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PubMed2005

Efficient determination of cluster boundaries for analysis of gene expression profile data using hierarchical clustering and wavelet transform.

The existing methods for clustering of gene expression profile data either require manual inspection and other biological knowledge or require some cut-off value which can not be directly calculated from the given data set. Thus, the problem of systematic and efficient determination of cluster boundaries of clusters in gene expression profile data still remains demanding. In this context, we have developed a procedure for automatic and systematic determination of the boundaries of clusters in the hierarchical clustering of gene expression data based on the ratio of with-in class variance and between-class variance, which can be fully calculated from the given expression data. After the determination of dendrogram based on agglomerative hierarchical clustering, this ratio is used to determine the cluster boundary. Except this ratio which can be completely calculated from the given expression profile data, unlike other existing approaches, our approach does not require any manual inspection or biological knowledge. Our results are favorably comparable and in some of cases better than existing method which does not utilize prior information or manual inspection. Moreover, gene expression profile data are often contaminated with various type of noise and in order to reduce this noise content, we have also applied image enhancing technique called discrete wavelet transform. We tested a number of mother wavelet functions to smooth the noise in the gene expression data set and obtained some improvements in the quality of the results.

Algorithms↗
PubMed2004

Wavelets and functional magnetic resonance imaging of the human brain.

The discrete wavelet transform (DWT) is widely used for multiresolution analysis and decorrelation or "whitening" of nonstationary time series and spatial processes. Wavelets are naturally appropriate for analysis of biological data, such as functional magnetic resonance images of the human brain, which often demonstrate scale invariant or fractal properties. We provide a brief formal introduction to key properties of the DWT and review the growing literature on its application to fMRI. We focus on three applications in particular: (i) wavelet coefficient resampling or "wavestrapping" of 1-D time series, 2- to 3-D spatial maps and 4-D spatiotemporal processes; (ii) wavelet-based estimators for signal and noise parameters of time series regression models assuming the errors are fractional Gaussian noise (fGn); and (iii) wavelet shrinkage in frequentist and Bayesian frameworks to support multiresolution hypothesis testing on spatially extended statistic maps. We conclude that the wavelet domain is a rich source of new concepts and techniques to enhance the power of statistical analysis of human fMRI data.

Algorithms↗
PubMed2004

Wavelet-based processing of neuronal spike trains prior to discriminant analysis.

Investigations of neural coding in many brain systems have focused on the role of spike rate and timing as two means of encoding information within a spike train. Recently, statistical pattern recognition methods, such as linear discriminant analysis (LDA), have emerged as a standard approach for examining neural codes. These methods work well when data sets are over-determined (i.e., there are more observations than predictor variables). But this is not always the case in many experimental data sets. One way to reduce the number of predictor variables is to preprocess data prior to classification. Here, a wavelet-based method is described for preprocessing spike trains. The method is based on the discriminant pursuit (DP) algorithm of Buckheit and Donoho [Proc. SPIE 2569 (1995) 540-51]. DP extracts a reduced set of features that are well localized in the time and frequency domains and that can be subsequently analyzed with statistical classifiers. DP is illustrated using neuronal spike trains recorded in the motor cortex of an awake, behaving rat [Laubach et al. Nature 405 (2000) 567-71]. In addition, simulated spike trains that differed only in the timing of spikes are used to show that DP outperforms another method for preprocessing spike trains, principal component analysis (PCA) [Richmond and Optican J. Neurophysiol. 57 (1987) 147-61].

Action Potentials↗
PubMed2001

Wavelets and imaging informatics: a review of the literature.

Modern medicine is a field that has been revolutionized by the emergence of computer and imaging technology. It is increasingly difficult, however, to manage the ever-growing enormous amount of medical imaging information available in digital formats. Numerous techniques have been developed to make the imaging information more easily accessible and to perform analysis automatically. Among these techniques, wavelet transforms have proven prominently useful not only for biomedical imaging but also for signal and image processing in general. Wavelet transforms decompose a signal into frequency bands, the width of which are determined by a dyadic scheme. This particular way of dividing frequency bands matches the statistical properties of most images very well. During the past decade, there has been active research in applying wavelets to various aspects of imaging informatics, including compression, enhancements, analysis, classification, and retrieval. This review represents a survey of the most significant practical and theoretical advances in the field of wavelet-based imaging informatics.

