Quantifying local field potential dynamics with amplitude and frequency stability between ON and OFF medication and stimulation in Parkinson's disease.

Neural oscillations are critical to understanding the synchronisation of neural activities and their relevance to neurological disorders. For instance, the amplitude of beta oscillations in the subthalamic nucleus has gained extensive attention, as it has been found to correlate with medication status and the therapeutic effects of continuous deep brain stimulation in people with Parkinson's disease. However, the frequency stability of subthalamic nucleus beta oscillations, which has been suggested to be associated with dopaminergic information in brain states, has not been well explored. Moreover, the administration of medicine can have inverse effects on changes in frequency and amplitude. In this study, we proposed a method based on the stationary wavelet transform to quantify the amplitude and frequency stability of subthalamic nucleus beta oscillations and evaluated the method using simulation and real data for Parkinson's disease patients. The results suggest that the amplitude and frequency stability quantification has enhanced sensitivity in distinguishing pathological conditions in Parkinson's disease patients. Our quantification shows the benefit of combining frequency stability information with amplitude and provides a new potential feedback signal for adaptive deep brain stimulation.

Improved T-wave detection in electrocardiogram signals based non-stationary wavelet transform and QRS complex cancellation with kurtosis analysis.

Objective. The T-wave in electrocardiogram (ECG) signal has the potential to enumerate various cardiac dysfunctions in the cardiovascular system. The primary objective of this research is to develop an efficient method for detecting T-waves in ECG signals, with potential applications in clinical diagnosis and continuous patient monitoring.Approach. In this work, we propose a novel algorithm for T-wave peak detection, which relies on a non-decimated stationary wavelet transform method (NSWT) and involves the cancellation of the QRS complex by utilizing its local extrema. The proposed scheme contains three stages: firstly, the technique is pre-processed using a two-stage median filter and Savitzky-Golay (SG) filter to remove the various artifacts from the ECG signal. Secondly, the NSWT technique is implemented using the bior 4.4 mother wavelet without downsampling, employing 24scale analysis, and involves the cancellation of QRS-complex using its local positions. After that, Sauvola technique is used to estimate the baseline and remove the P-wave peaks to enhance T-peaks for accurate detection in the ECG signal. Additionally, the moving average window and adaptive thresholding are employed to enhance and identify the location of the T-wave peaks. Thirdly, false positive T-peaks are corrected using the kurtosis coefficients method.Main results. The robustness and efficiency of the proposed technique have been corroborated by the QT database (QTDB). The results are also validated on a self-recorded database. In QTDB database, the sensitivity of 98.20%, positive predictivity of 99.82%, accuracy of 98.04%, and detection error rate of 1.95% have been achieved. The self-recorded dataset attains a sensitivity, positive predictivity, accuracy, and detection error rate of 99.94%, 99.96%, 99.90%, and 0.09% respectively.Significance. A T-wave peak detection based on NSWT and QRS complex cancellation, along with kurtosis analysis technique, demonstrates superior performance and enhanced detection accuracy compared to state-of-the-art techniques.

Improvement of pixel classification by the simultaneous use of spectral and spatial information in the framework of spectroscopic imaging.

Hyperspectral imaging technology is developing in a very fast way. We find it today in many analytical developments using different spectroscopies for sample classification purposes. Instrumental developments allow us to acquire more and more data in shorter and shorter periods of time while improving their quality. Therefore, we are going in the right direction as far as the measure is concerned. On the other hand, we can make a more mixed assessment for the hyperspectral imaging data processing. Indeed, the data acquired in spectroscopic imaging have the particularity of encoding both spectral and spatial information. Unfortunately, in chemometrics, almost all classification approaches today only use spectral information from three-dimensional hyperspectral data arrays. To be more precise, an approach encompassing the unfolding/refolding of such arrays is often applied beforehand because the majority of algorithms for analysing these data are not capable of handling them in their original structure. Spatial information is therefore lost during the chemometric exploration. The study of the spectral part of the acquired data array alone is clearly a limitation that we propose to overcome in this work. 2-D Stationary Wavelet Transform will be used in the data preprocessing phase to ensure the joint use of spectral and spatial information. Two spectroscopic datasets will then be used to evaluate the potential of our approach in the context of supervised classification.

