Spectral Domain Representation Research Articles

Convolutional neural networks combined with feature selection for radio‐frequency fingerprinting

AbstractRadio‐frequency fingerprinting is a technique for the authentication and identification of wireless devices using their intrinsic physical features and an analysis of the digitized signal collected during transmission. The technique is based on the fact that the unique physical features of the devices generate discriminating features in the transmitted signal, which can then be analyzed using signal‐processing and machine‐learning algorithms. Deep learning and more specifically convolutional neural networks (CNNs) have been successfully applied to the problem of radio‐frequency fingerprinting using a spectral domain representation of the signal. A potential problem is the large size of the data to be processed, because this size impacts on the processing time during the application of the CNN. We propose an approach to addressing this problem, based on dimensionality reduction using feature‐selection algorithms before the spectrum domain representation is given as an input to the CNN. The approach is applied to two public data sets of radio‐frequency devices using different feature‐selection algorithms for different values of the signal‐to‐noise ratio. The results show that the approach is able to achieve not only a shorter processing time; it also provides a superior classification performance in comparison to the direct application of CNNs.

Towards general-purpose representation learning of polygonal geometries

Neural network representation learning for spatial data (e.g., points, polylines, polygons, and networks) is a common need for geographic artificial intelligence (GeoAI) problems. In recent years, many advancements have been made in representation learning for points, polylines, and networks, whereas little progress has been made for polygons, especially complex polygonal geometries. In this work, we focus on developing a general-purpose polygon encoding model, which can encode a polygonal geometry (with or without holes, single or multipolygons) into an embedding space. The result embeddings can be leveraged directly (or finetuned) for downstream tasks such as shape classification, spatial relation prediction, building pattern classification, cartographic building generalization, and so on. To achieve model generalizability guarantees, we identify a few desirable properties that the encoder should satisfy: loop origin invariance, trivial vertex invariance, part permutation invariance, and topology awareness. We explore two different designs for the encoder: one derives all representations in the spatial domain and can naturally capture local structures of polygons; the other leverages spectral domain representations and can easily capture global structures of polygons. For the spatial domain approach we propose ResNet1D, a 1D CNN-based polygon encoder, which uses circular padding to achieve loop origin invariance on simple polygons. For the spectral domain approach we develop NUFTspec based on Non-Uniform Fourier Transformation (NUFT), which naturally satisfies all the desired properties. We conduct experiments on two different tasks: 1) polygon shape classification based on the commonly used MNIST dataset; 2) polygon-based spatial relation prediction based on two new datasets (DBSR-46K and DBSR-cplx46K) constructed from OpenStreetMap and DBpedia. Our results show that NUFTspec and ResNet1D outperform multiple existing baselines with significant margins. While ResNet1D suffers from model performance degradation after shape-invariance geometry modifications, NUFTspec is very robust to these modifications due to the nature of the NUFT representation. NUFTspec is able to jointly consider all parts of a multipolygon and their spatial relations during prediction while ResNet1D can recognize the shape details which are sometimes important for classification. This result points to a promising research direction of combining spatial and spectral representations.

A Fully Polarimetric Multilevel Fast Spectral Domain Algorithm for 3-D Imaging With Irregular Sample Locations

A fully polarimetric frequency-wavenumber domain algorithm for 3-D imaging using the synthetic aperture radar technique with irregular sample locations is introduced. At its core, the algorithm works with a multilevel plane-wave representation and relies on some of the concepts of the multilevel fast multipole method (MLFMM). By utilizing a recursive segmentation scheme, the presented algorithm efficiently handles irregular observation locations, which can vary along all three dimensions in space. The basic idea is to divide the observation region into subdomains of decreasing size, until the calculation of the spectral domain representation of the observation data in the individual subdomains by a discrete Fourier transform (DFT) without further acceleration is feasible. The overall uniformly sampled spectral representation of the observation data is then obtained by hierarchical aggregation of the subdomain spectra. The probe influence is fully compensated by the combined processing of several polarizations and solving small linear systems of equations related to the frequency-wavenumber samples on the coarsest level. The focused image is finally computed by fast Fourier transforms (FFTs). This approach, as opposed to conventional coherent back-projection algorithms (BPAs), allows for a fully polarimetric description of the scattering object and achieves good efficiency without loss of accuracy. To show the effectiveness of the algorithm, imaging results obtained from numerical simulations as well as from the evaluation of measured field data are presented and discussed.