Algorithms↗
PubMed2000

Wavelets in temporal and spatial processing of biomedical images.

We review some of the most recent advances in the area of wavelet applications in medical imaging. We first review key concepts in the processing of medical images with wavelet transforms and multiscale analysis, including time-frequency tiling, overcomplete representations, higher dimensional bases, symmetry, boundary effects, translational invariance, orientation selectivity, and best-basis selection. We next describe some applications in magnetic resonance imaging, including activation detection and denoising of functional magnetic resonance imaging and encoding schemes. We then present an overview in the area of ultrasound, including computational anatomy with three-dimensional cardiac ultrasound. Next, wavelets in tomography are reviewed, including their relationship to the radon transform and applications in position emission tomography imaging. Finally, wavelet applications in digital mammography are reviewed, including computer-assisted diagnostic systems that support the detection and classification of small masses and methods of contrast enhancement.

Algorithms↗
PubMed2002

Semi-automation of the 3D reconstruction of the spine using wavelets and splines.

We propose a wavelet multi-resolution analysis to localize specific features in both lateral and frontal radiographs. This analysis allows an elegant spectral investigation that leads simultaneously to image de-noising and edge extraction. It is combined with an a priori knowledge of the spine's morphology and a 3D spline curve characterization of its global shape. Actual work deals with identifying the contours of the vertebral bodies and the localization of vertebrae's endplates. However, this information could also lead to the selection of a 3D statistical model of the spine suited for the studied deformation. Working with retro-projections of the model, we aim at creating edge models for each vertebra that will be used to geometrically match the wavelet's edges. The manual feature identification could then be replaced in the reconstruction of the 3D representation of the spine.

Algorithms↗
PubMed1996

Predictive value of wavelet correlation functions of signal-averaged electrocardiogram in patients after anterior versus inferior myocardial infarction.

OBJECTIVES: This study sought to evaluate the prognostic value of wavelet correlation functions of the signal-averaged electrocardiogram (ECG) for arrhythmic events in patients after myocardial infarction. BACKGROUND: Wavelet transform of the signal-averaged ECG has been shown to be a nonstationary analysis technique describing the time evolution of frequency spectra throughout the QRS complex. To quantify the wavelet transform, we introduced the new concept of the wavelet correlation function. METHODS: The relation among wavelet correlation functions, ventricular late potentials and the site of infarction was investigated in 769 men < 66 years old who survived the acute phase of myocardial infarction (351 [46%] anterior, 418 [54%] inferior infarctions). Signal-averaged ECG recordings were obtained 2 to 3 weeks after infarction. During 6 months of follow-up, 33 patients (4.3%) experienced a malignant arrhythmic event. Wavelet correlation functions of the signal-averaged ECG were evaluated in a time-frequency plane ranging from 25 ms before QRS onset to 25 ms after QRS offset in the frequency range between 40 and 100 Hz. RESULTS: Patients with an anterior infarction had lower mean wavelet correlation coefficients (p < 0.001) and a lower incidence of ventricular late potentials than patients with an inferior infarction (32.3% vs. 42.7%, p = 0.003). The combination of wavelet correlation functions and late potentials increased the total predictive accuracy from 52% to 72% for inferior and from 64% to 76% for anterior infarctions. CONCLUSIONS: Spectral changes in the signal-averaged QRS complex are more prominent in anterior than inferior infarctions. Combination of late potential analysis and wavelet correlation functions increases the prognostic value for serious arrhythmic events after myocardial infarction.

Adult↗
PubMed2025

CaLMPhosKAN: prediction of general phosphorylation sites in proteins via fusion of codon aware embeddings with amino acid aware embeddings and wavelet-based Kolmogorov-Arnold network.