12-lead ECG signal processing and atrial fibrillation prediction in clinical practice.

BACKGROUND: Because clinically used 12-lead electrocardiography (ECG) devices have high falsepositive errors in automatic interpretations of atrial fibrillation (AF), they require substantial improvements before use. OBJECTIVE: A clinical 12-lead ECG pre-processing method with a parallel convolutional neural network (CNN) model for 12-lead ECG automatic AF recognition is introduced. METHODS: Raw AF diagnosis data from a 12-lead ECG device were collected and analyzed by two cardiologists to differentiate between true- and false-positives. Using a stationary wavelet transform (SWT) and independent component analysis (ICA) noise reduction was conducted and baseline wandering was corrected for the raw signals. AF patterns were learned and predicted using a parallel CNN deep learning (DL) model. (1) The proposed method alleviates the decreased ECG QRS amplitude enhances the signal-to-noise ratio and clearly shows atrial and ventricular activities. (2) After training, the CNNbased AF detector significantly reduced false-positive errors. The precision of AF diagnosis increased from 77.3% to 94.0 ± 1.5% as compared to ECG device interpretation. For AF screening, the model showed an average sensitivity of 96.8 ± 2.2%, specificity of 79.0 ± 5.8%, precision of 94.0 ± 1.5%, F1-measure of 95.2 ± 1.0%, and overall accuracy of 92.7 ± 1.5%. CONCLUSIONS: The method can bridge the gap between the research and clinical practice The ECG signal pre-processing and DL-based AF interpretation can be rapidly implemented clinically.

EEG artifact removal using sub-space decomposition, nonlinear dynamics, stationary wavelet transform and machine learning algorithms.

Blind source separation (BSS) methods have received a great deal of attention in electroencephalogram (EEG) artifact elimination as they are routine and standard signal processing tools to remove artifacts and reserve desired neural information. On the other hand, a classifier should follow BSS methods to automatically identify artifactual sources and remove them in the following steps. In addition, removing all detected artifactual components leads to loss of information since some desired information related to neural activity leaks to these sources. So, an approach should be employed to detect and suppress the artifacts and reserve neural activity. This study introduces a novel method based on EEG and Poincare planes in the phase space to detect artifactual components estimated by second-order blind identification (SOBI). Artifacts are detected using a mixture of well-known conventional classifiers and were removed employing stationary wavelet transform (SWT) to reserve neural information. The proposed method is a combination of signal processing techniques and machine learning algorithms, including multi-layer perceptron (MLP), K-nearest neighbor (KNN), naïve Bayes, and support vector machine (SVM) which have significant results while applying our proposed method to different scenarios. Simulated, semi-simulated, and real EEG signals are employed to evaluate the proposed method, and several evaluation criteria are calculated. We achieved acceptable results, for example, 98% average accuracy and 97% average sensitivity in artifactual EEG component detection or about 2% as mean square error in EEG reconstruction after artifact removal. Results showed that the proposed method is effective and can be used in future studies as we have considered different real-world scenarios to evaluate it.

Blind source separation of inspiration and expiration in respiratory sEMG signals.

