Imperial College London

ProfessorDaniloMandic

Faculty of EngineeringDepartment of Electrical and Electronic Engineering

Professor of Machine Intelligence
 
 
 
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Contact

 

+44 (0)20 7594 6271d.mandic Website

 
 
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Assistant

 

Miss Vanessa Rodriguez-Gonzalez +44 (0)20 7594 6267

 
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Location

 

813Electrical EngineeringSouth Kensington Campus

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Summary

 

Publications

Publication Type
Year
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736 results found

Davies HJ, Hammour G, Zylinski M, Nassibi A, Stankovic L, Mandic DPet al., 2024, The Deep-Match Framework: R-Peak Detection in Ear-ECG., IEEE Trans Biomed Eng, Vol: PP

The Ear-ECG provides a continuous Lead I like electrocardiogram (ECG) by measuring the potential difference related to heart activity by electrodes which are embedded within earphones. However, the significant increase in wearability and comfort enabled by Ear-ECG is often accompanied by a degradation in signal quality - a common obstacle that is shared by the majority of wearable technologies. We aim to resolve this issue by introducing a Deep Matched Filter (Deep-MF) for the highly accurate detection of R-peaks in wearable ECG, thus enhancing the utility of Ear-ECG in real-world scenarios. The Deep-MF consists of an encoder stage (trained as part of an encoder-decoder module to reproduce ground truth ECG), and an R-peak classifier stage. Through its operation as a Matched Filter, the encoder section searches for matches with an ECG template pattern in the input signal, prior to filtering these matches with the subsequent convolutional layers and selecting peaks corresponding to the ground truth ECG. The so condensed latent representation of R-peak information is then fed into a simple R-peak classifier, of which the output provides precise R-peak locations. The proposed Deep Matched Filter is evaluated using leave-one-subject-out cross-validation over 36 subjects with an age range of 18-75, with the Deep-MF outperforming existing algorithms for R-peak detection in noisy ECG. The Deep-MF is benchmarked against a ground truth ECG, in the form of either chest-ECG or arm-ECG, via both R-peak recall and R-peak precision metrics. The Deep-MF achieves a median R-peak recall of 94.9% and a median precision of 91.2% across subjects when evaluated with leave-one-subject-out cross validation. Moreover, when evaluated across a range of thresholds, the Deep-MF achieves an area under the curve (AUC) value of 0.97. The interpretability of Deep-MF as a Matched Filter is further strengthened by the analysis of its response to partial initialisation with an ECG template. We de

Journal article

Rakhmatulin I, Dao M-S, Nassibi A, Mandic Det al., 2024, Exploring Convolutional Neural Network Architectures for EEG Feature Extraction., Sensors (Basel), Vol: 24

The main purpose of this paper is to provide information on how to create a convolutional neural network (CNN) for extracting features from EEG signals. Our task was to understand the primary aspects of creating and fine-tuning CNNs for various application scenarios. We considered the characteristics of EEG signals, coupled with an exploration of various signal processing and data preparation techniques. These techniques include noise reduction, filtering, encoding, decoding, and dimension reduction, among others. In addition, we conduct an in-depth analysis of well-known CNN architectures, categorizing them into four distinct groups: standard implementation, recurrent convolutional, decoder architecture, and combined architecture. This paper further offers a comprehensive evaluation of these architectures, covering accuracy metrics, hyperparameters, and an appendix that contains a table outlining the parameters of commonly used CNN architectures for feature extraction from EEG signals.

Journal article

Davies HJ, Hammour G, Xiao H, Bachtiger P, Larionov A, Molyneaux PL, Peters NS, Mandic DPet al., 2024, Physically Meaningful Surrogate Data for COPD, IEEE Open Journal of Engineering in Medicine and Biology, Vol: 5, Pages: 148-156

