Péter Kovács

Eötvös Loránd University · Department of Numerical Analysis

The occipital cortex responds to visual stimuli regardless of a patient’s level of consciousness or attention, offering a noninvasive diagnostic tool for both ophthalmologists and neurologists. This response signal manifests as a unique waveform referred to as the visually evoked potential (VEP), which can be extracted from the electroencephalogram...

Thermographic imaging is a specific non-destructive evaluation (NDE) approach in which the investigated object is exposed to an initial thermal excitation. The utilization of infrared cameras to detect the induced surface temperature change enables the deduction of the internal structure of the inspected material. This requires addressing a large-s...

italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Goal: Recently, large datasets of biosignals acquired during surgery became available. As they offer multiple physiological signals measured in parallel, multimodal analysis – which involves their joint analysis – can be conducted and could provide dee...

Smart tire technologies offer a novel sensing methodology for vehicle environment perception by providing direct measurements of tire dynamics parameters. This information can be utilized in advanced driver assistance systems as well as autonomous vehicle control to enhance vehicle performance and safety. Considering these criteria, we develop algo...

In this paper, we develop the so-called variable projection support vector machine (VP-SVM) algorithm that is a generalization of the classical SVM. In fact, the VP block serves as an automatic feature extractor to the SVM, which are trained simultaneously. We consider the primal form of the arising optimization task and investigate the use of nonl...

Representation learning has become a crucial area of research in machine learning, as it aims to discover efficient ways of representing raw data with useful features to increase the effectiveness, scope and applicability of downstream tasks such as classification and prediction. In this paper, we propose a novel method to generate representations...

In contrast to wide/broad neural networks, shallow network topologies are attributed to lower FLOPS and thus a lower inference delay. This makes them a suitable candidate for AI-assisted edge computation as the overall usage cost is negligible compared to deep networks. However, shallowing a topology limits its representational power and generaliza...

There have been several attempts to quantify the diagnostic distortion caused by algorithms that perform low-dimensional electrocardiogram (ECG) representation. However, there is no universally accepted quantitative measure that allows the diagnostic distortion arising from denoising, compression, and ECG beat representation algorithms to be determ...

Edge-based Machine Learning (ML) has a pivotal role in revolutionizing smart healthcare by introducing a tangible improvement in the secure and discrete medical data analysis. This paper presents a novel neural network architecture by combining Variable Projections (VP) and Spiking Neural Networks (SNN). VPs are nonlinearly parameterized orthogonal...

There have been several attempts to quantify the diagnostic distortion caused by algorithms that perform low-dimensional electrocardiogram (ECG) representation. However, there is no universally accepted quantitative measure that allows the diagnostic distortion arising from denoising, compression, and ECG beat representation algorithms to be determ...

In analyzing non-stationary noisy signals with time-varying frequency content, it's convenient to use distribution methods in joint, time and frequency, domains. Besides different adaptive data-driven time-frequency (TF) representations, the approach with multiple orthogonal and optimally concentrated Hermite window functions is an effective soluti...

Thermographic imaging is a fast and contactless way of inspecting material parts. Usually, with model-driven evaluation procedures, lateral heat flow is ignored, and, thus, 1D reconstruction is applied to detect defects. However, to correctly size defects, the lateral heat flow must be considered, which requires a full 3D reconstruction. The 3D the...

Intelligent tires can be used for a wide array of applications ranging from tire pressure monitoring to analyzing tire/road interactions, wheel loading, and tread wear monitoring. In this article, we develop a measurement system for intelligent tires equipped with a 3-D piezoresistive force sensor. The output of the sensor is segmented into tire re...

In this paper, we introduce VPNet, a novel model-driven neural network architecture based on variable projection (VP). Applying VP operators to neural networks results in learnable features, interpretable parameters, and compact network structures. This paper discusses the motivation and mathematical background of VPNet and presents experiments. Th...

Tensor-based estimation has been of particular interest of the scientific community for several years now. While showing promising results on system estimation and other tasks, one big downside is the tremendous amount of computational power and memory required – especially during training – to achieve satisfactory performance. We present a novel f...

The electrocardiogram (ECG) follows a characteristic shape, which has led to the development of several mathematical models for extracting clinically important information. Our main objective is to resolve limitations of previous approaches, that means to simultaneously cope with various noise sources, perform exact beat segmentation, and to retain...

In this manuscript we demonstrate that accurate road abnormality detection based on signals from a 3D force measuring sensor implanted into the tires of a vehicle is possible. We discuss approximating the sensor's output using adaptive Hermite-functions [4] and present an experiment that shows the connection between abnormal road conditions and the...