A Comparison of Linear Inverse Scattering Models for Contactless GPR Imaging

Ground-penetrating radars operating at a stand-off distance from the probed domain are attractive diagnostic tools in several contexts. Despite notable advantages offered in terms of noninvasiveness and flexibility, the usage of stand-off configurations makes the imaging process more difficult. Indeed, an accurate reconstruction of the subsurface/hidden scene requires accounting for the presence of the air–soil interface into the scattering model. This article deals with a comparison of three different linear models for describing the scattering phenomenon under a stand-off configuration, where the presence of the layered medium is explicitly accounted for in the scattering model. The first model is rigorous and based on the spectral domain representation of the incident field and Green’s function for the half-space scenario. The second model exploits a ray representation of the wave propagation from the radar to the target and vice versa by accounting for the refraction phenomenon at the interface. The third model is an approximated one, where the layered nature of the scenario is taken into account by means of an equivalent wavenumber, which allows a straightforward evaluation of the incident field and Green’s function. The resolution performance of each inversion approach is assessed by means of a numerical analysis. Moreover, data referred to an experiment carried out in controlled conditions are processed and reconstructions are provided to support the comparative analysis among the three imaging approaches.

Epileptic Seizure Detection in EEG Signals Using a Unified Temporal-Spectral Squeeze-and-Excitation Network.

The intelligent recognition of epileptic electro-encephalogram (EEG) signals is a valuable tool for the epileptic seizure detection. Recent deep learning models fail to fully consider both spectral and temporal domain representations simultaneously, which may lead to omitting the nonstationary or nonlinear property in epileptic EEGs and further produce a suboptimal recognition performance consequently. In this paper, an end-to-end EEG seizure detection framework is proposed by using a novel channel-embedding spectral-temporal squeeze-and-excitation network (CE-stSENet) with a maximum mean discrepancy-based information maximizing loss. Specifically, the CE-stSENet firstly integrates both multi-level spectral and multi-scale temporal analysis simultaneously. Hierarchical multi-domain representations are then captured in a unified manner with a variant of squeeze-and-excitation block. The classification net is finally implemented for epileptic EEG recognition based on features extracted in previous subnetworks. Particularly, to address the fact that the scarcity of seizure events results in finite data distribution and the severe overfitting problem in seizure detection, the CE-stSENet is coordinated with a maximum mean discrepancy-based information maximizing loss for mitigating the overfitting problem. Competitive experimental results on three EEG datasets against the state-of-the-art methods demonstrate the effectiveness of the proposed framework in recognizing epileptic EEGs, indicating its powerful capability in the automatic seizure detection.

Alzheimer's Disease Diagnosis and Severity Level Detection Based on Electroencephalography Modulation Spectral "Patch" Features.

Over the last two decades, electroencephalography (EEG) has emerged as a reliable tool for the diagnosis of cortical disorders such as Alzheimer's disease (AD). Typically, resting-state EEG (rsEEG) signals have been used, and traditional frequency bands (delta, theta, alpha, beta and gamma) have been explored. Recent studies, however, have suggested that non-conventional bands may lead to improved diagnostic performance. In this work, we propose a new type of features derived from the 2-dimensional modulation spectral domain representation of the rsEEG signal in order to characterize the neuromodulatory deficit emergent with AD. The proposed features are computed as the power in specific "patches" or regions of interest in the power modulation spectrogram, which are shown to be highly discriminant of AD severity levels. The proposed features were compared with traditional features used in the rsEEG AD monitoring literature. Results showed the proposed features not only achieving improved performance at discriminating between healthy normal elderly controls (Nold) and AD patients with varying severity levels, but also at monitoring severity levels (i.e., mild AD versus moderate AD). Moreover, the proposed features were shown to outperform traditional rsEEG features. Finally, we validated the biological origin of the proposed features by using source localization and comparing the obtained results with ones reported in the AD literature.

