Deep brain stimulation (DBS) is a critical neuromodulation technique that has been widely applied in the treatment of neurological disorders such as Parkinson's disease (PD) and epilepsy. As an important functional neuroimaging modality, magnetoencephalography (MEG) has played a key role in DBS research. In particular, the next-generation MEG based on optically pumped magnetometers (OPM-MEG), offers greater potential for clinical applications. However, the strong electromagnetic interference generated by DBS systems makes data acquisition and analysis challenging in OPM-MEG recordings from patients with implanted devices. To the best of our knowledge, there have been no studies that systematically investigate the characteristics or suppression of DBS-induced artifacts in OPM-MEG recordings from human subjects. In this paper, we describe a novel OPM-MEG interference suppression algorithm called extended homogeneous field correction based on oblique projection (opHFC), developed for suppressing environmental noise in OPM-MEG. To illustrate the practical application of opHFC in clinical settings, particularly for patients with DBS implants. We evaluate the performance of opHFC in denoising OPM-MEG data from PD patients with DBS implants. By applying opHFC to real-world clinical data, we assess its ability to reduce DBS-induced artifacts while preserving neural activity patterns and conduct a comprehensive comparison between opHFC and several commonly used artifact suppression techniques in OPM-MEG. Our results show that opHFC significantly enhances signal quality and achieves the most effective suppression performance, demonstrating its potential as a reliable tool for advancing OPM-MEG applications in challenging clinical environments. This study highlights the practical value of opHFC in improving OPM-MEG data quality for PD patients with DBS, paving the way for more accurate neuroscientific research and clinical diagnostics.

Magnetocardiography (MCG) is gaining prominence in medical technology. However, owing to the semi-open magnetic shielding, MCG is still severely interfered by low-frequency, non-Gaussian noise, particularly in clinical settings. The spatial distribution of low-frequency non-Gaussian noise is not accurately captured by linear mixing models. In addition, this noise completely overlaps with MCG signals in both the time and frequency domains, distorting the physiological information encoded in the waveform morphology and two-dimensional MCG image, which is important for diagnosis. To address this, we propose a multi-channel non-local means (NLM) method based on Hermite approximation, exploiting the high synchronization between channels and the repeatability within each channel without requiring additional reference channels. First, a matrix that contains magnetocardiographic image morphology information is computed through Hermite approximation of the reference channels. Next, clustering is performed on all data, and the standard deviation of the clustering results is utilized to calculate the adaptive Gaussian smoothing parameters. Finally, the multi-channel adaptive NLM algorithm is applied to denoise the MCG signals. Simulation, semi-physical, and real-case experiments using self-developed MCG equipment demonstrate that the proposed method effectively restores the waveform characteristics and time-frequency domain information of MCG images under low-frequency non-Gaussian noise. This method outperforms existing techniques in noise reduction and establishes a solid foundation for future clinical applications.

A novel dual-broadband end-fire filtering antenna for fifth-generation (5G) Internet of Things (IoT) applications, derived from the traditional single-layer Vivaldi antenna, is proposed. It employs a differential feedline to enable seamless integration with widely applied differential systems. First, by strategically designing the length of the feedline, an interband radiation null is generated, and its second-order radiation null is located at the upper stopband of the higher band (HB), thus achieving a dual-band operation with a certain filtering capability. Second, leveraging the property of these slots on the antenna’s tapered aperture position can be equivalent to the serial shorted branches with band-stop characteristics, the suppression effects within the interband and the upper stopband of the HB are enhanced by loading slots with different lengths. Finally, a pair of half-wavelength shorted stubs are loaded on the feedline to generate an extra radiation null, further strengthening the suppression level of the HB’s upper stopband and optimizing the overall impedance matching of the antenna. The designed prototype was fabricated and measured, validating that it has the –10 dB impedance fractional bandwidth of 73.3% and 34.3%, peak realized gains of 10.0 dBi and 10.0 dBi, and exhibits good out-of-band suppression performance without employing extra filtering circuits.