The rapidly increasing prevalence of debilitating breathing disorders, such as chronic obstructive pulmonary disease (COPD), calls for a meaningful integration of artificial intelligence (AI) into respiratory healthcare. Deep learning techniques are 'data hungry' whilst patient-based data is invariably expensive and time consuming to record. To this end, we introduce a novel COPD-simulator, a physical apparatus with an easy to replicate design which enables rapid and effective generation of a wide range of COPD-like data from healthy subjects, for enhanced training of deep learning frameworks. To ensure the faithfulness of our domain-aware COPD surrogates, the generated waveforms are examined through both flow waveforms and photoplethysmography (PPG) waveforms (as a proxy for intrathoracic pressure) in terms of duty cycle, sample entropy, FEV1/FVC ratios and flow-volume loops. The proposed simulator operates on healthy subjects and is able to generate FEV1/FVC obstruction ratios ranging from greater than 0.8 to less than 0.2, mirroring values that can observed in the full spectrum of real-world COPD. As a final stage of verification, a simple convolutional neural network is trained on surrogate data alone, and is used to accurately detect COPD in real-world patients. When training solely on surrogate data, and testing on real-world data, a comparison of true positive rate against false positive rate yields an area under the curve of 0.75, compared with 0.63 when training solely on real-world data.

Journal article

Yarici M, Von Rosenberg W, Hammour G, Davies H, Amadori P, Ling N, Demiris Y, Mandic DPet al., 2024, Hearables: feasibility of recording cardiac rhythms from single in-ear locations., R Soc Open Sci, Vol: 11, ISSN: 2054-5703

The ear is well positioned to accommodate both brain and vital signs monitoring, via so-called hearable devices. Consequently, ear-based electroencephalography has recently garnered great interest. However, despite the considerable potential of hearable based cardiac monitoring, the biophysics and characteristic cardiac rhythm of ear-based electrocardiography (ECG) are not yet well understood. To this end, we map the cardiac potential on the ear through volume conductor modelling and measurements on multiple subjects. In addition, in order to demonstrate real-world feasibility of in-ear ECG, measurements are conducted throughout a long-time simulated driving task. As a means of evaluation, the correspondence between the cardiac rhythms obtained via the ear-based and standard Lead I measurements, with respect to the shape and timing of the cardiac rhythm, is verified through three measures of similarity: the Pearson correlation, and measures of amplitude and timing deviations. A high correspondence between the cardiac rhythms obtained via the ear-based and Lead I measurements is rigorously confirmed through agreement between simulation and measurement, while the real-world feasibility was conclusively demonstrated through efficacious cardiac rhythm monitoring during prolonged driving. This work opens new avenues for seamless, hearable-based cardiac monitoring that extends beyond heart rate detection to offer cardiac rhythm examination in the community.

Journal article

Bermond M, Davies HJ, Occhipinti E, Nassibi A, Mandic DPet al., 2023, Reducing racial bias in SpO2 estimation: the effects of skin pigmentation, 2023 45th Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC), ISSN: 1557-170X

Accurate pulse-oximeter readings are critical for clinical decisions, especially when arterial blood-gas tests - the gold standard for determining oxygen saturation levels - are not available, such as when determining COVID-19 severity. Several studies demonstrate that pulse oxygen saturation estimated from photoplethysmography (PPG) introduces a racial bias due to the more profound scattering of light in subjects with darker skin due to the increased presence of melanin. This leads to an overestimation of blood oxygen saturation in those with darker skin that is increased for low blood oxygen levels and can result in a patient not receiving potentially life-saving supplemental oxygen. This racial bias has been comprehensively studied in conventional finger pulse oximetry but in other less commonly used measurement sites, such as in-ear pulse oximetry, it remains unexplored. Different measurement sites can have thinner epidermis compared with the finger and lower exposure to sunlight (such as is the case with the ear canal), and we hypothesise that this could reduce the bias introduced by skin tone on pulse oximetry. To this end, we compute SpO2 in different body locations, during rest and breath-holds, and compare with the index finger. The study involves a participant pool covering 6-pigmentation categories from Fitzpatrick's Skin Pigmentation scale. These preliminary results indicate that locations characterized by cartilaginous highly vascularized tissues may be less prone to the influence of melanin and pigmentation in the estimation of SpO2, paving the way for the development of non-discriminatory pulse oximetry devices.

