Noise reduction by perfect-translation-invariant complex discrete wavelet transforms for fetal electrocardiography and magnetocardiography

2014 ◽  
Vol 12 (04) ◽  
pp. 1460008 ◽  
Author(s):  
Yasuhiro Ishikawa ◽  
Hitoshi Horigome ◽  
Akihiko Kandori ◽  
Hiroshi Toda ◽  
Zhong Zhang
Keyword(s):  
Noise Reduction ◽  
Wavelet Transforms ◽  
Body Movement ◽  
Internal Noise ◽  
P Wave ◽  
Time Interval ◽  
Discrete Wavelet ◽  
Translation Invariance ◽  
Qrs Complex ◽  
Fetal Electrocardiography

Echocardiography is widely used for the diagnosis of fetal cardiac arrhythmias. However, this method does not detect configurational changes in the electrocardiogram (ECG) such as life-threatening changes in QRS and the prolongation of the QT interval. Fetal magnetocardiography (fMCG) and fetal electrocardiography (fECG) are valuable tools for the detection of electrophysiological cardiac signals although both have certain limitations. Such techniques must deal with excess internal noise such as maternal respiratory movements, fetal movements, muscle contraction and fetal body movement and external noise (e.g., electromagnetic waves). Heart rate variability (HRV) is a well-known phenomenon with fluctuation in the time interval between heartbeats. The lack of translation invariance is a serious defect in the conventional wavelet transforms (discrete wavelet transform (DWT)). Fluctuation of the impulse response at each energy level is observed in the multi-resolution analysis (MRA). Configurational changes in the ECG waveforms are frequently observed after noise reduction by the conventional wavelet transforms. Both the lack of translation invariance of conventional wavelet transforms and HRV cause deformation of the ECG waveforms. We describe here the CDWTs with perfect translation invariance (PTI). Compared with conventional wavelets, PTI of the fECG and fMCG resulted in only minor configurational changes in the ECG waveforms. This technique yields persistently stable ECG waveforms, including P wave and QRS complex. First, an independent component analysis (ICA) was applied to fECG or fMCG data to remove noise. We provide an example to show that the morphological change in QRS complex is barely affected when PTI is applied to normal fECG. Examples of fetal arrhythmias, such as ventricular trigeminy, ventricular bigeminy and premature atrial contraction are demonstrated using this technique. The results lead us to the conclusion that ICA and noise reduction in fECG and fMCG by PTI are promising methods for the diagnosis of fetal arrhythmia.

Perfect-translation-invariant variable-density complex discrete wavelet transform

2014 ◽  
Vol 12 (04) ◽  
pp. 1460001 ◽  
Author(s):  
Hiroshi Toda ◽  
Zhong Zhang ◽  
Takashi Imamura
Keyword(s):  
Frequency Domain ◽  
Frequency Band ◽  
Time Domain ◽  
Wavelet Transforms ◽  
Filter Banks ◽  
Wavelet Packet ◽  
Discrete Wavelet ◽  
Translation Invariance ◽  
Logarithmic Scale ◽  
The Time Domain

The theorems giving the conditions for discrete wavelet transforms (DWTs) to achieve perfect translation invariance (PTI) have already been proven, and based on these theorems, the dual-tree complex DWT and the complex wavelet packet transform, achieving PTI, have already been proposed. However, there is not so much flexibility in their wavelet density. In the frequency domain, the wavelet density is fixed by octave filter banks, and in the time domain, each wavelet is arrayed on a fixed coordinate, and the wavelet packet density in the frequency domain can be only designed by dividing an octave frequency band equally in linear scale, and its density in the time domain is constrained by the division number of an octave frequency band. In this paper, a novel complex DWT is proposed to create variable wavelet density in the frequency and time domains, that is, an octave frequency band can be divided into N filter banks in logarithmic scale, where N is an integer larger than or equal to 3, and in the time domain, a distance between wavelets can be varied in each level, and its transform achieves PTI.