Automated analytical techniques for magnetocardiography (MCG) are essential for diagnosing and predicting cardiovascular diseases. Clinically acquired MCG signals are often contaminated by various types of noise, which negatively impact subsequent signal analysis. However, traditional methods have limitations in denoising long-term MCG signals with complex spatial structures. We propose a high-precision, robust representation learning method based on skip connection multi-scale feature fusion (SkipDAEformer) for effectively removing random mixed noise in MCG signals. SkipDAEformer integrates attention fusion mechanisms into a basic denoising autoencoder to extract and fuse critical temporal and spatial information from each feature map, thus enhancing the model's ability to capture long-range dependencies and spatial features in MCG signals. Meanwhile, we further supplement and refine the semantic information for the feature maps through a global feature fusion method. By fusing multi-scale features from different skip connections, SkipDAEformer can learn more comprehensive representations of MCG signals, enabling the effective separation of clean signals from noise. Experimental results demonstrate that SkipDAEformer outperforms existing methods in denoising performance, channel consistency, feature consistency, and generalization ability and can be extended to a self-supervised learning framework. In actual noise reduction and diagnostic classification tasks, SkipDAEformer shows superior clinical acceptability and diagnostic value, potentially advancing MCG data analysis.

Privacy policies have disrupted the multi-billion dollar online advertising market by making real-time and precise user data untraceable, which poses significant challenges to the optimization of Return-On-Investment (ROI) constrained products in the online advertising industry. Privacy protection strategies, including event aggregation and reporting delays, hinder access to detailed and instantaneous feedback data, thus incapacitating traditional identity-revealing attribution techniques. In this paper, we introduces a novel Spending Programmed Bidding (SPB) framework to navigate these challenges. SPB is a two-stage framework that separates long horizon delivery spend planning (the macro stage) and short horizon bidding execution (the micro stage). The macro stage models the target ROI to achieve maximum utility and derives the expected spend, whereas the micro stage optimizes the bid price given the expected spend. We further extend our framework to the cross-channel scenario where the agent bids in both privacy-constrained and identity-revealing attribution channels. We find that when privacy-constrained channels are present, SPB is superior to state-of-the-art bidding methods in both offline datasets and online experiments on a large ad platform.

The integral probability metric (IPM) equips generative adversarial nets (GANs) with the necessary theoretical support for comparing statistical moments in an embedded domain of the critic, while stabilising their training and mitigating the mode collapse issues. For enhanced intuition and physical insight, we introduce a generalisation of IPM-GANs which operates by directly comparing probability distributions rather than their moments. This is achieved through characteristic functions (CFs), a powerful tool that uniquely comprises all information about any general distribution. For rigour, we first theoretically prove the ability of the CF loss to compare probability distributions, and proceed to establish the physical meaning of the phase and amplitude of CFs. An optimal sampling strategy is then developed to calculate the CFs, and an equivalence between the embedded and data domains is proved under the reciprocal theory. This makes it possible to seamlessly combine IPM-GAN with an auto-encoder structure by an advanced anchor architecture, which adversarially learns a semantic low-dimensional manifold for both generation and reconstruction. This efficient reciprocal CF GAN (RCF-GAN) structure, uses only two modules and a simple training strategy to achieve the state-of-the-art bi-directional generation. Experiments demonstrate the superior performance of RCF-GAN on both regular (images) and irregular (graph) domains.

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.

An online censoring (OC) based weighted-frequency Fourier linear combiner (OC-WFLC) adaptive filtering structure is proposed to reduce data processing costs in the estimation of pathological hand tremor (PHT) measurements. The proposed OC-WFLC is combined with the Fourier linear combiner (FLC) to effectively separate the PHT and voluntary movement from the hand tremor signal. The OC-WFLC is shown to adaptively extract the most informative frequency information, that is readily employed within the FLC to adaptively decompose the measurement signal into its PHT and voluntary movement components. The utilization of the OC strategy in the proposed framework is shown to significantly reduce data processing costs without adverse effects on the performance. Simulation results on real-world PHT data demonstrate the ability of the proposed OC-WFLC to yield a dramatic reduction of the processing time, a prerequisite for real-time rehabilitative, wearable, and assistive technology designed for PHT patients.