Conference paper

Charlton PH, Allen J, Bailón R, Baker S, Behar JA, Chen F, Clifford GD, Clifton DA, Davies HJ, Ding C, Ding X, Dunn J, Elgendi M, Ferdoushi M, Franklin D, Gil E, Hassan MF, Hernesniemi J, Hu X, Ji N, Khan Y, Kontaxis S, Korhonen I, Kyriacou PA, Laguna P, Lázaro J, Lee C, Levy J, Li Y, Liu C, Liu J, Lu L, Mandic DP, Marozas V, Mejía-Mejía E, Mukkamala R, Nitzan M, Pereira T, Poon CCY, Ramella-Roman JC, Saarinen H, Shandhi MMH, Shin H, Stansby G, Tamura T, Vehkaoja A, Wang WK, Zhang Y-T, Zhao N, Zheng D, Zhu Tet al., 2023, The 2023 wearable photoplethysmography roadmap., Physiol Meas, Vol: 44

Photoplethysmography is a key sensing technology which is used in wearable devices such as smartwatches and fitness trackers. Currently, photoplethysmography sensors are used to monitor physiological parameters including heart rate and heart rhythm, and to track activities like sleep and exercise. Yet, wearable photoplethysmography has potential to provide much more information on health and wellbeing, which could inform clinical decision making. This Roadmap outlines directions for research and development to realise the full potential of wearable photoplethysmography. Experts discuss key topics within the areas of sensor design, signal processing, clinical applications, and research directions. Their perspectives provide valuable guidance to researchers developing wearable photoplethysmography technology.

Journal article

Mandic D, Bermond M, Occhipinti E, Davies HJ, Hammour G, Nassibi Aet al., 2023, In Your Ear: A Multimodal Hearables Device for the Assessment of the State of Body and Mind, IEEE Pulse, Vol: 14, Pages: 17-23, ISSN: 2154-2287

It is predicted that the global shipment of smart wearables will approach 302.2 million devices in 2023, increasing from 222.9 million devices in 2019 [1]. It was also forecast in 2019 that the number of ear-worn devices - so-called hearables - would rise to 105.3 million in 2023, from 72 million in 2019 [2]. Given the relatively fixed position of the head with respect to the brain and vital organs in most of the daily activities, hearables provide more consistent recordings compared to more mobile parts of the body, such as the wrists. This allows for robust recordings of the both electroencephalogram (EEG) [3], [4], [5], electrocardiogram (ECG) [6], and photoplethysmogram (PPG) [7], together with the derived measures including the heart rate (HR) [4], respiratory rate [8], blood oxygen saturation (SpO2) [7], and blood glucose levels [9].

Journal article

Davies HJ, Mandic DP, 2023, Rapid extraction of respiratory waveforms from photoplethysmography: A deep corr-encoder approach, BIOMEDICAL SIGNAL PROCESSING AND CONTROL, Vol: 85, ISSN: 1746-8094

Journal article

Poushpas S, Normahani P, Kisil I, Szubert B, Mandic DP, Jaffer Uet al., 2023, Tensor decomposition and machine learning for the detection of arteriovenous fistula stenosis: An initial evaluation, PLOS ONE, Vol: 18, ISSN: 1932-6203

Journal article

Xu YL, Konstantinidis K, Mandic DP, 2023, Graph-Regularized Tensor Regression: A Domain-Aware Framework for Interpretable Modeling of Multiway Data on Graphs, NEURAL COMPUTATION, Vol: 35, Pages: 1404-1429, ISSN: 0899-7667

Journal article

Davies HJ, Zylinski M, Bermond M, Liu Z, Khaleghimeybodi M, Mandic DPet al., 2023, Feasibility of transfer learning from finger PPG to in-ear PPG, 2023 45th Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC), Publisher: IEEE, ISSN: 1557-170X

The success of deep learning methods has enabled many modern wearable health applications, but has also highlighted the critical caveat of their extremely data hungry nature. While the widely explored wrist and finger photoplethysmography (PPG) sites are less affected, given the large available databases, this issue is prohibitive to exploring the full potential of novel recording locations such as in-ear wearables. To this end, we assess the feasibility of transfer learning from finger PPG to in-ear PPG in the context of deep learning for respiratory monitoring. This is achieved by introducing an encoder-decoder framework which is set up to extract respiratory waveforms from PPG, whereby simultaneously recorded gold standard respiratory waveforms (capnography, impedance pneumography and air flow) are used as a training reference. Next, the data augmentation and training pipeline is examined for both training on finger PPG and the subsequent fine tuning on in-ear PPG. The results indicate that, through training on two large finger PPG data sets (95 subjects) and then retraining on our own small in-ear PPG data set (6 subjects), the model achieves lower and more consistent test error for the prediction of the respiratory waveforms, compared to training on the small in-ear data set alone. This conclusively demonstrates the feasibility of transfer learning from finger PPG to in-ear PPG, leading to better generalisation across a wide range of respiratory rates.