MOTIVATION: The mapping from codon to amino acid is surjective due to codon degeneracy, suggesting that codon space might harbor higher information content. Embeddings from the codon language model have recently demonstrated success in various protein downstream tasks. However, predictive models for residue-level tasks such as phosphorylation sites, arguably the most studied Post-Translational Modification (PTM), and PTM sites prediction in general, have predominantly relied on representations in amino acid space. RESULTS: We introduce a novel approach for predicting phosphorylation sites by utilizing codon-level information through embeddings from the codon adaptation language model (CaLM), trained on protein-coding DNA sequences. Protein sequences are first reverse-translated into reliable coding sequences by mapping UniProt sequences to their corresponding NCBI reference sequences and extracting the exact coding sequences from their GenBank format using a dynamic programming-based global pairwise alignment. The resulting coding sequences are encoded using the CaLM encoder to generate codon-aware embeddings, which are subsequently integrated with amino acid-aware embeddings obtained from a protein language model, through an early fusion strategy. Next, a window-level representation of the site of interest, retaining the full sequence context, is constructed from the fused embeddings. A ConvBiGRU network extracts feature maps that capture spatiotemporal correlations between proximal residues within the window. This is followed by a prediction head based on a Kolmogorov-Arnold network (KAN) using the derivative of gaussian wavelet transform to generate the inference for the site. The overall model, dubbed CaLMPhosKAN, performs better than the existing approaches across multiple datasets. AVAILABILITY AND IMPLEMENTATION: CaLMPhosKAN is publicly available at https://github.com/KCLabMTU/CaLMPhosKAN.

Codon↗
PubMed1989

Fast activity and oscillatory potential of carp retina in the frequency domain.

There are two kinds of fast activity in the ERG: fast retinal potentials (FRP), an irregular series of spiky wavelets and oscillatory potentials (OP), a rhythmic sequence of events. Corneal ERG from nine intact young carps, evoked by extended pulses of diffuse white light under mesopic adaptation, displayed two different groups of wavelets related to ON and OFF, respectively. Stimulation and recording conditions were established to permit separate Fourier analysis of both groups of wavelets. Power distributions of normalized ON spectra showed both a wide dispersion and a high inter-subject variability. All normalized OFF spectra showed, instead, components within a narrow band from 52 to 56 Hz, most of them maximum relative power peaks. It is concluded that FRP originating in highly labile sources dominate ON fast activity, while the predominant OFF fast activity are OP originating in a stable discrete source.

Animals↗
PubMed2006

[Electrocardiographic signal feature extraction and its instrument development based on continuous wavelet transform].

This paper introduces a virtual recording and analysis instrumentation system for recording and identifying electrocardiographic (ECG) signals. The system developed is aimed at constructing a PC-based virtual instrumentation which enables to record. investigate and measure the ECG signal of 12 leads simultaneously and perfectly in order to improve the measuring precision of ECG. Based on the proper feature in time domain of Mexican hat wavelet expressed by positioning and analysis precision for QRS complex, the instrumentation system uses continuous wavelet transform(CWT) and uses the Mexican hat as the wavelet base to measure precisely the characteristic information and generate the precise characteristic parameters of ECG. The analysis of measured ECG signals in hospital demonstrated that even in the condition with serious noise interference, the method presented is still easily to describe the characteristics of ECG on line precisely which makes the instrumentation system valuable in practical application.

Algorithms↗
PubMedDate not supplied

Introduction of wavelet analyses to rainfall/runoffs relationship for a karstic basin: the case of Licq-Atherey karstic system (France).

