Notations. Introduction. Chapter 1. A Guided Tour. Chapter 2. Mathematical Framework. Chapter 3. From Wavelet Bases to the Fast Algorithm. Chapter 4. Wavelet Families. Chapter 5. Finding and Designing a Wavelet. Chapter 6. A Short 1D Illustrated Handbook. Chapter 7. Signal Denoising and Compression. Chapter 8. Image Processing with Wavelets. Chapter 9. An Overview of Applications. Appendix: The EZW Algorithm. Bibliography. Index.

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Wavelets and their applications

Wavelet-based electrocardiogram signal compression methods and their performances: A prospective review

The main advantage related to wavelet transforms is that they are localized both in the frequency and time domains. This paper presents an algorithm, based on the wavelet transform, for feature extraction from an electrocardiograph (ECG) signal and recognition of abnormal heartbeats. A method for choosing an optimal mother wavelet from a set of orthogonal and bi-orthogonal wavelet filter bank by means of the best correlation with the ECG signal, was developed. The ECG signal is first denoised by a soft or hard threshold with limitation of 99.99 reconstructs ability and then each PQRST cycle is decomposed into a coefficients vector by the optimal wavelet function. The coefficients, approximations of the last scale level and the details of the all levels, are used for the ECG analyzed. The coefficients of each cycle are divided into three segments, which are related to the P-wave, QRS complex and T-wave, and summed to obtained a features vector of the signal cycles.

ECG feature extraction using optimal mother wavelet

A direct waveform mean-shape vector quantization (MSVQ) is proposed here as an alternative for electrocardiographic (ECG) signal compression. In this method, the mean values for short ECG signal segments are quantized as scalars and compression of the single-lead ECG by average beat substraction and residual differencing their waveshapes coded through a vector quantizer. An entropy encoder is applied to both, mean and vector codes, to further increase compression without degrading the quality of the reconstructed signals. In this paper, the fundamentals of MSVQ are discussed, along with various parameters specifications such as duration of signal segments, the wordlength of the mean-value quantization and the size of the vector codebook. The method is assessed through percent-residual-difference measures on reconstructed signals, whereas its computational complexity is analyzed considering its real-time implementation. As a result, MSVQ has been found to be an efficient compression method, leading to high compression ratios (CRs) while maintaining a low level of waveform distortion and, consequently, preserving the main clinically interesting features of the ECG signals. CRs in excess of 39 have been achieved, yielding low data rates of about 140 bps. This compression factor makes this technique especially attractive in the area of ambulatory monitoring.

Mean-shape vector quantizer for ECG signal compression

Chapter 7 – ECG Signal Processing

An improved wavelet compression algorithm for ECG signals has been developed with the use of vector quantization on wavelet coefficients. Vector quantization on scales of long duration and low dynamic range retains feature integrity of the ECG with a very low bit-per-sample rate. Preliminary results indicate that the proposed method excels over standard techniques for high fidelity compression. >

G. Rodrigue

Papers

Vector quantization of ECG wavelet coefficients