Conference paper

Zylinski M, Occhipinti E, Mandic D, 2023, Generalization Error of a Regression Model for Non-Invasive Blood Pressure Monitoring using a Single Photoplethysmography (PPG) Signal., Annu Int Conf IEEE Eng Med Biol Soc, Vol: 2023, Pages: i-iv

Photoplethysmography (PPG) sensors integrated in wearable devices offer the potential to monitor arterial blood pressure (ABP) in patients. Such cuffless, non-invasive, and continuous solution is suitable for remote and ambulatory monitoring. A machine learning model based on PPG signal can be used to detect hypertension, estimate beat-by-beat ABP values, and even reconstruct the shape of the ABP. Overall, models presented in literature have shown good performance, but there is a gap between research and potential real-world use cases. Usually, models are trained and tested on data from the same dataset and same subjects, which may lead to overestimating their accuracy. In this paper: we compare cross-validation, where the test data are from the same dataset as training data, and external validation, where the model is tested on samples from a new dataset, on a regression model which predicts diastolic blood pressure from PPG features. The results show that, in the cross-validation, the predicted and the real values are linearly dependent, while in the external validation, the predicted values are not related to the real ones, but probably just through an average value.

Journal article

Tian H, Occhipinti E, Nassibi A, Mandic DPet al., 2023, Hearables: Heart Rate Variability from Ear Electrocardiogram and Ear Photoplethysmogram (Ear-ECG and Ear-PPG)., Annu Int Conf IEEE Eng Med Biol Soc, Vol: 2023, Pages: 1-5

This work aims to classify physiological states using heart rate variability (HRV) features extracted from electrocardiograms recorded in the ears (ear-ECG). The physiological states considered in this work are: (a) normal breathing, (b) controlled slow breathing, and (c) mental exercises. Since both (b) and (c) cause higher variance in heartbeat intervals, breathing-related features (SpO2 and mean breathing interval) from the ear Photoplethysmogram (ear-PPG) are used to facilitate classification. This work: 1) proposes a scheme that, after initialization, automatically extracts R-peaks from low signal-to-noise ratio ear-ECG; 2) verifies the feasibility of extracting meaningful HRV features from ear-ECG; 3) quantitatively compares several ear-ECG sites; and 4) discusses the benefits of combining ear-ECG and ear-PPG features.

Journal article

Hammour G, Atzori G, Monica CD, Ravindran KKG, Revell V, Dijk D-J, Mandic DPet al., 2023, Hearables: Automatic Sleep Scoring from Single-Channel Ear-EEG in Older Adults., Annu Int Conf IEEE Eng Med Biol Soc, Vol: 2023, Pages: 1-4

Sleep disorders are a prevalent problem among older adults, yet obtaining an accurate and reliable assessment of sleep quality can be challenging. Traditional polysomnography (PSG) is the gold standard for sleep staging, but is obtrusive, expensive, and requires expert assistance. To this end, we propose a minimally invasive single-channel single ear-EEG automatic sleep staging method for older adults. The method employs features from the frequency, time, and structural complexity domains, which provide a robust classification of sleep stages from a standardised viscoelastic earpiece. Our method is verified on a dataset of older adults and achieves a kappa value of at least 0.61, indicating substantial agreement. This paves the way for a non-invasive, cost-effective, and portable alternative to traditional PSG for sleep staging.

Journal article

Liu C, Ma X, Zhan Y, Ding L, Tao D, Du B, Hu W, Mandic DPet al., 2023, Comprehensive Graph Gradual Pruning for Sparse Training in Graph Neural Networks, IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, ISSN: 2162-237X

Journal article

Davies HJ, Williams I, Hammour G, Yarici M, Stacey MJ, Seemungal BM, Mandic DPet al., 2023, In-ear SpO2 for classification of cognitive workload, IEEE Transactions on Cognitive and Developmental Systems, Vol: 15, Pages: 950-958, ISSN: 2379-8920

