Multichannel Compressive Sensing MRI Using Noiselet Encoding

The incoherence between measurement and sparsifying transform matrices and the restricted isometry property (RIP) of measurement matrix are two of the key factors in determining the performance of compressive sensing (CS). In CS-MRI, the randomly under-sampled Fourier matrix is used as the measurement matrix and the wavelet transform is usually used as sparsifying transform matrix. However, the incoherence between the randomly under-sampled Fourier matrix and the wavelet matrix is not optimal, which can deteriorate the performance of CS-MRI. Using the mathematical result that noiselets are maximally incoherent with wavelets, this paper introduces the noiselet unitary bases as the measurement matrix to improve the incoherence and RIP in CS-MRI. Based on an empirical RIP analysis that compares the multichannel noiselet and multichannel Fourier measurement matrices in CS-MRI, we propose a multichannel compressive sensing (MCS) framework to take the advantage of multichannel data acquisition used in MRI scanners. Simulations are presented in the MCS framework to compare the performance of noiselet encoding reconstructions and Fourier encoding reconstructions at different acceleration factors. The comparisons indicate that multichannel noiselet measurement matrix has better RIP than that of its Fourier counterpart, and that noiselet encoded MCS-MRI outperforms Fourier encoded MCS-MRI in preserving image resolution and can achieve higher acceleration factors. To demonstrate the feasibility of the proposed noiselet encoding scheme, a pulse sequences with tailored spatially selective RF excitation pulses was designed and implemented on a 3T scanner to acquire the data in the noiselet domain from a phantom and a human brain. The results indicate that noislet encoding preserves image resolution better than Fouirer encoding.     

Time/frequency events of surface mechanomyographic signals resolved by nonlinearly scaled wavelets

The purpose of this investigation is to introduce a wavelet analysis designed for analyzing short events reflecting bursts of muscle activity in non-stationary mechanomyographic (MMG) signals. A filter bank of eleven nonlinearly scaled wavelets that maintain the optimal combination of time and frequency resolution across the frequency range of MMG signals (5–100 Hz) was used for the analysis. A comparison with the short-time Fourier transform, Wigner-Ville transform and continuous wavelet transform using a test signal with known time–frequency characteristics showed that the MMG wavelet analysis resolved the intensity, timing, and frequencies of events in a more distinct way without overemphasizing high or low frequencies or generating interference terms. The analysis was used to process MMG signals from the vastus lateralis, rectus femoris, and vastus medialis muscles obtained during maximal concentric and eccentric isokinetic movements. Muscular events were observed that were precisely located in time and frequency in a muscle-specific way, thereby showing periods of synergistic contractions of the quadriceps muscles. The MMG wavelet spectra showed different spectral bands for concentric and eccentric isokinetic movements. In addition, the high and low frequency bands seemed to be activated independently during the isokinetic movement. What generates these bands is not yet known, however, the MMG wavelet analysis was able to resolve them, and is therefore applicable to non-stationary MMG signals.     

Time-frequency analysis of phonocardiogram signals using wavelet transform: a comparative study

Analysis of phonocardiogram (PCG) signals provides a non-invasive means to determine the abnormalities caused by cardiovascular system pathology. In general, time-frequency representation (TFR) methods are used to study the PCG signal because it is one of the non-stationary bio-signals. The continuous wavelet transform (CWT) is especially suitable for the analysis of non-stationary signals and to obtain the TFR, due to its high resolution, both in time and in frequency and has recently become a favourite tool. It decomposes a signal in terms of elementary contributions called wavelets, which are shifted and dilated copies of a fixed mother wavelet function, and yields a joint TFR. Although the basic characteristics of the wavelets are similar, each type of the wavelets produces a different TFR. In this study, eight real types of the most known wavelets are examined on typical PCG signals indicating heart abnormalities in order to determine the best wavelet to obtain a reliable TFR. For this purpose, the wavelet energy and frequency spectrum estimations based on the CWT and the spectra of the chosen wavelets were compared with the energy distribution and the autoregressive frequency spectra in order to determine the most suitable wavelet. The results show that Morlet wavelet is the most reliable wavelet for the time-frequency analysis of PCG signals.     