Objective.Surface electromyography (sEMG) is a noninvasive option for monitoring respiratory effort in ventilated patients. However, respiratory sEMG signals are affected by crosstalk and cardiac activity. This work addresses the blind source separation (BSS) of inspiratory and expiratory electrical activity in single- or two-channel recordings. The main contribution of the presented methodology is its applicability to the addressed muscles and the number of available channels.Approach.We propose a two-step procedure consisting of a single-channel cardiac artifact removal algorithm, followed by a single- or multi-channel BSS stage. First, cardiac components are removed in the wavelet domain. Subsequently, a nonnegative matrix factorization (NMF) algorithm is applied to the envelopes of the resulting wavelet bands. The NMF is initialized based on simultaneous standard pneumatic measurements of the ventilated patient.Main results.The proposed estimation scheme is applied to twelve clinical datasets and simulated sEMG signals of the respiratory system. The results on the clinical datasets are validated based on expert annotations using invasive pneumatic measurements. In the simulation, three measures evaluate the separation success: The distortion and the correlation to the known ground truth and the inspiratory-to-expiratory signal power ratio. We find an improvement across all SNRs, recruitment patterns, and channel configurations. Moreover, our results indicate that the initialization strategy replaces the manual matching of sources after the BSS.Significance.The proposed separation algorithm facilitates the interpretation of respiratory sEMG signals. In crosstalk affected measurements, the developed method may help clinicians distinguish between inspiratory effort and other muscle activities using only noninvasive measurements.

Brain Tumor Identification by Hybrid CNN-SWT Model.

OBJECTIVE: Detecting brain tumor using the segmentation technique is a big challenge for researchers and takes a long time in medical image processing. Magnetic resonance image analysis techniques facilitate the accurate detection of tissues and abnormal tumors in the brain. The size of a brain tumor can vary with the individual and the specifics of the tumor. Radiologists face great difficulty in diagnosing and classifying brain tumors. METHOD: This paper proposed a hybrid model-based convolutional neural network with a stationary wavelet trans-form named "CNN-SWT" to segment brain tumors using MR brain big data. We utilized 7 layers for classification in the proposed model that include 3 convolutional and 3 ReLU. Firstly, the input MR image is divided into multiple patches, and then the central pixel value of each patch is provided to the CNN-SWT. Secondly, the pre-processing stage is per-formed using the mean filter to remove the noise. Then the convolution neural network-layer approach is utilized to segment brain tumors. After segmentation, robust feature extraction such as information-extraction methods is used for the feature extraction process. Finally, a CNN-based hybrid scheme based on the stationary wavelet transform technique is used to detect tumors using MR brain images. MATERIALS: These experiments were obtained using 11500 MR brain images data from the hospital national of oncology. RESULTS: It was proved that the proposed hybrid achieved a high classification accuracy of (98.7 %) as compared with existing methods. CONCLUSION: The advantage of the hybrid novelty of the model and the ability to detect the tumor area achieved excellent overall performance using different values.

Effect of different anesthetic dose of pentobarbital on respiratory activity in rabbits.

Anesthetics inhibit the respiratory muscles and even cause upper airway to collapse. Diaphragm electromyography (EMGdi) and airflow signals are usually extracted to assess the degree of respiration inhibition by anesthetics. However, the ECG interference in EMGdi affects the accuracy of its time domain and frequency domain information extraction. We studied the changes in EMGdi (left EMGdi and right EMGdi) and airflow characteristics under two pentobarbital anesthetic doses. First, we filtered out the ECG in EMGdi based on the combination of stationary wavelet transform and the positioning of ECG to obtain EMGdi without ECG interference (EMGdip). The effectiveness of filtering algorithm was verified by calculating the power spectrum before and after noise reduction. Second, root mean square (RMS), average rectified value (ARV), and fixed sample entropy (fSampEn) were used to quantify EMGdi (left EMGdi, left EMGdip and right EMGdi). Median frequency (MF) and centroid frequency (fc) of EMGdi were calculated. Tidal volume, respiratory cycle duration and peak airflow were calculated from airflow. Finally, the average and standard deviation of these parameters for all rabbits (n = 10) were compared and analyzed under two anesthesia states. Our results indicate that anesthesia induced by an increase in pentobarbital dose leads to decrease in ventilation and EMGdi amplitude. There was no significant change in diaphragm power spectrum (MF and fc) with the increase of anesthesia dose.