The brain is the most metabolically active organ in the body, which increases its metabolic activity, and thus oxygen consumption, with increasing cognitive demand. This motivates us to question whether increased cognitive workload may be measurable through changes in blood oxygen saturation. To this end, we explore the feasibility of cognitive workload tracking based on in-ear SpO2 measurements, which are known to be both robust and exhibit minimal delay. We consider cognitive workload assessment based on an N-back task with randomised order. It is shown that the 2-back and 3-back tasks (high cognitive workload) yield either the lowest median absolute SpO2 or largest median decrease in SpO2 in all of the subjects, indicating a measurable and statistically significant decrease in blood oxygen in response to increased cognitive workload. This makes it possible to classify the four N-back task categories, over 5 second epochs, with a mean accuracy of 90.6%, using features derived from in-ear pulse oximetry, including SpO2, pulse rate and respiration rate. These findings suggest that in-ear SpO2 measurements provide sufficient information for the reliable classification of cognitive workload over short time windows, which promises a new avenue for real time cognitive workload tracking.

Journal article

Stankovic L, Mandic D, 2023, Convolutional Neural Networks Demystified: A Matched Filtering Perspective-Based Tutorial, IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS, Vol: 53, Pages: 3614-3628, ISSN: 2168-2216

Journal article

Sau A, 2023, Artificial intelligence-enabled electrocardiogram to distinguish atrioventricular re-entrant tachycardia from atrioventricular nodal re-entrant tachycardia, Cardiovascular Digital Health Journal, Vol: 4, Pages: 60-67, ISSN: 2666-6936

BackgroundAccurately determining arrhythmia mechanism from a 12-lead electrocardiogram (ECG) of supraventricular tachycardia can be challenging. We hypothesized a convolutional neural network (CNN) can be trained to classify atrioventricular re-entrant tachycardia (AVRT) vs atrioventricular nodal re-entrant tachycardia (AVNRT) from the 12-lead ECG, when using findings from the invasive electrophysiology (EP) study as the gold standard.MethodsWe trained a CNN on data from 124 patients undergoing EP studies with a final diagnosis of AVRT or AVNRT. A total of 4962 5-second 12-lead ECG segments were used for training. Each case was labeled AVRT or AVNRT based on the findings of the EP study. The model performance was evaluated against a hold-out test set of 31 patients and compared to an existing manual algorithm.ResultsThe model had an accuracy of 77.4% in distinguishing between AVRT and AVNRT. The area under the receiver operating characteristic curve was 0.80. In comparison, the existing manual algorithm achieved an accuracy of 67.7% on the same test set. Saliency mapping demonstrated the network used the expected sections of the ECGs for diagnoses; these were the QRS complexes that may contain retrograde P waves.ConclusionWe describe the first neural network trained to differentiate AVRT from AVNRT. Accurate diagnosis of arrhythmia mechanism from a 12-lead ECG could aid preprocedural counseling, consent, and procedure planning. The current accuracy from our neural network is modest but may be improved with a larger training dataset.

Journal article

Liu J, Xu D, Lu Y, Kong J, Mandic DPet al., 2023, Last-iterate convergence analysis of stochastic momentum methods for neural networks, NEUROCOMPUTING, Vol: 527, Pages: 27-35, ISSN: 0925-2312

Journal article

Hammour G, Mandic DP, 2023, An In-Ear PPG-Based Blood Glucose Monitor: A Proof-of-Concept Study, SENSORS, Vol: 23

Journal article

Stankovica L, Mandic DP, 2023, Understanding the Basis of Graph Convolutional Neural Networks via an Intuitive Matched Filtering Approach [Lecture Notes], IEEE SIGNAL PROCESSING MAGAZINE, Vol: 40, Pages: 155-165, ISSN: 1053-5888

Journal article

Li S, Yu Z, Xiang M, Mandic Det al., 2023, Reciprocal GAN Through Characteristic Functions (RCF-GAN), IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, Vol: 45, Pages: 2246-2263, ISSN: 0162-8828

Journal article

Qing Z, Ni J, Li Z, Menguc EC, Chen J, Mandic DPet al., 2023, Performance analysis of the augmented complex-valued least mean kurtosis algorithm, SIGNAL PROCESSING, Vol: 203, ISSN: 0165-1684

