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PubMed2004

Integrated wavelet processing and spatial statistical testing of fMRI data.

We introduce an integrated framework for detecting brain activity from fMRI data, which is based on a spatial discrete wavelet transform. Unlike the standard wavelet-based approach for fMRI analysis, we apply the suitable statistical test procedure in the spatial domain. For a desired significance level, this scheme has one remaining degree of freedom, characterizing the wavelet processing, which is optimized according to the principle of minimal approximation error. This allows us to determine the threshold values in a way that does not depend on data. While developing our framework, we make only conservative assumptions. Consequently, the detection of activation is based on strong evidence. We have implemented this framework as a toolbox (WSPM) for the SPM2 software, taking advantage of multiple options and functions of SPM such as the setup of the linear model and the use of the hemodynamic response function. We show by experimental results that our method is able to detect activation patterns; the results are comparable to those obtained by SPM even though statistical assumptions are more conservative.

Attention↗
PubMed2003

Robust ab initio calculation of condensed matter: transparent convergence through semicardinal multiresolution analysis.

We present the first wavelet-based all-electron density-functional calculations to include gradient corrections and the first in a solid. Direct comparison shows this approach to be unique in providing systematic "transparent" convergence, convergence with a priori prediction of errors, to beyond chemical (millihartree) accuracy. The method is ideal both for exploration of materials under novel conditions where there is little experience with how traditional methods perform and for the development and use of chemically accurate density functionals, which demand access to such precision.

Journal Article↗
PubMed2005

Texture analysis of foot sole soft tissue images in diabetic neuropathy using wavelet transform.

The paper presents a new method of characterisation of texture changes in foot sole soft tissue ultrasound (US) images, as observed to occur in diabetic subjects, using wavelet transforms. US images of the soft tissue subcutaneous layer were taken with a 7.5 MHz linear transducer probe placed parallel to the skin surface. The foot sole hardness was characterised by Shore level. A 2D discrete wavelet transform was performed on the US images to extract features that encode the internal state of the foot sole soft tissue. The global energy feature computed at the output of each wavelet channel was found to achieve excellent delineation between the normal and the diabetic groups. An important finding was a strong correlation, in the order of 0.84 and above, between the feature values that reflect changes in the internal arrangement of the tissue, and the externally measurable hardening of the skin, characterised by the Shore levels, with the latter known to be high for diabetics. A comparison drawn between diabetic ulcer and non-ulcer groups established a change in the order of 122-311% in the textural parameter, as influenced by a corresponding 66.7-200% change in the respective Shore values. Thus US examination of foot sole soft tissue and its texture analysis may serve as sources of valuable information regarding the internal changes taking place with progressive hardening of the soft tissue and thereby help the clinician in taking appropriate preventive measures.

Adult↗
PubMed2004

Wavelet support vector machine.

An admissible support vector (SV) kernel (the wavelet kernel), by which we can construct a wavelet support vector machine (SVM), is presented. The wavelet kernel is a kind of multidimensional wavelet function that can approximate arbitrary nonlinear functions. The existence of wavelet kernels is proven by results of theoretic analysis. Computer simulations show the feasibility and validity of wavelet support vector machines (WSVMs) in regression and pattern recognition.

Journal Article↗
PubMed2002

Wavelet transforming characteristic of a lens.

Based on the wave-front filtering concept of wavelet optics, which we proposed, here we consider that the wave fronts of a light wave are filtered by the lens when the wave fronts pass through the lens. After filtering, the weight of the light field is redistributed, and a Gaussian frequency-modulated complex-valued wavelet function is introduced with the weight function. Subsequent analysis indicates that the lens has a wavelet-transforming characteristic and that the introduction of a Gaussian frequency-modulated complex-valued wavelet function conforms to the actual lens.

Journal Article↗
PubMed1999

Coherence of multiscale features for enhancement of digital mammograms.

Mammograms depict most of the significant changes in breast disease. The primary radiographic signs of cancer are related to tumor mass, density, size, borders, and shape, and local distribution of calcifications. We show that each of these features can be well described by coherence and orientation measures and provide visual cues for radiologists to identify possible lesions more easily without increasing false positives. In this paper, an artifact-free enhancement algorithm based on overcomplete multiscale representations is presented. First, an image was decomposed using a fast wavelet transform algorithm. At each level of analysis, energy and phase information are computed via a set of separable steerable filters. Then, a measure of coherence within each level was obtained by weighting an energy measure with the ratio of projections of local energy within a specified window. Each projection was computed onto the central point of a window with respect to the total energy within that window. Finally, a nonlinear operation, integrating coherence and orientation information, was applied to modify transform coefficients within distinct levels of analysis. These modified coefficients were then reconstructed, via an inverse fast wavelet transform, resulting in an improved visualization of significant mammographic features. The novelty of this algorithm lies in the detection of directional multiscale features and the removal of aliased perturbations. Compared to existing multiscale enhancement techniques, images processed with this method appeared more familiar to radiologists due to localized enhancement of features.