Thermographic imaging is a contactless and nondestructive way to detect defects inside the specimen. The current state-of-the-art approach combines model-and deep learning-based reconstructions in a hybrid fashion. The recently developed virtual wave concept (VWC) provides a framework to develop such hybrid solutions, and allows to utilize physical...

Objective: The electrocardiogram (ECG) follows a characteristic shape, which has led to the development of several mathematical models for extracting clinically important information. Our main objective is to resolve limitations of previous approaches, that means to simultaneously cope with various noise sources, perform exact beat segmentation, a...

In this paper, we investigate two deep learning approaches to recovering initial temperature profiles from thermographic images in nondestructive material testing. First, we trained a deep neural network (DNN) in an end-to-end fashion by directly feeding the surface temperature measurements to the DNN. Second, we turned the surface temperature meas...

It is a teaser to our journal paper about thermography and deep learning.

In this paper, we introduce VPNet, a novel model-driven neural network architecture based on variable projections (VP). The application of VP operators in neural networks implies learnable features, interpretable parameters, and compact network structures. This paper discusses the motivation and mathematical background of VPNet as well as experimen...

We propose a hybrid method for reconstructing thermo-graphic images by combining the recently developed virtual wave concept with deep neural networks. The method can be used to detect defects inside materials in a non-destructive way. We propose two architectures along with a thorough evaluation that shows a substantial improvement compared to sta...

The estimation of the frequencies of multiple complex sinusoids in the presence of noise is required in many applications such as sonar, speech processing, communications, and power systems. According to previous work, this problem can be reformulated as a separable nonlinear least squares problem (SNLLS). In this paper, such formulation is derived...

In this work, we are focusing on the problem of heartbeat classification in electrocardiogram (ECG) signals. First we develop a patient-specific feature extraction scheme by using adaptive orthogonal transformations based on wavelets, B-splines, Hermite and rational functions. The so-called variable projection provides the general framework to find...

Biomedical signal processing frequently deals with information extraction for clinical decision support. A major challenge in this field is to reveal diagnostic information by eliminating undesired interfering influences. In case of the electrocardiogram, e.g., a frequently arising interference is caused by respiration, which possibly superimposes...

In this paper, we present a nonlinear least-squares fitting algorithm using B-splines with free knots. Since its performance strongly depends on the initial estimation of the free parameters (i.e. the knots), we also propose a fast and efficient knot-prediction algorithm that utilizes numerical properties of first-order B-splines. Using $\ell_p\;(p...

We demonstrated four ECG compression algorithms based on free knot splines, Hermite functions, adaptive wavelets and wavelet packets. The animations work in adobe acrobat reader.

We demonstrated the efficiency of the proposed algorithm in ECG signal compression, which showed a great improvement compared to the state-of-the-art. In the comparative study, we implemented four ECG compression algorithms based on free knot splines, Hermite functions, adaptive wavelets and wavelet packets. The interactive version of the implemen...

In this paper we develop an adaptive transform-domain technique based on rational function systems. It is of general importance in several areas of signal theory, including filter design, transfer function approximation, system identification, control theory etc. The construction of the proposed method is discussed in the framework of a general mat...

In this paper we develop an adaptive transform-domain technique based on rational function systems. It is of general importance in several areas of signal theory, including filter design, transfer function approximation, system identification, control theory etc. The construction of the proposed method is discussed in the framework of a general mat...

In this paper, we present a nonlinear least-squares fitting algorithm using B-splines with free knots. Since its performance strongly depends on the initial estimation of the free parameters (i.e. the knots), we also propose a fast and efficient knot-prediction algorithm that utilizes numerical properties of first-order B-splines. Using ℓp (p=1,2,∞...

Modern medical science demands sophisticated signal representation methods in order to cope with the increasing amount of data. Important criteria for these methods are mainly low computational and storage costs, whereas the underlying mathematical model should still be interpretable and meaningful for the data analyst. One of the most promising mo...

In photoacoustic imaging, ultrasound waves generated by a temperature rise after illumination of light absorbing structures are measured on the sample surface. These measurements are then used to reconstruct the optical absorption. We develop a method for reconstructing the absorption inside the sample based on a discrete linear state space reformu...

In photoacoustic imaging, ultrasound waves generated by a temperature rise after illumination of light absorbing structures are measured on the sample surface. These measurements are then used to reconstruct the optical absorption. We develop a method for reconstructing the absorption inside the sample based on a discrete linear state space reformu...

In this paper we consider the problem of sparse signal modeling by means of rational functions. Our dictionary is composed by a finite collection of elementary rational functions. In order to represent the signal with minimal error, we select an optimal number of basis from this set. The mutual coherence is a fundamental attribute of the dictionary...