Investigations on coronary artery plaque detection and subclassification using machine learning classifier.

Coronary artery diseases are one of the high-risk diseases, which occur due to the insufficient blood supply to the heart. The different types of plaques formed inside the artery leads to the blockage of the blood stream. Understanding the type of plaques along with the detection and classification of plaques supports in reducing the mortality of patients. The objective of this study is to present a novel clustering method of plaque segmentation followed by wavelet transform based feature extraction. The extracted features of all different kinds of calcified and sub calcified plaques are applied to first train and test three machine learning classifiers including support vector machine, random forest and decision tree classifiers. The bootstrap ensemble classifier then decides the best classification result through a voting method of three classifiers. A training dataset including 64 normal CTA images and 73 abnormal CTA images is used, while a testing dataset consists of 111 normal CTA images and 103 abnormal CTA images. The evaluation metrics shows better classification rate and accuracy of 97.7%. The Sensitivity and Specificity rates are 97.8% and 97.5%, respectively. As a result, our study results demonstrate the feasibility and advantages of developing and applying this new image processing and machine learning scheme to assist coronary artery plaque detection and classification.

[Research on the detection algorithm of electrocardiogram characteristic wave based on energy segmentation and stationary wavelet transform].

The detection of electrocardiogram (ECG) characteristic wave is the basis of cardiovascular disease analysis and heart rate variability analysis. In order to solve the problems of low detection accuracy and poor real-time performance of ECG signal in the state of motion, this paper proposes a detection algorithm based on segmentation energy and stationary wavelet transform (SWT). Firstly, the energy of ECG signal is calculated by segmenting, and the energy candidate peak is obtained after moving average to detect QRS complex. Secondly, the QRS amplitude is set to zero and the fifth component of SWT is used to locate P wave and T wave. The experimental results show that compared with other algorithms, the algorithm in this paper has high accuracy in detecting QRS complex in different motion states. It only takes 0.22 s to detect QSR complex of a 30-minute ECG record, and the real-time performance is improved obviously. On the basis of QRS complex detection, the accuracy of P wave and T wave detection is higher than 95%. The results show that this method can improve the efficiency of ECG signal detection, and provide a new method for real-time ECG signal classification and cardiovascular disease diagnosis.

Wavelet Frequency Separation Attention Network for Chest X-ray Image Super-Resolution.

Medical imaging is widely used in medical diagnosis. The low-resolution image caused by high hardware cost and poor imaging technology leads to the loss of relevant features and even fine texture. Obtaining high-quality medical images plays an important role in disease diagnosis. A surge of deep learning approaches has recently demonstrated high-quality reconstruction for medical image super-resolution. In this work, we propose a light-weight wavelet frequency separation attention network for medical image super-resolution (WFSAN). WFSAN is designed with separated-path for wavelet sub-bands to predict the wavelet coefficients, considering that image data characteristics are different in the wavelet domain and spatial domain. In addition, different activation functions are selected to fit the coefficients. Inputs comprise approximate sub-bands and detail sub-bands of low-resolution wavelet coefficients. In the separated-path network, detail sub-bands, which have more sparsity, are trained to enhance high frequency information. An attention extension ghost block is designed to generate the features more efficiently. All results obtained from fusing layers are contracted to reconstruct the approximate and detail wavelet coefficients of the high-resolution image. In the end, the super-resolution results are generated by inverse wavelet transform. Experimental results show that WFSAN has competitive performance against state-of-the-art lightweight medical imaging methods in terms of quality and quantitative metrics.

Short duration Vectorcardiogram based inferior myocardial infarction detection: class and subject-oriented approach.

