We present an overview of the various uses of the wavelet transform (WT) in medicine and biology. We start by describing the wavelet properties that are the most important for biomedical applications. In particular we provide an interpretation of the the continuous wavelet transform (CWT) as a prewhitening multiscale matched filter. We also briefly indicate the analogy between the WT and some of the the biological processing that occurs in the early components of the auditory and visual system. We then review the uses of the WT for the analysis of 1-D physiological signals obtained by phonocardiography, electrocardiography (ECG), mid electroencephalography (EEG), including evoked response potentials. Next, we provide a survey of wavelet developments in medical imaging. These include biomedical image processing algorithms (e.g., noise reduction, image enhancement, and detection of microcalcifications in mammograms), image reconstruction and acquisition schemes (tomography, and magnetic resonance imaging (MRI)), and multiresolution methods for the registration and statistical analysis of functional images of the brain (positron emission tomography (PET) and functional MRI (fMRI)). In each case, we provide the reader with same general background information and a brief explanation of how the methods work.

A review of wavelets in biomedical applications

https://www.internationaljournalofcardiology.com/article/S0167-5273(12)00326-9/pdf

How accurate is pulse rate variability as an estimate of heart rate variability?: A review on studies comparing photoplethysmographic technology with an electrocardiogram

The application of wavelet denoising to infrared spectra was
investigated. Six different wavelet denoising methods (SURE, VISU, HYBRID,
MINMAX, MAD and WAVELET PACKETS) were applied to pure infrared spectra
with various added levels of homo- and heteroscedastic noise. The
performances of the wavelet denoising methods were compared with the
standard Fourier and moving mean filtering in terms of root mean square
errors between the pure and denoised spectra and visual quality of the
denoised spectrum. The use of predictive ability as a possible objective
criterion for denoising performance was also investigated. The main
conclusion is that for very low signal-to-noise ratios (S/N) the standard
denoising methods (Fourier and moving mean) are comparable to the more
sophisticated methods. At higher S/N levels the wavelet denoising methods,
in particular the HYBRID and VISU methods, are better. Wavelet methods are
also better in restoring the visual quality of the denoised infrared
spectra.

http://plaza.ufl.edu/yiz21cn/refer/wavelet%20denoising.pdf

Wavelet Denoising of Infrared Spectra

List of Figures. Foreword M. Vetterli. Preface. 1. Signal Models and Analysis-Synthesis. 2. Sinusoidal Modeling. 3. Multiresolution Sinusoidal Modeling. 4. Residual Modeling. 5. Pitch-Synchronous Models. 6. Matching Pursuit and Atomic Models. 7. Conclusions. Appendix A: Two-Channel Filter Banks. Appendix B: Fourier Series Representations. References. References for Poetry Excerpts. Index.

Adaptive Signal Models: Theory, Algorithms, and Audio Applications

To investigate the differences between heart rate (HR) variability and pulse rate (PR) variability, short-term variability of finger pulse wave and ECG signals were studied in 10 children with a fixed ventricular pacemaker rhythm (80 beats/min). Ten healthy children in sinus rhythm served as a reference population. Distal PR and HR were measured continuously using a Finapres device and an ECG respectively. Power spectra for HR and PR were calculated in both the supine and orthostatic positions. In paced subjects, PR spectra exhibited the characteristic respiratory peak, although the HR spectra were flat. Similarly, in healthy children the respiratory fluctuations were more pronounced when calculated from the finger pulse wave signal compared with the ECG signal. The overestimation of HR respiratory fluctuation resulting from distal PR measurement was more pronounced in the standing position; however, this postural effect was demonstrated only in healthy subjects. We observed mechanical respiratory modulation of distal PR independent of classical HR modulations. Our results suggest a mechanical respiratory influence via cardiac output and aortic transmural pressure changes on pulse wave velocity. We conclude that respiratory PR variability does not precisely reflect respiratory HR variability in standing healthy subjects and in patients with low HR variability. Consequently, HR modulation should be studied using the ECG signal rather than the distal pulse wave signal. However, when ECG recording is not available, the distal pulse wave is an acceptable alternative.

Pulse rate variability is not a surrogate for heart rate variability

Wavelet packets-based high-resolution spectral estimation

This article presents two applications of modern processing techniques for cardiovascular monitoring. These two applications are quite different in terms of theory as well as application, but they nevertheless present similarities. In both cases, the incentive for using new techniques came from the need for higher performance in order to achieve desired goals. The results obtained are not limited to the particular cases presented here and may lead to original developments in pure signal processing. The first application deals with automatic in-vivo estimation of microvascular pulmonary pressure (P/sub mv/). New structures of multirate adaptive filtering based on wavelet packets have been developed to remove the respiratory artifact present. The other application investigates the possibility of using chaos and fractal theory to analyze heart rate variability. The use of chaos might help predict cardiac events, such as ventricular tachycardia or fibrillation, with better accuracy than conventional methods.

Improving cardiovascular monitoring through modern techniques

The authors present a scheme for subband adaptive filtering, where the subband decomposition is performed using a novel mutual wavelet packets decomposition scheme. They contrast the performance and algorithmic complexity of this new structure to that of regular subband adaptive filtering and point out its usefulness in achieving better filtering performance. The use of this mutual wavelet packets decomposition allows the partitioning of the frequency axis into nonuniform subbands adapted to the spectral content of the signals to be filtered. A criterion maximizing the cross-correlation between the signals is proposed for this purpose. Simulations on both synthetic and real signals confirmed the improvement achieved in performance. >

Subband adaptive filtering: The mutual wavelet packets approach

A new mutual wavelet packets scheme is proposed for subband adaptive filtering. Its relation to the existing literature on the subject is outlined. The proposed scheme performs a decomposition of the two signals used in the adaptation process onto the same optimal basis. That basis is chosen so that it favors the adaptation performance. A new criterion, based on a functional of the two signals, is introduced. This proposed criterion consists in the maximization of the magnitude of the cross-correlation samples of the two signals considered. This maximizes the cross-correlation vector of the well known normal equations. At the expense of a slightly higher computational complexity, the mutual wavelet packets scheme reduces the aliasing drawback of regular subband adaptive filtering, preserving its main advantages. Simulations have been performed on pulmonary capillary pressure transients for respiratory interference cancelling. The method proved to be more efficient than classical methods. >

Analyzing pulmonary capillary pressure

In this paper two techniques for the measurement of Heart Rate Variability are briefly described. These techniques are applied to the ECG signal and the finger blood pressure signal. Comparison of the spectra obtained from the same patient shows that there is a great similarity for low frequencies. However the spectra differ for high frequencies.

http://ieeexplore.ieee.org/iel5/1028/5761012/05761108.pdf

M. Karrakchou

Papers

Wavelet packets-based high-resolution spectral estimation

Improving cardiovascular monitoring through modern techniques

Subband adaptive filtering: The mutual wavelet packets approach

Analyzing pulmonary capillary pressure

Analysis of heart rate variability: Comparison between spectra obtained from ECG and finger blood pressure