Graph Spectral Domain Feature Learning With Application to in-Air Hand-Drawn Number and Shape Recognition

This paper addresses the problem of recognition of dynamic shapes by representing the structure in a shape as a graph and learning the graph spectral domain features. Our proposed method includes pre-processing for converting the dynamic shapes into a fully connected graph, followed by analysis of the eigenvectors of the normalized Laplacian of the graph adjacency matrix for forming the feature vectors. The method proposes to use the eigenvector corresponding to the lowest eigenvalue for formulating the feature vectors as it captures the details of the structure of the graph. The use of the proposed graph spectral domain representation has been demonstrated in an in-air hand-drawn number and symbol recognition applications. It has achieved average accuracy rates of 99.56% and 99.44%, for numbers and symbols, respectively, outperforming the existing methods for all datasets used. It also has the added benefits of fast real-time operation and invariance to rotation and flipping, making the recognition system robust to different writing and drawing variations.

On data-driven Saak transform

Being motivated by the multilayer RECOS (REctified-COrrelations on a Sphere) transform, we develop a data-driven Saak (Subspace approximation with augmented kernels) transform in this work. The Saak transform consists of three steps: (1) building the optimal linear subspace approximation with orthonormal bases using the second-order statistics of input vectors, (2) augmenting each transform kernel with its negative, (3) applying the rectified linear unit (ReLU) to the transform output. The Karhunen-Loéve transform (KLT) is used in the first step. The integration of Steps 2 and 3 is powerful since they resolve the sign confusion problem, remove the rectification loss and allow a straightforward implementation of the inverse Saak transform at the same time. Multiple Saak transforms are cascaded to transform images of a larger size. All Saak transform kernels are derived from the second-order statistics of input random vectors in a one-pass feedforward manner. Neither data labels nor backpropagation is used in kernel determination. Multi-stage Saak transforms offer a family of joint spatial-spectral representations between two extremes; namely, the full spatial-domain representation and the full spectral-domain representation. We select Saak coefficients of higher discriminant power to form a feature vector for pattern recognition, and use the MNIST dataset classification problem as an illustrative example.

Sampling and reconstruction of sparse signals on circulant graphs – an introduction to graph-FRI

With the objective of employing graphs toward a more generalized theory of signal processing, we present a novel sampling framework for (wavelet-)sparse signals defined on circulant graphs which extends basic properties of Finite Rate of Innovation (FRI) theory to the graph domain, and can be applied to arbitrary graphs via suitable approximation schemes. At its core, the introduced Graph-FRI-framework states that any K-sparse signal on the vertices of a circulant graph can be perfectly reconstructed from its dimensionality-reduced representation in the graph spectral domain, the Graph Fourier Transform (GFT), of minimum size 2K. By leveraging the recently developed theory of e-splines and e-spline wavelets on graphs, one can decompose this graph spectral transformation into the multiresolution low-pass filtering operation with a graph e-spline filter, with subsequent transformation to the spectral graph domain; this allows to infer a distinct sampling pattern, and, ultimately, the structure of an associated coarsened graph, which preserves essential properties of the original, including circularity and, where applicable, the graph generating set.

Network representations of angular regions for electromagnetic scattering.

Network modeling in electromagnetics is an effective technique in treating scattering problems by canonical and complex structures. Geometries constituted of angular regions (wedges) together with planar layers can now be approached with the Generalized Wiener-Hopf Technique supported by network representation in spectral domain. Even if the network representations in spectral planes are of great importance by themselves, the aim of this paper is to present a theoretical base and a general procedure for the formulation of complex scattering problems using network representation for the Generalized Wiener Hopf Technique starting basically from the wave equation. In particular while the spectral network representations are relatively well known for planar layers, the network modelling for an angular region requires a new theory that will be developed in this paper. With this theory we complete the formulation of a network methodology whose effectiveness is demonstrated by the application to a complex scattering problem with practical solutions given in terms of GTD/UTD diffraction coefficients and total far fields for engineering applications. The methodology can be applied to other physics fields.