Wavelet transform as a potential tool for ECG analysis and compression

The recently introduced wavelet transform is a member of the class of time-frequency representations which include the Gabor short-time Fourier transform and Wigner-Ville distribution. Such techniques are of significance because of their ability to display the spectral content of a signal as time elapses. The value of the wavelet transform as a signal analysis tool has been demonstrated by its successful application to the study of turbulence and processing of speech and music. Since, in common with these subjects, both the time and frequency content of physiological signals are often of interest (the ECG being an obvious example), the wavelet transform represents a particularly relevant means of analysis. Following a brief introduction to the wavelet transform and its implementation, this paper describes a preliminary investigation into its application to the study of both ECG and heart rate variability data. In addition, the wavelet transform can be used to perform multiresolution signal decomposition. Since this process can be considered as a sub-band coding technique, it offers the opportunity for data compression, which can be implemented using efficient pyramidal algorithms. Results of the compression and reconstruction of ECG data are given which suggest that the wavelet transform is well suited to this task.     

The Influence of Wavelets on Multiscale Analysis and Parametrization of Midlatency Auditory Evoked Potentials

This work shows methodological aspects of heuristic pattern recognition in auditory evoked potentials. A linear and a nonlinear transformation based on wavelet transform are presented. They result in a statistical error model and an entropy function related to the Gibbs function and describe changes in midlatency auditory evoked potentials induced by general anaesthesia. The same transformations were calculated using 12 common wavelets. We present a method to compare the two defined parametrizations with respect to their ability to discriminate two defined states which is responsive and unresponsive depending on the wavelet used for the analysis. Auditory evoked potentials of 60 patients undergoing general anaesthesia were analysed. We propose the defined statistical error model and the entropy function as a very robust measure of changes in auditory evoked potentials. The influence of the wavelets suggest that for each parametrization the goodness of the wavelet should be validated.     

Wavelet transform to quantify heart rate variability and to assess its instantaneous changes.

Heart rate variability is a recognized parameter for assessing autonomous nervous system activity. Fourier transform, the most commonly used method to analyze variability, does not offer an easy assessment of its dynamics because of limitations inherent in its stationary hypothesis. Conversely, wavelet transform allows analysis of nonstationary signals. We compared the respective yields of Fourier and wavelet transforms in analyzing heart rate variability during dynamic changes in autonomous nervous system balance induced by atropine and propranolol. Fourier and wavelet transforms were applied to sequences of heart rate intervals in six subjects receiving increasing doses of atropine and propranolol. At the lowest doses of atropine administered, heart rate variability increased, followed by a progressive decrease with higher doses. With the first dose of propranolol, there was a significant increase in heart rate variability, which progressively disappeared after the last dose. Wavelet transform gave significantly better quantitative analysis of heart rate variability than did Fourier transform during autonomous nervous system adaptations induced by both agents and provided novel temporally localized information.     

The use of the Mexican Hat and the Morlet wavelets for detection of ecological patterns

In this paper, we compare the relationship between scale and period in ecological pattern analysis and wavelet analysis. We also adapt a commonly used wavelet, the Morlet, to ecological pattern analysis. Using Monte Carlo assessments, we apply methods of statistical significance test to wavelet analysis for pattern analysis. In order to understand the inherent strength and weakness of the Morlet and the Mexican Hat wavelets, we also investigate and compare the properties of two frequently used wavelets by testing with field data and four artificial transects of different typical patterns which is often encountered in ecological research. It is shown that the Mexican Hat provides better detection and localization of patch and gap events over the Morlet, whereas the Morlet offers improved detection and localization of scale over the Mexican Hat. There is always a trade-off between the detection and localization of scale versus patch and gap events. Therefore, the best composite analysis is the combination of their advantages. The properties of wavelet in dealing with ecological data may be affected by characteristics intrinsic to wavelet itself. The peaks of different scales in isograms of wavelet power spectrum from the Mexican Hat may overlap with each other. Alternatively, these peaks of different scales in isograms of wavelet power spectrum may combine with each other unless the size of the analyzed scales is significantly different. These overlapping or combining lead to combining of peaks for different scales, or the masking of trough between peaks of different scales in the scalogram. Ecologists should combine all the information in scalogram and isograms of wavelet coefficient and wavelet power spectrum from different wavelets, which can provide us a broader view and precise pattern information.     