Karstic systems are highly heterogeneous geological formations characterized by a multiscale temporal and spatial hydrologic behavior with more or less localized temporal and spatial structures. Classical correlation and spectral analyses cannot take into account these properties. Therefore, it is proposed to introduce a new kind of transformation: the wavelet transform. Here we focus particularly on the use of wavelets to study temporal behavior of local precipitation and watershed runoffs from a part of the karstic system. In the first part of the paper, a brief mathematical overview of the continuous Morlet wavelet transform and of the multiresolution analysis is presented. An analogy with spectral analyses allows the introduction of concepts such as wavelet spectrum and cross-spectrum. In the second part, classical methods (spectral and correlation analyses) and wavelet transforms are applied and compared for daily rainfall rates and runoffs measured on a French karstic watershed (Pyrénées) over a period of 30 years. Different characteristic time scales of the rainfall and runoff processes are determined. These time scales are typically on the order of a few days for floods, but they also include significant half-year and one-year components and multi-annual components. The multiresolution cross-analysis also provides a new interpretation of the impulse response of the system. To conclude, wavelet transforms provide a valuable amount of information, which may be now taken into account in both temporal and spatially distributed karst modeling of precipitation and runoff.

Disasters↗
PubMed1996

Interpretation of calcifications in screen/film, digitized, and wavelet-enhanced monitor-displayed mammograms: a receiver operating characteristic study.

RATIONALE AND OBJECTIVES: The acceptance of filmless digital mammography is currently limited by digitization and display drawbacks, as well as bias toward hard-copy interpretation. In the current study, we evaluated a wavelet-based image enhancement method for the filmless interpretation of breast calcifications. METHODS: A set of 100 mammograms (58 with calcification clusters) was digitized at 105 microns and 4,096 gray levels per pixel and was processed with nonlinear filters and wavelets. Standard receiver operating characteristic analysis was performed by four radiologists, who independently read the films, the unprocessed digital images, and unprocessed and wavelet-enhanced digital images presented simultaneously. RESULTS: Statistical differences were observed between screen/film and unprocessed digitized mammography displayed on monitors. Differences were not significant when wavelet enhancement was included in the monitor display. Interobserver variation in the digitized reading was greater than in film reading, but the wavelet enhancement reduced the difference. CONCLUSION: Wavelet-enhanced digital mammograms may assist radiologists in diagnosing calcifications directly from computer monitors and may compensate for current technologic limitations. A study with a larger data-base is needed before this method is accepted for clinical use.

Breast Diseases↗
PubMed1999

Estimation of latency changes and relative amplitudes in somatosensory evoked potentials using wavelets and regression.

Changes in onset latency and relative amplitudes of somatosensory evoked potentials (SEP) may be a convenient and reliable neurophysiological indicator of depth of anesthesia. However, to derive the components is very difficult mathematically and visual inspection or alternatively the peak-latency estimation is usually employed. A methodology for estimating the components was developed for both real-time and off-line applications based on the combination of the wavelet transforms (WT), geometric analysis, artificial intelligence (AI), and mathematical analysis of the first positive wave of SEPs. The WT together with AI constitutes a feature extraction engine for localizing the first positive peak and negative valley and hence relative amplitudes. The latency change between two averages is obtained by shifting one average toward another to achieve a best match along the positive inflections. The inflection, based on the peak, is modeled as a regression line and is refined using a steepness inference algorithm. Results from simulation and anesthetized rats show that it is reliable in comparison with visual inspection, robust to amplitude variation and signal distortion, and efficient in computation, and hence it is suitable for automation. Comparisons of interobserver variability and analysis of method agreement suggest that the method can be used as a substitute for estimations by visual inspection.

Algorithms↗
PubMed2004

Attention to a painful cutaneous laser stimulus modulates electrocorticographic event-related desynchronization in humans.

OBJECTIVE: To test the hypothesis that attention to painful cutaneous laser stimuli enhances event-related desynchronization (ERD) in cortical regions receiving nociceptive input. METHODS: We used wavelet time-frequency analysis and bandpass filtering to measure ERD quantitatively in subdural electrocorticographic recordings while subjects either attended to, or were distracted from, a painful cutaneous laser stimulus. RESULTS: ERD were observed over primary somatosensory and parasylvian (PS) cortices in all 4 subjects, and over medial frontal cortex in 1 subject. Laser-evoked potentials were also observed in all 3 regions. In all subjects, ERD was more widespread and intense, particularly over PS, during attention to laser stimuli (counting stimuli) than during distraction from the stimuli (reading for comprehension). CONCLUSIONS: These findings suggest that pain-associated ERD is modulated by attention, particularly over PS. SIGNIFICANCE: This study suggests that thalamocortical circuits are involved in attentional modulation of pain because of the proposed role of these circuits in the mechanisms of ERD.