Myocardial infarction (MI) happens when blood stops circulating to an explicit segment of the heart causing harm to the heart muscles. Vectorcardiography (VCG) is a technique of recording direction and magnitude of the signals that are produced by the heart in a 3-lead representation. In this work, we present a technique for detection of MI in the inferior portion of heart using short duration VCG signals. The raw signal was pre-processed using the median and Savitzky-Golay (SG) filter. The Stationary Wavelet Transform (SWT) was used for time-invariant decomposition of the signal followed by feature extraction. The selected features using minimum-redundancy-maximum-relevance (mRMR) based feature selection method were applied to the supervised classification methods. The efficacy of the proposed method was assessed under both class-oriented and a more real-life subject-oriented approach. An accuracy of 99.14 and 89.37% were achieved respectively. Results of the proposed technique are better than existing state-of-art methods and used VCG segment is shorter. Thus, a shorter segment and a high accuracy can be helpful in the automation of timely and reliable detection of MI. The satisfactory performance achieved in the subject-oriented approach shows reliability and applicability of the proposed technique.

Stationary wavelet transform based ECG signal denoising method.

Electrocardiogram (ECG) signals are used to diagnose cardiovascular diseases. During ECG signal acquisition, various noises like power line interference, baseline wandering, motion artifacts, and electromyogram noise corrupt the ECG signal. As an ECG signal is non-stationary, removing these noises from the recorded ECG signal is quite tricky. In this paper, along with the proposed denoising technique using stationary wavelet transform, various denoising techniques like lowpass filtering, highpass filtering, empirical mode decomposition, Fourier decomposition method, discrete wavelet transform are studied to denoise an ECG signal corrupted with noise. Signal-to-noise ratio, percentage root-mean-square difference, and root mean square error are used to compare the ECG signal denoising performance. The experimental result showed that the proposed stationary wavelet transform based ECG denoising technique outperformed the other ECG denoising techniques as more ECG signal components are preserved than other denoising algorithms.

Fusing spectral and spatial information with 2-D stationary wavelet transform (SWT 2-D) for a deeper exploration of spectroscopic images.

Nowadays, it is clear that there is an increasing importance in spectroscopic imaging in all fields of science. Obviously, one bulk analysis can no longer be satisfactory, as the interest focuses more on the chemical nature and the location of the compounds present within a given complex matrix. This is, evidently, due to the fact that for a more comprehensive exploration of complex samples, one single acquired hyperspectral data cube can provide both spectral and spatial information simultaneously. Although many techniques were proposed by the chemometric community in explorations of these specific datasets, unfortunately, they are almost always focusing on spectral information, even if chemical images were ultimately observed. In other words, spatial information is not well exploited, and therefore lost during the actual chemometric calculation phase. The goal of this short communication is to present a very simple and fast spectral/spatial fusion approach based on 2-D stationary wavelet transform (SWT 2-D) which is able to improve the obtainable information, compared with a classical data analysis, in which the spatial domain would not be considered nor used.

Research on the detection algorithm of electrocardiogram characteristic wave based on energy segmentation and stationary wavelet transform / 生物医学工程学杂志

The detection of electrocardiogram (ECG) characteristic wave is the basis of cardiovascular disease analysis and heart rate variability analysis. In order to solve the problems of low detection accuracy and poor real-time performance of ECG signal in the state of motion, this paper proposes a detection algorithm based on segmentation energy and stationary wavelet transform (SWT). Firstly, the energy of ECG signal is calculated by segmenting, and the energy candidate peak is obtained after moving average to detect QRS complex. Secondly, the QRS amplitude is set to zero and the fifth component of SWT is used to locate P wave and T wave. The experimental results show that compared with other algorithms, the algorithm in this paper has high accuracy in detecting QRS complex in different motion states. It only takes 0.22 s to detect QSR complex of a 30-minute ECG record, and the real-time performance is improved obviously. On the basis of QRS complex detection, the accuracy of P wave and T wave detection is higher than 95%. The results show that this method can improve the efficiency of ECG signal detection, and provide a new method for real-time ECG signal classification and cardiovascular disease diagnosis.

Wavelet denoising as a post-processing enhancement method for non-invasive foetal electrocardiography.

