This review systematically analyzes the latest advancements in preprocessing techniques for Electrocardiography (ECG) and Magnetocardiography (MCG) signals over the past decade. ECG and MCG play crucial roles in cardiovascular disease (CVD) detection, but both are susceptible to noise interference. This paper categorizes and compares different ECG denoising methods based on noise types, such as baseline wander (BW), electromyographic noise (EMG), power line interference (PLI), and composite noise. It also examines the complexity of MCG signal denoising, highlighting the challenges posed by environmental and instrumental interference. This review is the first to systematically compare the characteristics of ECG and MCG signals, emphasizing their complementary nature. MCG holds significant potential for improving the precision of CVD clinical diagnosis. Additionally, it evaluates the limitations of current denoising methods in clinical applications and outlines future directions, including the potential of explainable neural networks, multi-task neural networks, and the combination of deep learning with traditional methods to enhance denoising performance and diagnostic accuracy. In summary, while traditional filtering techniques remain relevant, hybrid strategies combining machine learning offer substantial potential for advancing signal processing and clinical diagnostics. This review contributes to the field by providing a comprehensive framework for selecting and improving denoising techniques, better facilitating signal quality enhancement and the accuracy of CVD diagnostics.

Quaternion adaptive filters have been widely used for the processing of 3D and 4D phenomena, but complete analysis of their performance is still lacking, partly due to the cumbersomeness of multivariate quaternion analysis. This causes difficulties in both understanding their behaviour and designing optimal filters. Based on a thorough exploration of the augmented statistics of quaternion random vectors, this paper extends an analysis framework for real-valued adaptive filters to the mean and mean square convergence analyses of general quaternion adaptive filters in non-stationary environments. The extension is non-trivial, considering the non-commutative quaternion algebra, only recently resolved issues with quaternion gradient, and the multidimensional augmented quaternion statistics. Also, for rigour, in order to model a non-stationary environment, the system weights are assumed to vary according to a first-order random-walk model. Transient and steady-state performance of a general class of quaternion adaptive filters is provided by exploiting the augmented quaternion statistics. An innovative quaternion decorrelation technique allows us to develop intuitive closed-form expressions for the performance of quaternion least mean square (QLMS) filters with Gaussian inputs, which provide new insights into the relationship between the filter behaviour and the complete second-order statistics of the input signal, that is, quaternion noncircularity. The closed-form expressions for the performance of strictly linear, semi-widely linear, and widely linear QLMS filters are investigated in detail, while numerical simulations for the three classes of QLMS filters with correlated Gaussian inputs support the theoretical analysis.

In recent years, optically pumped magnetometer (OPM)-based magnetoencephalography (MEG) has shown potential for analyzing brain activity. It has a flexible sensor configuration and comparable sensitivity to conventional SQUID-MEG. We constructed a 32-channel OPM-MEG system and used it to measure cortical responses to median and ulnar nerve stimulations. Traditional magnetic source imaging methods tend to blur the spatial extent of sources. Accurate estimation of the spatial size of the source is important for studying the organization of brain somatotopy and for pre-surgical functional mapping. We proposed a new method called variational free energy-based spatial smoothing estimation (FESSE) to enhance the accuracy of mapping somatosensory cortex responses. A series of computer simulations based on the OPM-MEG showed better performance than the three types of competing methods under different levels of signal-to-noise ratios, source patch sizes, and co-registration errors. FESSE was then applied to the source imaging of the OPM-MEG experimental data.

Quaternion state estimation techniques have been used in various applications, yet they are only suitable for dynamical systems represented by a single known model. In order to deal with model uncertainty, this paper proposes a class of widely linear quaternion multiple-model adaptive estimation (WL-QMMAE) algorithms based on widely linear quaternion Kalman filters and Bayesian inference. The augmented second-order quaternion statistics is employed to capture complete second-order statistical information in improper quaternion signals. Within the WL-QMMAE framework, a widely linear quaternion interacting multiple-model algorithm is proposed to track time-variant model uncertainty, while a widely linear quaternion static multiple-model algorithm is proposed for time-invariant model uncertainty. A performance analysis of the proposed algorithms shows that, as expected, the WL-QMMAE reduces to semiwidely linear QMMAE for Cη-improper signals and further reduces to strictly linear QMMAE for proper signals. Simulation results indicate that for improper signals, the proposed WL-QMMAE algorithms exhibit an enhanced performance over their strictly linear counterparts. The effectiveness of the proposed recursive performance analysis algorithm is also validated.

Objective. This study aimed to develop an automatic and accurate method for severity assessment and localization of coronary artery disease (CAD) based on an optically pumped magnetometer magnetocardiography (MCG) system. Approach. We proposed spatiotemporal features based on the MCG one-dimensional signals, including amplitude, correlation, local binary pattern, and shape features. To estimate the severity of CAD, we classified the stenosis as absence or mild, moderate, or severe cases and extracted a subset of features suitable for assessment. To localize CAD, we classified CAD groups according to the location of the stenosis, including the left anterior descending artery (LAD), left circumflex artery (LCX), and right coronary artery (RCA), and separately extracted a subset of features suitable for determining the three CAD locations. Main results. For CAD severity assessment, a support vector machine (SVM) achieved the best result, with an accuracy of 75.1%, precision of 73.9%, sensitivity of 67.0%, specificity of 88.8%, F1-score of 69.8%, and area under the curve of 0.876. The highest accuracy and corresponding model for determining locations LAD, LCX, and RCA were 94.3% for the SVM, 84.4% for a discriminant analysis model, and 84.9% for the discriminant analysis model. Significance . The developed method enables the implementation of an automated system for severity assessment and localization of CAD. The amplitude and correlation features were key factors for severity assessment and localization. The proposed machine learning method can provide clinicians with an automatic and accurate diagnostic tool for interpreting MCG data related to CAD, possibly promoting clinical acceptance.

The advent of optically pumped magnetometers (OPMs) facilitates the development of on-scalp magnetoencephalography (MEG). In particular, the triaxial OPM emerged recently, making simultaneous measurements of all three orthogonal components of vector fields possible. The detection of triaxial magnetic fields improves the interference suppression capability and achieves higher source localization accuracy using fewer sensors. The source localization accuracy of MEG is based on the accurate co-registration of MEG and MRI. In this study, we proposed a triaxial co-registration method according to combined principal component analysis and iterative closest point algorithms for use of a flexible cap. A reference phantom with known sensor positions and orientations was designed and constructed to evaluate the accuracy of the proposed method. Experiments showed that the average co-registered position errors of all sensors were approximately 1 mm and average orientation errors were less than 2.5° in the X - and Y orientations and less than 1.6° in the Z orientation. Furthermore, we assessed the influence of co-registration errors on the source localization using simulations. The average source localization error of approximately 1 mm reflects the effectiveness of the co-registration method. The proposed co-registration method facilitates future applications of triaxial sensors on flexible caps.