Journal article

Liang Y, Xu D, Zhang N, Mandic DPet al., 2023, Almost sure convergence of stochastic composite objective mirror descent for non-convex non-smooth optimization, OPTIMIZATION LETTERS, ISSN: 1862-4472

Journal article

Yarici MC, Thornton M, Mandic DP, 2023, Ear-EEG sensitivity modeling for neural sources and ocular artifacts, FRONTIERS IN NEUROSCIENCE, Vol: 16

Journal article

Zylinski M, Nassibi A, Rakhmatulin I, Malik A, Papavassiliou C, Mandic DPet al., 2023, Deployment of Artificial Intelligence Models on Edge Devices: A Tutorial Brief, IEEE Transactions on Circuits and Systems II: Express Briefs, ISSN: 1549-7747

Artificial intelligence (AI) on an edge device has enormous potential, including advanced signal filtering, event detection, optimization in communications and data compression, improving device performance, advanced on-chip process control, and enhancing energy efficiency. In this tutorial, we provide a brief overview of AI deployment on edge devices, and describe the process of building and deploying a neural network model on a digital edge device. The primary challenge when deploying an AI model in circuits is to fit the model within the constraints of the limited resources as the restricted memory capacity on IoT circuits and the finite computational power impose constraints on the utilization of deep neural networks on IoT. We address this issue by elucidating methods for optimizing neural network models. Part of the tutorial also covers the deployment of deep neural network on logic circuits, as significantly enhanced computational speed can be attained by transitioning the AI paradigm from neural networks to learning automata algorithms. This shift involves a move from arithmetic-based calculations to logic-based approaches. This transformation facilitates the deployment of AI onto Field-Programmable Gate Arrays (FPGAs). The last part of the tutorial covers the emerging topic of in-memory computation of the multiply-accumulate operation. Transferring computations to analog memories has the potential to improve speed and energy efficiency compared to digital architectures, potentially achieving improvements of several orders of magnitude. It is our hope that this tutorial will assist researchers and engineers to integrate AI models on edge devices, facilitating rapid and reliable implementation.

Journal article

Arya AN, Lei Xu Y, Stankovic L, Mandic DPet al., 2023, Hierarchical Graph Learning for Stock Market Prediction Via a Domain-Aware Graph Pooling Operator, ISSN: 1520-6149

The utility of Graph Neural Networks (GNN) for the paradigm of forecasting short-term stock price movements is investigated. In particular, a finance-specific graph pooling operation, referred to as StockPool, is introduced to efficiently coarsen the stock graph. This is achieved by employing domain knowledge to cluster stocks, depending on some task-specific characteristics (e.g. industries, sub-industries, etc.). Unlike fully end-to-end learnable graph pooling strategies (e.g. differentiable pooling, MinCUT pooling, etc.), such a deterministic pooling operator is considerably more computationally efficient and thus scalable to larger stock graphs. Experimentations on the S&P500 stock index demonstrate that the StockPool operator outperforms existing graph pooling strategies on the prediction of price movements. Finally, different graph pooling methods are utilized to create a set of highly uncorrelated GNN models; these are used to construct a graph ensemble model with an improved performance.

Conference paper

Jayne C, Mandic D, Duro R, 2023, Preface, Procedia Computer Science, Vol: 222

Journal article

Sun S, Diao Q, Xu D, Bourigault P, Mandic DPet al., 2023, Convex Quaternion Optimization for Signal Processing: Theory and Applications, IEEE Transactions on Signal Processing, Vol: 71, Pages: 4106-4115, ISSN: 1053-587X

Convex optimization methods have been extensively used in communications and signal processing. However, the theory of quaternion optimization is currently not as fully developed and systematic as that of complex and real optimization. To this end, we establish the convex optimization theory in quaternion variables based on the generalized Hamilton-real (GHR) calculus. This is achieved in a way that conforms with traditional complex and real optimization theory. We present several discriminant theorems for convex quaternion functions analogous to their complex counterparts. We also provide several discriminant criteria for strongly convex functions by the theorems of convex quaternion functions. Furthermore, we prove that the quaternion Newton method can converge in one step for positive definite quadratic quaternion functions and provide two applications in quaternion signal processing. These results provide a solid theoretical foundation for convex quaternion optimization and open avenues for further developments in quaternion signal processing applications.

Journal article

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