Discrete wavelet transform: a tool in smoothing kinematic data

Motion analysis systems typically introduce noise to the displacement data recorded. Butterworth digital filters have been used to smooth the displacement data in order to obtain smoothed velocities and accelerations. However, this technique does not yield satisfactory results, especially when dealing with complex kinematic motions that occupy the low- and high-frequency bands. The use of the discrete wavelet transform, as an alternative to digital filters, is presented in this paper. The transform passes the original signal through two complementary low- and high-pass FIR filters and decomposes the signal into an approximation function and a detail function. Further decomposition of the signal results in transforming the signal into a hierarchy set of orthogonal approximation and detail functions. A reverse process is employed to perfectly reconstruct the signal (inverse transform) back from its approximation and detail functions. The discrete wavelet transform was applied to the displacement data recorded by Pezzack et al., 1977. The smoothed displacement data were twice differentiated and compared to Pezzack et al.'s acceleration data in order to choose the most appropriate filter coefficients and decomposition level on the basis of maximizing the percentage of retained energy (PRE) and minimizing the root mean square error (RMSE). Daubechies wavelet of the fourth order (Db4) at the second decomposition level showed better results than both the biorthogonal and Coiflet wavelets (PRE = 97.5%, RMSE = 4.7 rad s-2). The Db4 wavelet was then used to compress complex displacement data obtained from a noisy mathematically generated function. Results clearly indicate superiority of this new smoothing approach over traditional filters.     

Evaluation of texture features in spatial and frequency domain for automatic discrimination of histologic tissue

OBJECTIVE: To investigate the applicability of different texture features in automatic discrimination of microscopic views from benign common nevi and malignant melanoma lesions. STUDY DESIGN: In tissue counter analysis (TCA) the images are dissected into square elements used for feature calculation. The first class of features is based on the histogram, the co-occurrence matrix and the texture moments. The second class is derived from spectral properties of the wavelet Daubechie 4 and the Fourier transform. Square elements from images of a training set are classified by Classification and Regression Trees analysis. RESULTS: Features from the histogram and the co-occurrence matrix enable correct classification of 94.7% of nevi elements and 92.6% of melanoma elements in the training set. Classification results are applied to individual test set cases. Discriminant analysis based on the percentage of "malignant elements" showed correct classification of all nevi cases and 95% of melanoma cases. Features derived from the wavelet and Fourier spectrum showed correct results for 88.8% and 79.3% of nevi and 85.6% and 81.5% of melanoma elements, respectively. CONCLUSION: TCA is a potential diagnostic tool in automatic analysis of melanocytic skin tumors. Histogram and co-occurrence matrix features are superior to the wavelet and the Fourier features.     

Relationship Between Time- and Frequency-Domain Analyses of Angular Head Movements in the Squirrel Monkey

We used the three-dimensional magnetic search-coil recording technique to study the range of active angular head movements made by squirrel monkeys. There were two goals in this study: (1) to determine the range of angular velocities and accelerations as well as the bandwidth and other frequency characteristics of active head movements and (2) to compare analyses of transients of velocity and acceleration that are studied by residual analysis, Fourier transform, and wavelet transform of the head velocity signal.The residual analysis showed that the shape and duration of the transients affected the bandwidth. During the time after the head had begun to accelerate, the frequency content of the head movement extended into the range of 6 to 12 Hz. When considering all three planes of rotation, approximately 75% of the transients had peak acceleration between 2,000 and 10,000 deg/s² and a peak velocity of 50 to 400 deg/s. A peak acceleration of >10,000 deg/s² was recorded in 10% of the transients.These findings indicate that active head movements in squirrel monkeys cover a higher range of frequencies, accelerations, and velocities than have typically been used in previous eye-movement and neuronal studies of the reflexes that control gaze. We further conclude that the choice of a method for analyzing transient, time-varying biological signals is dependent on the desired information. Residual analysis provides detailed resolution in the time domain, but estimation of the frequency content of the signal is dependent on the portions selected for analysis and the choice of filters. Fourier transform provides a representation of the power spectrum in the frequency domain but without any inherent temporal resolution. We show that the wavelet transform, a novel method as applied to the signal analysis goals of this study, is the most useful technique for relating time- and frequency-domain information during a continuous signal.     