BACKGROUND AND OBJECTIVE: The detection of a clean and undistorted foetal electrocardiogram (fECG) from non-invasive abdominal recordings is an open research issue. Several physiological and instrumental noise sources hamper this process, even after that powerful fECG extraction algorithms have been used. Wavelet denoising is widely used for the improvement of the SNR in biomedical signal processing. This work aims to systematically assess conventional and unconventional wavelet denoising approaches for the post-processing of fECG signals by providing evidence of their effectiveness in improving fECG SNR while preserving the morphology of the signal of interest. METHODS: The stationary wavelet transform (SWT) and the stationary wavelet packet transform (SWPT) were considered, due to their different granularity in the sub-band decomposition of the signal. Three thresholds from the literature, either conventional (Minimax and Universal) and unconventional, were selected. To this aim, the unconventional one was adapted for the first time to SWPT by trying different approaches. The decomposition depth was studied in relation to the characteristics of the fECG signal. Synthetic and real datasets, publicly available for benchmarking and research, were used for quantitative analysis in terms of noise reduction, foetal QRS detection performance and preservation of fECG morphology. RESULTS: The adoption of wavelet denoising approaches generally improved the SNR. Interestingly, the SWT methods outperformed the SWPT ones in morphology preservation (p<0.04) and SNR (p<0.0003), despite their coarser granularity in the sub-band analysis. Remarkably, the Han et al. threshold, adopted for the first time for fECG processing, provided the best quality improvement (p<0.003). CONCLUSIONS: The findings of our systematic analysis suggest that particular care must be taken when selecting and using wavelet denoising for non-invasive fECG signal post-processing. In particular, despite the general noise reduction capability, signal morphology can be significantly altered on the basis of the parameterization of the wavelet methods. Remarkably, the adoption of a finer sub-band decomposition provided by the wavelet packet was not able to improve the quality of the processing.

Uncovering the prognostic gene signatures for the improvement of risk stratification in cancers by using deep learning algorithm coupled with wavelet transform.

BACKGROUND: The aim of gene expression-based clinical modelling in tumorigenesis is not only to accurately predict the clinical endpoints, but also to reveal the genome characteristics for downstream analysis for the purpose of understanding the mechanisms of cancers. Most of the conventional machine learning methods involved a gene filtering step, in which tens of thousands of genes were firstly filtered based on the gene expression levels by a statistical method with an arbitrary cutoff. Although gene filtering procedure helps to reduce the feature dimension and avoid overfitting, there is a risk that some pathogenic genes important to the disease will be ignored. RESULTS: In this study, we proposed a novel deep learning approach by combining a convolutional neural network with stationary wavelet transform (SWT-CNN) for stratifying cancer patients and predicting their clinical outcomes without gene filtering based on tumor genomic profiles. The proposed SWT-CNN overperformed the state-of-art algorithms, including support vector machine (SVM) and logistic regression (LR), and produced comparable prediction performance to random forest (RF). Furthermore, for all the cancer types, we firstly proposed a method to weight the genes with the scores, which took advantage of the representative features in the hidden layer of convolutional neural network, and then selected the prognostic genes for the Cox proportional-hazards regression. The results showed that risk stratifications can be effectively improved by using the identified prognostic genes as feature, indicating that the representative features generated by SWT-CNN can well correlate the genes with prognostic risk in cancers and be helpful for selecting the prognostic gene signatures. CONCLUSIONS: Our results indicated that gene expression-based SWT-CNN model can be an excellent tool for stratifying the prognostic risk for cancer patients. In addition, the representative features of SWT-CNN were validated to be useful for evaluating the importance of the genes in the risk stratification and can be further used to identify the prognostic gene signatures.

Force decoding using local field potentials in primary motor cortex: PLS or Kalman filter regression?

