the proposed algorithm is evaluated using the selected ECG arrhythmia signal 10 sec long (each) from the selected records 102/V5, 107/II, 111/II, 118/VI and 119/II, referred to as set i data -V.
Discussion
In this case, the subjective evaluation is used to quantify the dissatisfaction of the compressed ECG signal. In Section 4.5, subjective quality assessment of the clinical characteristics of the compressed signal is presented.
Background and Problem Statement
Chen [129] suggested a new distortion measure, weighted PRD to improve the local distortion measure for evaluating the fidelity of the compressed ECG signal. A wavelet-based quality measure, WWPRD, is based on decomposing the segment of interest into subbands, and a weighted score is given to the band depending on its dynamic range and diagnostic significance.
Wavelet Energy Based Diagnostic Distortion Measure
Local-wave Energies of the ECG Signal
The average value of the original ECG signal and the compressed signal is measured and then subtracted from them as a first step. In this paper, the five-level analysis structure is used to decompose ECG signals.
Formulation of WEDD Measure
Preliminary Evaluation of the WEDD Measure
Evaluation of the Local Errors by Zeroing of Wavelet Coefficients
Performance of the WEDD Measure under Noisy Conditions
Subjective Quality Measure
Quantitative and Qualitative Analysis of WEDD Measure
Correlation between MOS error and Distortion Measures
Statistical Predictability of Distortion Measure
Discussion
Background and Motivation
Guaranteeing Quality Using WEDD criterion
Approach 1-By Adaptive Wavelet Coding with JTQ Strategy
Search Range for Threshold Adaptation
Search Range for Width of Outer-zone
Results of the Quality-Driven Wavelet Coding with JTQ Strategy
Approach 2-By Adaptive Subband Coding with JTQ Strategy
Approach 3-By SPIHT Coding Strategy
Automatic Quality Controlled SPIHT Coding Procedure
Results of Quality-Driven SPIHT Coding Scheme
Discussion
Background and Problem Statement
Wavelet Compression of PCG Signals
Preprocessing (Blocking, Mean Removal and Multirate Sampling)
Wavelet Decomposition of the PCG Signal
Coding of the Wavelet Coefficients
Distortion Measures
Evaluation of the PCG Compression Method
Selection of Signal Block Size
Comparison with Other Wavelet Compression Methods
Performance of the WEDD Measure for Distorted PCG Signals
Computational Complexity
Results of Quality Controlled PCG Compression
Scope for Future Work
Introduction
The effects of noise on the velocity distortion performance of the proposed methods and the SPIHT-based methods are demonstrated in the previous chapter. 4.3) provides a hierarchical and fast scheme for calculating the wavelet coefficients for a given signal.