Integration of wavelet transform with PCA and ANN for metabolomics data-mining

PCA (principal components analysis) and ANN (artificial neural network) are two broadly used pattern recognition methods in metabolomics data-mining. Yet their limitations sometimes are great obstacles for researchers. In this paper the wavelet transform (WT) method was used to integrate with PCA and ANN to improve their performance in manipulating metabolomics data. A dataset was decomposed by wavelets and then reconstructed. The "hard thresholding" algorithm was used, through which the detail information was discarded, and the entire "metabolomics image" reconstructed on the significant information. It was supposed that the most relevant information was captured after this process. It was found that, thanks to its ability in denoising data, the WT method could significantly improve the performance of the non-linear essence-extracting method ANN in classifying samples; further integration of WT with PCA showed that WT could greatly enhance the ability of PCA in distinguishing one group of samples from another and also its ability in identifying potential biomarkers. The results highlighted WT as a promising resolution in bridging the gap between huge bytes of data and the instructive biological information.     

Wavelet analysis of DNA walks.

A wavelet transform of the DNA "walk" constructed from a genomic sequence offers a direct visualization of short and long-range patterns in nucleotide sequences. We study sequences that encode diverse biological functions, taken from a variety of genomes. Pattern irregularities in the transform are frequently associated with sequences of biological interest. Exonic regions, for example, visualize differently under wavelet analysis than introns, and ribosomal RNA regions display distinct universal signatures. DNA walk wavelet analysis can provide a sensitive and rapid assessment of the putative biological significance of genomic DNA.     

Association dynamics and lateral transport in biological membranes

A theoretical analysis is presented for the interrelated effects of lateral diffusion and a simple form of molecular association (A + B ? C) in biological membranes. Expressions are derived for the characteristic functions measured in fluorescence redistribution after photobleaching experiments, corresponding to both the Fourier transform analysis of concentration in a plane and the normal mode analysis for a spherical surface. The results are related to the reputed binding of integral membrane proteins to submembranous cytoskeletal elements.     

Discrete wavelet transform analysis of surface electromyography for the fatigue assessment of neck and shoulder muscles

Assessment of neuromuscular fatigue is essential for early detection and prevention of risks associated with work-related musculoskeletal disorders. In recent years, discrete wavelet transform (DWT) of surface electromyography (SEMG) has been used to evaluate muscle fatigue, especially during dynamic contractions when the SEMG signal is non-stationary. However, its application to the assessment of work-related neck and shoulder muscle fatigue is not well established. Therefore, the purpose of this study was to establish DWT analysis as a suitable method to conduct quantitative assessment of neck and shoulder muscle fatigue under dynamic repetitive conditions. Ten human participants performed 40 min of fatiguing repetitive arm and neck exertions while SEMG data from the upper trapezius and sternocleidomastoid muscles were recorded. The ten of the most commonly used wavelet functions were used to conduct the DWT analysis. Spectral changes estimated using power of wavelet coefficients in the 12–23 Hz frequency band showed the highest sensitivity to fatigue induced by the dynamic repetitive exertions. Although most of the wavelet functions tested in this study reasonably demonstrated the expected power trend with fatigue development and recovery, the overall performance of the “Rbio3.1” wavelet in terms of power estimation and statistical significance was better than the remaining nine wavelets.     

Noise Reduction in Electron Tomographic Reconstructions Using Nonlinear Anisotropic Diffusion

Electron tomography is a powerful technique capable of giving unique insights into the three-dimensional structural organization of pleomorphic biological objects. However, visualization and interpretation of the resulting volumetric data are hampered by an extremely low signal-to-noise ratio, especially when ice-embedded biological specimens are investigated. Usually, isosurface representation or volume rendering of such data is hindered without any further signal enhancement. We propose a novel technique for noise reduction based on nonlinear anisotropic diffusion. The approach combines efficient noise reduction with excellent signal preservation and is clearly superior to conventional methods (e.g., low-pass and median filtering) and invariant wavelet transform filtering. The gain in the signal-to-noise ratio is verified and demonstrated by means of Fourier shell correlation. Improved visualization performance after processing the 3D images is demonstrated with two examples, tomographic reconstructions of chromatin and of a mitochondrion. Parameter settings and discretization stencils are presented in detail.     