Algorithms↗
PubMed2001

Gamma band activity in an auditory oddball paradigm studied with the wavelet transform.

OBJECTIVES: To examine the characteristics of evoked and induced gamma band oscillatory responses occurring during P300 development in an auditory oddball paradigm. METHODS: A time-frequency analysis method was applied to an auditory oddball paradigm in 7 healthy subjects. This method combines a multiresolution wavelet algorithm for signal extraction and the Gabor transform to represent the temporal evolution of the selected frequency components. Phase-locked or evoked activity and also non-phase-locked activity were computed for both standard and target stimuli. RESULTS: The gamma band frequency components differed between target and non-target stimuli processing. The study showed an early and mainly phase-locked oscillatory response appearing around 26--28 ms after both standard and target stimuli onset. This response showed a spectral peak around 44 Hz for both stimuli. A late oscillatory activity peaking at 37 Hz with a latency around 360 ms was observed appearing only for target stimuli. The latency of this late oscillatory activity had a high correlation (P=0.002) to the latency of the P300 wave. CONCLUSIONS: EEG signal analysis with wavelet transform allows the identification of an early oscillatory cortical response in the gamma frequency range, as well as a late P300-related response.

Acoustic Stimulation↗
PubMed2006

Application of wavelet-based tools to study the dynamics of biological processes.

The article makes use of three different examples (sensory information processing in the rat trigeminal complex, intracellular interaction in snail neurons and multimodal dynamics in nephron autoregulation) to demonstrate how modern approaches to time-series analysis based on the wavelet-transform can provide information about the underlying complex biological processes.

Animals↗
PubMed2006

Motion compensation via redundant-wavelet multihypothesis.

Multihypothesis motion compensation has been widely used in video coding with previous attention focused on techniques employing predictions that are diverse spatially or temporally. In this paper, the multihypothesis concept is extended into the transform domain by using a redundant wavelet transform to produce multiple predictions that are diverse in transform phase. The corresponding multiple-phase inverse transform implicitly combines the phase-diverse predictions into a single spatial-domain prediction for motion compensation. The performance advantage of this redundant-wavelet-multihypothesis approach is investigated analytically, invoking the fact that the multiple-phase inverse involves a projection that significantly reduces the power of a dense-motion residual modeled as additive noise. The analysis shows that redundant-wavelet multihypothesis is capable of up to a 7-dB reduction in prediction-residual variance over an equivalent single-phase, single-hypothesis approach. Experimental results substantiate the performance advantage for a block-based implementation.

Algorithms↗
PubMed2005

Raman spectroscopy for diagnosis of atherosclerosis: a rapid analysis using neural networks.

Near-infrared Raman spectroscopy (NIRS) is one of the novel techniques that has a potential for in vivo diagnosis of atherosclerosis in human arteries. For such real time clinical applications, a rapid collection and analysis of the data is needed. One of the major problems with the fast data collection is that the noise generated by the detector has the same level as the Raman signal from the tissue, which makes the analysis difficult. In this work, NIRS measurements have been carried out on a total of 60 samples from human coronary arteries. Raman spectral data with the correlated histopathological analysis have been used as a basis to stimulate the cases of severe noise conditions. The main objective of this paper is the comparison of different processing algorithms that have been developed based on either wavelet transformation or principal component analysis for compressing the Raman spectral vectors and a rapid data classification based on different neural network architectures. The developed algorithms found to provide promising diagnosis results with classification errors smaller than 5%, even in the cases of Raman data with collection times as small as 20 ms. It has been concluded that the developed algorithms would be very much useful in the development of Raman spectroscopy systems for in vivo biological applications.

Algorithms↗
PubMed2006

A method to produce evolving functional connectivity maps during the course of an fMRI experiment using wavelet-based time-varying Granger causality.

Functional magnetic resonance imaging (fMRI) is widely used to identify neural correlates of cognitive tasks. However, the analysis of functional connectivity is crucial to understanding neural dynamics. Although many studies of cerebral circuitry have revealed adaptative behavior, which can change during the course of the experiment, most of contemporary connectivity studies are based on correlational analysis or structural equations analysis, assuming a time-invariant connectivity structure. In this paper, a novel method of continuous time-varying connectivity analysis is proposed, based on the wavelet expansion of functions and vector autoregressive model (wavelet dynamic vector autoregressive-DVAR). The model also allows identification of the direction of information flow between brain areas, extending the Granger causality concept to locally stationary processes. Simulation results show a good performance of this approach even using short time intervals. The application of this new approach is illustrated with fMRI data from a simple AB motor task experiment.