The development of brain-computer interface (BCI) systems is an important approach in brain studies. Control of communication devices and prostheses in real-world scenarios requires complex movement parameters. Decoding a variety of neural signals captured by micro-wire arrays is a potential applicant for extracting movement-related information. The present work was conducted to compare the functionality of partial least square (PLS) regression and Kalman filter to predict the force parameter from local field potential (LFP) signals of the primary motor cortex (M1). The signals were recorded using a 16-channel micro-wire array from the forelimb-related area of the M1 of three rats performing a behavioral task in which the force signal of the rat's forelimb paw was generated. Our results show that PLS regression and Kalman filters with the mean performance of 0.75 and 0.72 in terms of the correlation coefficient (CC) and 0.37 and 0.48 in terms of normalized mean square error (NMSE), respectively, are effective methods for decoding the force parameter from LFPs. Kalman filter underperforms PLS both in performance and speed. Although adding nonlinearity to the Kalman filter results in equally accurate CC performance as PLS, it has even more computational cost. Therefore, it is inferred that nonlinear methods do not necessarily have better functionality than linear ones and PLS, as a simple fast linear method could be an effectively applicable regression technique for BCIs.

CORE-PI: Non-iterative convolution-based reconstruction for parallel MRI in the wavelet domain.

PURPOSE: To develop and test a novel parameter-free non-iterative wavelet domain method for reconstruction of undersampled multicoil MR data. THEORY AND METHODS: A linear parallel MRI method that operates in the Stationary Wavelet Transform (SWT) domain is proposed. The method is coined COnvolution-based REconstruction for Parallel MRI (CORE-PI). This method computes the SWT of the unknown MR image directly from subsampled k-space measurements, without modifying the RF excitation pulse. It then reconstructs the image using the wavelet filter bank approach, with simple linear computations. The CORE-PI implementation is demonstrated by experiments with a numeric brain phantom and in vivo brain scans data, with various wavelet types and high reduction factors. It is compared to the well-known parallel MRI methods GRAPPA and l1-SPIRiT. RESULTS: The experimental results show that CORE-PI is suitable for different 1D Cartesian k-space undersampling schemes, including regular and irregular ones, and for wavelets of different families. CORE-PI accurately reconstructs the SWT coefficients of the unknown MR image; this wavelet-domain decomposition is fully computed despite the k-space undersampling. Furthermore, CORE-PI provides high-quality final reconstructions, with an average NRMSE of 0.013, which is significantly lower than that obtained by GRAPPA and l1-SPIRiT. Moreover, CORE-PI offers significantly faster computation times: the typical CORE-PI runtime is about 60 seconds, which is about 20% shorter than that of l1-SPIRiT and 55%-75% shorter than that of GRAPPA. CONCLUSION: COnvolution-based REconstruction for Parallel MRI advantageously offers: (a) flexible 1D undersampling of a Cartesian k-space, (b) a parameter-free non-iterative implementation, (c) reconstruction performance comparable or better than that of GRAPPA and l1-SPIRiT, and (d) robust fast computations.

Combining Multi-Scale Wavelet Entropy and Kernelized Classification for Bearing Multi-Fault Diagnosis.

Discriminative feature extraction and rolling element bearing failure diagnostics are very important to ensure the reliability of rotating machines. Therefore, in this paper, we propose multi-scale wavelet Shannon entropy as a discriminative fault feature to improve the diagnosis accuracy of bearing fault under variable work conditions. To compute the multi-scale wavelet entropy, we consider integrating stationary wavelet packet transform with both dispersion (SWPDE) and permutation (SWPPE) entropies. The multi-scale entropy features extracted by our proposed methods are then passed on to the kernel extreme learning machine (KELM) classifier to diagnose bearing failure types with different severities. In the end, both the SWPDE-KELM and the SWPPE-KELM methods are evaluated on two bearing vibration signal databases. We compare these two feature extraction methods to a recently proposed method called stationary wavelet packet singular value entropy (SWPSVE). Based on our results, we can say that the diagnosis accuracy obtained by the SWPDE-KELM method is slightly better than the SWPPE-KELM method and they both significantly outperform the SWPSVE-KELM method.