Analysis of coronary angiography related psychophysiological responses

Background

Numerous studies have been conducted regarding a heartbeat classification algorithm over the past several decades. However, many algorithms have also been studied to acquire robust performance, as biosignals have a large amount of variation among individuals. Various methods have been proposed to reduce the differences coming from personal characteristics, but these expand the differences caused by arrhythmia.

Methods

In this paper, an arrhythmia classification algorithm using a dedicated wavelet adapted to individual subjects is proposed. We reduced the performance variation using dedicated wavelets, as in the ECG morphologies of the subjects. The proposed algorithm utilizes morphological filtering and a continuous wavelet transform with a dedicated wavelet. A principal component analysis and linear discriminant analysis were utilized to compress the morphological data transformed by the dedicated wavelets. An extreme learning machine was used as a classifier in the proposed algorithm.

Results

A performance evaluation was conducted with the MIT-BIH arrhythmia database. The results showed a high sensitivity of 97.51%, specificity of 85.07%, accuracy of 97.94%, and a positive predictive value of 97.26%.

Conclusions

The proposed algorithm achieves better accuracy than other state-of-the-art algorithms with no intrasubject between the training and evaluation datasets. And it significantly reduces the amount of intervention needed by physicians.     

小波变换及滚球算法在单分子荧光能量共振转移图像分析中的应用

单分子荧光共振能量转移技术是通过检测单个分子内的荧光供体及受体间荧光能量转移的效率来研究分子构象的变化．要得到这些生物大分子的信息就需要对大量的单分子信号进行统计分析,人工分析这些信息,既费时费力又不具备客观性和可重复性,因此本文将小波变换及滚球算法应用到单分子荧光能量共振转移图像中对单分子信号进行统计分析．在保证准确检测到单分子信号的前提下,文章对滚球算法和小波变换算法处理图像后的线性进行了分析,结果表明,滚球算法和小波变换算法不但能够很好地去除单分子FRET图像的背景噪声,同时还能很好地保持单分子荧光信号的线性．最后本文还利用滚球算法处理单分子FRET图像及统计15 bp DNA的FRET效率的直方图,通过计算得到了15 bp DNA的FRET效率值．     

信号处理技术在生物分子序列分析中的应用

信号处理技术在生物分子序列分析中的应用主要包括周期分析、基因预测、相似和重复序列分析、蛋白质分子结构预测等。涉及的技术方法有：Fourier变换、小波变换、相关分析、分形技术、非线性信号处理技术等。本文将全面回顾这些应用。     

A new algorithm for wavelet-based heart rate variability analysis

One of the most promising non-invasive markers of the activity of the autonomic nervous system is heart rate variability (HRV). HRV analysis toolkits often provide spectral analysis techniques using the Fourier transform, which assumes that the heart rate series is stationary. To overcome this issue, the Short Time Fourier Transform (STFT) is often used. However, the wavelet transform is thought to be a more suitable tool for analyzing non-stationary signals than the STFT. Given the lack of support for wavelet-based analysis in HRV toolkits, such analysis must be implemented by the researcher. This has made this technique underutilized.This paper presents a new algorithm to perform HRV power spectrum analysis based on the Maximal Overlap Discrete Wavelet Packet Transform (MODWPT). The algorithm calculates the power in any spectral band with a given tolerance for the band's boundaries. The MODWPT decomposition tree is pruned to avoid calculating unnecessary wavelet coefficients, thereby optimizing execution time. The center of energy shift correction is applied to achieve optimum alignment of the wavelet coefficients. This algorithm has been implemented in RHRV, an open-source package for HRV analysis. To the best of our knowledge, RHRV is the first HRV toolkit with support for wavelet-based spectral analysis.