We address the estimation problem for general finite mixture models, with a particular focus on the elliptical mixture models (EMMs). Compared to the widely adopted Kullback–Leibler divergence, we show that the Wasserstein distance provides a more desirable optimisation space. We thus provide a stable solution to the EMMs that is both robust to initialisations and reaches a superior optimum by adaptively optimising along a manifold of an approximate Wasserstein distance. To this end, we first provide a unifying account of computable and identifiable EMMs, which serves as a basis to rigorously address the underpinning optimisation problem. Due to a probability constraint, solving this problem is extremely cumbersome and unstable, especially under the Wasserstein distance. To relieve this issue, we introduce an efficient optimisation method on a statistical manifold defined under an approximate Wasserstein distance, which allows for explicit metrics and computable operations, thus significantly stabilising and improving the EMM estimation. We further propose an adaptive method to accelerate the convergence. Experimental results demonstrate the excellent performance of the proposed EMM solver.

Generative adversarial nets (GANs) have become a preferred tool for tasks involving complicated distributions. To stabilise the training and reduce the mode collapse of GANs, one of their main variants employs the integral probability metric (IPM) as the loss function. This provides extensive IPM-GANs with theoretical support for basically comparing moments in an embedded domain of the \textit{critic}. We generalise this by comparing the distributions rather than their moments via a powerful tool, i.e., the characteristic function (CF), which uniquely and universally comprising all the information about a distribution. For rigour, we first establish the physical meaning of the phase and amplitude in CF, and show that this provides a feasible way of balancing the accuracy and diversity of generation. We then develop an efficient sampling strategy to calculate the CFs. Within this framework, we further prove an equivalence between the embedded and data domains when a reciprocal exists, where we naturally develop the GAN in an auto-encoder structure, in a way of comparing everything in the embedded space (a semantically meaningful manifold). This efficient structure uses only two modules, together with a simple training strategy, to achieve bi-directionally generating clear images, which is referred to as the reciprocal CF GAN (RCF-GAN). Experimental results demonstrate the superior performances of the proposed RCF-GAN in terms of both generation and reconstruction.

A new quaternion-valued adaptive filtering algorithm based on extrapolated weight methods is proposed. The proposed algorithm belongs to the class of conjugate direction algorithms [1]. This class of extrapolation (momentum) based algorithms is preferred to RLS-based algorithms when the matrix inversion should be avoided, e.g. in the case of non-vector signals, sparse signals or non-stationary signals. This paper introduces Nesterov's optimal gradient methods in widely linear quaternion adaptive filtering. The resulting class of algorithm is shown to both have similar computational complexity and comparable performance to WLQRLS; however, the proposed method is more stable and outperforms WLQRLS in the non-stationary case.

Widely linear (WL) models have been demonstrated to be superior to conventional strictly linear models for the estimation of noncircular complex and quaternion signals. Existing studies on their performance bounds focus on the analysis of mean square error (MSE). However, the single degree of freedom within standard MSE allows for only the minimization of error power, with no means to understand how the error contribution is distributed across the data channels. To this end, we introduce novel complex and quaternion valued complementary quadratic cost functions for complex and quaternion signal estimation, which are extensions of the recently proposed complementary MSE metric. It is shown that for WL minimum MSE estimation and least squares regression, the complementary cost function and the standard cost function attain the same stationary point. We also show that for the former, the stationary point is a saddle point. This novel finding provides insight into the performance of complex and quaternion WL estimators, and offers a rigorous foundation for further developments in this field.

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 [Formula: see text]-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.

Widely linear processing has been shown to be superior to the traditional strictly linear processing in quaternion minimum mean square error (MMSE) estimation. However, a quantifiable performance difference between strictly and widely linear processing and the relationship between the performance and quaternion impropriety are still lacking. To this end, we present a proof for the performance advantage of widely linear estimation and relate the performance bounds to signal properties by exploiting the approximate joint diagonalisation of quaternion covariance matrices. In that sense, this work can be seen as a generalisation of complex-valued MMSE estimation, and can thus also be applied to the complex-valued case. Simulations on synthetic signals support the analysis.