This package contains all the MatLab implementations that are related to the paper: 1) constraints for approximating ECG signals; 2) adjusting the parameters to a specific heartbeat via optimization; 3) scripts for testing and evaluating various inverse pole configurations. Note that the test results are available at my website: http://numanal.in...

In this paper we develop an adaptive electrocardiogram (ECG) model based on rational functions. We approximate the original signal by the partial sums of the corresponding Malmquist–Takenaka–Fourier series. Our aim in the construction of the model was twofold. Namely, besides good approximation an equally important point was to have direct connecti...

Abstract In this paper, we address the problem of off-line supervised detection of epileptic seizures in long-term Electroencephalography (EEG) records. A novel feature extraction method is proposed based on the sparse rational decomposition and the Local Gabor Binary Patterns (LGBP). Namely, we decompose the channels of the EEG record into 8 spars...

This dissertation is concerned with the application of the theory of rational functions in signal processing. The PhD thesis summarizes the corresponding results of the author’s research. Since the systems of rational functions are defined by the collection of inverse poles with multiplicities, the following parameters should be determined: the num...

In modern medical science evaluation of electrocardiogram (ECG) has proven to be an important task for doctors. These signals contain valuable information on the patients' condition; however analysis of them has encountered numerous challenges, such as storage of long-term recordings, �ltering, and segmentation of signals. Resolving these problems...

The Singular Value Decomposition (SVD) can be efficiently used to detect motion in videos captured by a static camera. However, the SVD is computationally demanding when a large matrix - a spatio-temporal data window typically composed of ten to thirty frames-is repeatedly processed. Recently, a running (incremental) version [1] of the SVD has been...

A system for epileptic seizure detection in Electroencephalography (EEG) is described in the paper. One of the challenges is to distinguish rhythmic discharges from nonstationary patterns occurring during seizures. The proposed approach is based on an adaptive and localized time-frequency representation of EEG signals by means of rational functions...

This work deals with an adaptive and localized time-frequency representation of time-series signals based on rational functions. The proposed rational Discrete Short Time Fourier Transform (DSTFT) is used for extracting discriminative features in EEG data. We take the advantages of bagging ensemble learning and Alternating Decision Tree (ADTree) cl...

Aims: Our aim is to improve the accuracy of existing heart beat detection algorithms in order to provide reliable heart beat locations in a multi-modal beat detection scheme. Methods: A rhythm-based algorithm is presented which on top of a base beat detection method processes the detected beats by rejecting annotations and filling in gaps while min...

The rational function systems proved to be useful in several areas including system and control theories and signal processing. In this paper, we present an extension of the well-known particle swarm optimization (PSO) method based on the hyperbolic geometry. We applied this method on digital signals to determine the optimal parameters of the ratio...

There is a wide range of applications of non-equidistant discretization of real signals. For instance, in computer graphics, Fourier analysis, identification and control theories, etc. They have the common ability to describe dynamical systems as well. In this paper we provide a fast algorithm based on an existing mathematical model to compute a no...

The rational function systems proved to be useful in several areas including system and control theories and signal processing. In this paper, we present an extension of the well-known particle swarm optimization (PSO) method based on the hyperbolic geometry. We applied this method on digital signals to determine the optimal parameters of the ratio...

There is a wide range of applications of rational function systems. Including in system, control theories and signal processing. A special class of rational functions, the so-called Blaschke functions and the orthonormal Malmquist--Takenaka (MT) systems are effectively used for representing signals especially electrocardiograms. We present our pr...

There is a wide range of applications of rational function systems. Including in system, control theories and signal processing. A special class of rational functions, the so-called Blaschke functions and the orthonormal Malmquist-Takenaka (MT) systems are effectively used for representing signals especially electrocardiograms. We present our proje...

We introduce a novel approach for the processing of ECG signals (ElectroCardioGrams), which are frequently used in medical diagnostics. (They describe the functioning of the human heart.) The use of Fourier, wavelet and Gabor transforms has been already widely studied in the case of analysing medical signals. In our approach we shall use rational f...

The main topic of this paper is the relation between the QRS complexes recorded from different pairs of electrodes of the same ECG signal. The electrode combinations I, II, III, aVR, aVL, aVF will be considered. Our aim is to provide a simple mathematical model for explaining and demonstrating the relation between the records. The model we construc...

Electrocardiograms are widely used in biomedical signal processing to diagnose abnormal heart functioning. Many algorithms have been constructed to analyse, measure and compress these signals. These methods are hard to test because real ECG signals are distorted by several types of noise. We present an algorithm which generates realistic synthetic...