Adult↗
PubMed2000

Identification of post-myocardial infarction patients prone to ventricular tachycardia using time-frequency analysis of QRS and ST segments.

BACKGROUND: Late potentials (LPs) in the terminal portion of the QRS complex are commonly sought to identify post-myocardial infarction patients prone to ventricular tachyarrthythmias (VT) or sudden death. More recent time frequency signal processing tools have been shown to provide new parameters for the quantification of LPs and abnormal activities buried within the QRS complex. METHODS AND RESULTS: The study population comprised 23 myocardial infarction patients with documented sustained VT (MI+VT), 40 myocardial infarction patients without VT (MI - VT) and 31 normal subjects. The reproducibility of the method was tested in an additional set of 66 patients. The signal-averaged high-resolution electrocardiograms (HRECGs) were quantified by deconstructing the unfiltered X, Y and Z leads using a 511-orthogonal wavelet network. Using receiver operating characteristics (ROC) curves and discriminant analysis applied to the wavelet coefficients, we extracted the most significant wavelets to classify the post MI patients. These wavelets detected time-frequency alterations both in the ST segment and within the QRS complex, characterizing patients prone to VTs. The same statistical methods were applied to the conventional time-domain measurements. The combined application in our population of the orthogonal wavelet deconstruction method and discriminant analysis had 91% sensitivity and 95% specificity, an improvement of 22% and 25%, respectively, compared with the conventional time domain method. Reproducibility was 82%. CONCLUSIONS: In post-myocardial infarction patients, orthogonal wavelet transforms can detect alterations in high-frequency components within the QRS and ST segment. Our findings support the view that wavelet-related parameters are more relevant than those of the time domain method in predicting subsequent malignant tachyarrhythmias.

Adult↗
PubMed2005

Dynamic scaling form in wavelet-discriminated Edwards-Wilkinson growth equation.

We present an analysis of dynamic scaling of the Edwards-Wilkinson growth model from wavelets' perspective. Scaling function for the surface width is determined using wavelets' formalism, by computing the surface width for each wavelet scale, we show that an exact and simple form of the scaling function is obtained. These predictions are confirmed by computer simulation of a growth model described by the EW equation, and by numerical calculations.

Journal Article↗
PubMed1998

Evaluation of EMG signals from rehabilitated patients with lower back pain using wavelets.

This paper reports the preliminary results of an analysis of surface EMG signals obtained from rehabilitated patients with lower back problems using discrete wavelet transform techniques. In our study, 12 patients with lower back pain were tested before and after rehabilitation. The reaction time difference (before and after rehabilitation) from the erector spinae muscle caused by sudden loading was determined. The results indicated that the reaction time after rehabilitation was shorter than that before rehabilitation for about 45% of the tested cases.

Artifacts↗
PubMed2005

Automated detection of elementary calcium release events using the á trous wavelet transform.

We developed an algorithm for the automated detection and analysis of elementary Ca2+ release events (ECRE) based on the two-dimensional nondecimated wavelet transform. The transform is computed with the "à trous" algorithm using the cubic B-spline as the basis function and yields a multiresolution analysis of the image. This transform allows for highly efficient noise reduction while preserving signal amplitudes. ECRE detection is performed at the wavelet levels, thus using the whole spectral information contained in the image. The algorithm was tested on synthetic data at different noise levels as well as on experimental data of ECRE. The noise dependence of the statistical properties of the algorithm (detection sensitivity and reliability) was determined from synthetic data and detection parameters were selected to optimize the detection of experimental ECRE. The wavelet-based method shows considerably higher detection sensitivity and less false-positive counts than previously employed methods. It allows a more efficient detection of elementary Ca2+ release events than conventional methods, in particular in the presence of elevated background noise levels. The subsequent analysis of the morphological parameters of ECRE is reliably reproduced by the analysis procedure that is applied to the median filtered raw data. Testing the algorithm more rigorously showed that event parameter histograms (amplitude, rise time, full duration at half-maximum, and full width at half-maximum) were faithfully extracted from synthetic, "in-focus" and "out-of-focus" line scan sparks. Most importantly, ECRE obtained with laser scanning confocal microscopy of chemically skinned mammalian skeletal muscle fibers could be analyzed automatically to reproducibly establish event parameter histograms. In summary, our method provides a new valuable tool for highly reliable automated detection of ECRE in muscle but can also be adapted to other preparations.

Algorithms↗