scholarly journals Delineation of electrocardiogram morphologies by using discrete wavelet transforms

2021 ◽  
Vol 22 (1) ◽  
pp. 159
Author(s):  
Annisa Darmawahyuni ◽  
Siti Nurmaini ◽  
Hanif Habibie Supriansyah ◽  
Muhammad Irham Rizki Fauzi ◽  
Muhammad Naufal Rachmatullah ◽  
...  
Keyword(s):  
Wavelet Transforms ◽  
Noise Removal ◽  
P Wave ◽  
Discrete Wavelet ◽  
Wave Localization ◽  
T Wave ◽  
Wave Morphology ◽  
Cardiac Disorders ◽  
Non Stationary Signal ◽  
Different Characteristics

<span>The accuracy of electrocardiogram (ECG) delineation can affect the precise diagnose for cardiac disorders interpretation. Some nonideal ECG presentation can make a false decision in precision medicine. Besides, the physiological variation of heart rate and different characteristics of the different ECG waves in terms of shape, frequency, amplitude, and duration is also affected. <span>This paper proposes a discrete wavelet transform (DWT), non-stationary signal analysis for noise removal, and onset-offset of PQRST feature extraction. A well-known database from Physionet: QT database (QTDB) is used to validate the DWT function for detecting the onset and offset of P-wave, QRS-complex, and T-wave localization. From the results, P-peak detection gets the highest result that achieves 2.19 and 13.62 milliseconds of mean error and standard deviation, respectively. In contrast, Toff has obtained the highest error value due to differences in the T-wave morphology. It can be affected by inverted o</span>r biphasic T-waves and others.</span>

High-Accuracy Characterization of Ambulatory Holter Electrocardiogram Events

2012 ◽  
Vol 1 (3) ◽  
pp. 40-71 ◽  
Author(s):  
Mohammad Reza Homaeinezhad ◽  
Seyyed Amir Hoseini Sabzevari ◽  
Ali Ghaffari ◽  
Mohammad Daevaeiha
Keyword(s):  
High Accuracy ◽  
P Wave ◽  
Discrete Wavelet ◽  
Ecg Signal ◽  
Qrs Complex ◽  
First Derivative ◽  
Time Distance ◽  
Noise Robust ◽  
Electrocardiogram Ecg

In this paper, three noise-robust high-accuracy methods aiming at the detection and delineation of the electrocardiogram (ECG) events (QRS complex, P-wave, T-wave) were developed. The ECG signal was initially appropriately preprocessed by application of a bandpass FIR filter and Discrete Wavelet Transform (DWT). The first detection-delineation method was the Walsh-Hadamard Transform (WHT). The WHT coefficients were divided into two groups and the signal was reconstructed using the second group coefficients. By this reconstruction, the values of first derivative of events are made stronger rather than the values of other parts of signal. In the second method, a feed forward artificial neural network was implemented to detect all events of the ECG signal. In the third method, the first derivative of signal was computed using a new signal smoothing algorithm with corresponding statistical properties. For decreasing False Positive (FP) errors associated with P-wave detection, a discriminating border was introduced as the post processing stage specified by three QRS parameters: the duration of a QRS complex, the time distance from the former and latter QRS complexes, and the potential difference from former QRS complex J-location and the latter QRS complex fiducial location. The proposed methods were applied to DAY general hospital high resolution holter data.