Adult↗
PubMed2005

Ultrasonic vibration dectection with wavelets: preliminary results.

Several arterial disorders are known to cause systolic audio vibrations in tissue: they include stenoses, vasospasm, aneurysms, bleeds and arteriovenous fistulas. High-amplitude vibrations can be discovered with conventional Doppler ultrasound (US) instruments; however, differentiating brief, low-amplitude vibrations from other nonstationary echo sources is difficult. Further, characterizing the frequency and amplitude of vibrations is not feasible with conventional Doppler US. The automated detection and estimation of both the frequency and amplitude of vibrations with durations less than 100 ms and amplitudes of a micrometer or less have remained a signal-processing challenge. These vibrations may be associated with both nonstationary colored noise and strong low-frequency clutter. The normalized continuous Morlet wavelet power-spectrum analysis of quadrature Doppler echoes, followed by a binary hypothesis test for noise, results in simulated detection rates above 99.9%, with 0.1% false alarms for signal-on signal-to-noise ratios (SNRs) as low as one. Two clinical examples are included.

Algorithms↗
PubMed2001

Perception of pain coincides with the spatial expansion of electroencephalographic dynamics in human subjects.

The dynamics of cortex driven by painful median nerve stimulation were investigated in event-related oscillation (ERO). We applied a wavelet time-frequency analysis to differentiate the brain dynamics between painful and non-painful somatosensory stimulation. The observed pattern to pain-induced effects exhibited a stepwise decrease of frequencies over time, starting around 26 ms over somatosensory cortex at 80 Hz, intermediate oscillations at 40 and 20 Hz around 40 ms, and reaching down to 10 Hz after 160 ms. This step-wise frequency decrease of ERO, coincident with spatial shift from the contralateral somatosensory area at 80 Hz to the centro-frontal brain at 40/20 Hz and final spatial expansion to the large region of centro-parietal areas at 10 Hz, may represent the cortical processes necessary to transfer sensory information from perceptual stages to subsequent cognitive stages in consciousness.

Adult↗
PubMedDate not supplied

Early online detection of upper airway obstructions in obstructive sleep apnoea syndrome (OSAS) patients.

The obstructive sleep apnoea syndrome (OSAS) is a diagnosis related to snoring and caused by a collapse in the upper airway. OSAS patients suffer from desaturated oxygen levels during sleep as well as daytime sleepiness. In this paper, we propose a system able to identify and detect respiratory disorders online based on monitoring the airflow amplitude from a sleeping OSAS patient. By the use of chi(2)-analysis and a Haar wavelet transform on signals performed offline, reference templates indicating the specific apnoea pattern for four different patients are constructed and used for similarity matching against online signals. Detection is performed in the early stages of an upcoming airway dysfunction, thus providing an opportunity to alert the patient at sleep. The system-testing results indicate robust performance and flexibility for the patient. Our proposed solution can in turn operate as an alternative to today's OSAS treatment of choice, the continuous positive airway pressure (CPAP).

Airway Obstruction↗
PubMed1996

Quantitative Inspection of Broken Wire in Wire Ropes: Method and Apparatus.

This article introduces a complete system for automatic inspection of broken wire in wire ropes. The development of this technique is reviewed. It is followed by a description of the hardware and software of the apparatus. The hardware uses magnetic concentrators and Hall-effect sensors. Signal analysis is based on wavelet processing. Quantitative identification of broken wire in wire ropes is based on a pattern recognition approach of the neural network.

magnetic concentration detector↗