PERFECT-TRANSLATION-INVARIANT CUSTOMIZABLE COMPLEX DISCRETE WAVELET TRANSFORM

2013 ◽  
Vol 11 (04) ◽  
pp. 1360003 ◽  
Author(s):  
HIROSHI TODA ◽  
ZHONG ZHANG ◽  
TAKASHI IMAMURA
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Frequency Domain ◽  
Wavelet Transforms ◽  
Wavelet Packet ◽  
Variable Density ◽  
Discrete Wavelet ◽  
Translation Invariance ◽  
Translation Invariant ◽  
High Degree

The theorems, giving the condition of perfect translation invariance for discrete wavelet transforms, have already been proven. Based on these theorems, the dual-tree complex discrete wavelet transform, the 2-dimensional discrete wavelet transform, the complex wavelet packet transform, the variable-density complex discrete wavelet transform and the real-valued discrete wavelet transform, having perfect translation invariance, were proposed. However, their customizability of wavelets in the frequency domain is limited. In this paper, also based on these theorems, a new type of complex discrete wavelet transform is proposed, which achieves perfect translation invariance with high degree of customizability of wavelets in the frequency domain.

THE DESIGN OF COMPLEX WAVELET PACKET TRANSFORMS BASED ON PERFECT TRANSLATION INVARIANCE THEOREMS

2010 ◽  
Vol 08 (04) ◽  
pp. 537-558 ◽  
Author(s):  
HIROSHI TODA ◽  
ZHONG ZHANG ◽  
TAKASHI IMAMURA
Keyword(s):  
Wavelet Transforms ◽  
Wavelet Packet ◽  
Wavelet Packets ◽  
Discrete Wavelet ◽  
Translation Invariance ◽  
Discrete Wavelet Transforms ◽  
Wide Range ◽  
Different Shapes ◽  
Complex Wavelet ◽  
Meyer Wavelet

The useful theorems for achieving perfect translation invariance have already been proved, and based on these theorems, dual-tree complex discrete wavelet transforms with perfect translation invariance have been proposed. However, due to the complication of frequency divisions with wavelet packets, it is difficult to design complex wavelet packet transforms with perfect translation invariance. In this paper, based on the aforementioned theorems, novel complex wavelet packet transforms are designed to achieve perfect translation invariance. These complex wavelet packet transforms are based on the Meyer wavelet, which has the important characteristic of possessing a wide range of shapes. In this paper, two types of complex wavelet packet transforms are designed with the optimized Meyer wavelet. One of them is based on a single Meyer wavelet and the other is based on a number of different shapes of the Meyer wavelets to create good localization of wavelet packets.

A New Method for Characterizing Replacement Rate Variation in Molecular Sequences: Application of the Fourier and Wavelet Models to Drosophila and Mammalian Proteins

Genetics ◽  
2000 ◽  
Vol 154 (1) ◽  
pp. 381-395
Author(s):  
Pavel Morozov ◽  
Tatyana Sitnikova ◽  
Gary Churchill ◽  
Francisco José Ayala ◽  
Andrey Rzhetsky
Keyword(s):  
Wavelet Transforms ◽  
Parametric Bootstrap ◽  
Real Data ◽  
New Method ◽  
Rate Variation ◽  
Discrete Wavelet ◽  
Data Sets ◽  
Ratio Test ◽  
Replacement Rate ◽  
New Models

Abstract We propose models for describing replacement rate variation in genes and proteins, in which the profile of relative replacement rates along the length of a given sequence is defined as a function of the site number. We consider here two types of functions, one derived from the cosine Fourier series, and the other from discrete wavelet transforms. The number of parameters used for characterizing the substitution rates along the sequences can be flexibly changed and in their most parameter-rich versions, both Fourier and wavelet models become equivalent to the unrestricted-rates model, in which each site of a sequence alignment evolves at a unique rate. When applied to a few real data sets, the new models appeared to fit data better than the discrete gamma model when compared with the Akaike information criterion and the likelihood-ratio test, although the parametric bootstrap version of the Cox test performed for one of the data sets indicated that the difference in likelihoods between the two models is not significant. The new models are applicable to testing biological hypotheses such as the statistical identity of rate variation profiles among homologous protein families. These models are also useful for determining regions in genes and proteins that evolve significantly faster or slower than the sequence average. We illustrate the application of the new method by analyzing human immunoglobulin and Drosophilid alcohol dehydrogenase sequences.

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