Spectral style transfer for human motion between independent actions

Human motion is complex and difficult to synthesize realistically. Automatic style transfer to transform the mood or identity of a character's motion is a key technology for increasing the value of already synthesized or captured motion data. Typically, state-of-the-art methods require all independent actions observed in the input to be present in a given style database to perform realistic style transfer. We introduce a spectral style transfer method for human motion between independent actions, thereby greatly reducing the required effort and cost of creating such databases. We leverage a spectral domain representation of the human motion to formulate a spatial correspondence free approach. We extract spectral intensity representations of reference and source styles for an arbitrary action, and transfer their difference to a novel motion which may contain previously unseen actions. Building on this core method, we introduce a temporally sliding window filter to perform the same analysis locally in time for heterogeneous motion processing. This immediately allows our approach to serve as a style database enhancement technique to fill-in non-existent actions in order to increase previous style transfer method's performance. We evaluate our method both via quantitative experiments, and through administering controlled user studies with respect to previous work, where significant improvement is observed with our approach.

Graph Signal Denoising via Trilateral Filter on Graph Spectral Domain

This paper presents a graph signal denoising method with the trilateral filter defined in the graph spectral domain. The original trilateral filter (TF) is a data-dependent filter that is widely used as an edge-preserving smoothing method for image processing. However, because of the data-dependency, one cannot provide its frequency domain representation. To overcome this problem, we establish the graph spectral domain representation of the data-dependent filter, i.e., a spectral graph TF (SGTF). This representation enables us to design an effective graph signal denoising filter with a Tikhonov regularization. Moreover, for the proposed graph denoising filter, we provide a parameter optimization technique to search for a regularization parameter that approximately minimizes the mean squared error w.r.t. the unknown graph signal of interest. Comprehensive experimental results validate our graph signal processing-based approach for images and graph signals.

Temporal and spectral analysis of internal carotid artery Doppler signal for normal and abnormal flow detection.

Detection of carotid artery stenosis is presently highly dependent on ultrasound imaging systems. This work presents a method that can detect the normal and abnormal blood flow in the carotid structure independent of Doppler angle by analysing the time and spectral domain representation of Doppler signal. In the proposed approach, time and spectral domain based features are extracted from the Doppler signals of internal carotid arteries. Further, these features are used in supervised machine learning approach to identify the presence of abnormal blood flow. The proposed method is evaluated on 100 subjects (200 signals) with equal number of normal and abnormal flow profiles. Experimental results show that the maximum classification accuracies of 79.3% and 82.9% are observed with k-nearest neighbours and support vector machine classifiers, respectively.

Integral representations and properties of operator fractional Brownian motions

Operator fractional Brownian motions (OFBMs) are (i) Gaussian, (ii) operator self-similar and (iii) stationary increment processes. They are the natural multivariate generalizations of the well-studied fractional Brownian motions. Because of the possible lack of time-reversibility, the defining properties (i)–(iii) do not, in general, characterize the covariance structure of OFBMs. To circumvent this problem, the class of OFBMs is characterized here by means of their integral representations in the spectral and time domains. For the spectral domain representations, this involves showing how the operator self-similarity shapes the spectral density in the general representation of stationary increment processes. The time domain representations are derived by using primary matrix functions and taking the Fourier transforms of the deterministic spectral domain kernels. Necessary and sufficient conditions for OFBMs to be time-reversible are established in terms of their spectral and time domain representations. It is also shown that the spectral density of the stationary increments of an OFBM has a rigid structure, here called the dichotomy principle. The notion of operator Brownian motions is also explored.

Libpsht – algorithms for efficient spherical harmonic transforms

Libpsht (or "library for Performant Spherical Harmonic Transforms") is a collection of algorithms for efficient conversion between spatial-domain and spectral-domain representations of data defined on the sphere. The package supports transforms of scalars as well as spin-1 and spin-2 quantities, and can be used for a wide range of pixelisations (including HEALPix, GLESP and ECP). It will take advantage of hardware features like multiple processor cores and floating-point vector operations, if available. Even without this additional acceleration, the employed algorithms are among the most efficient (in terms of CPU time as well as memory consumption) currently being used in the astronomical community. The library is written in strictly standard-conforming C90, ensuring portability to many different hard- and software platforms, and allowing straightforward integration with codes written in various programming languages like C, C++, Fortran, Python etc. Libpsht is distributed under the terms of the GNU General Public License (GPL) version 2 and can be downloaded from http://sourceforge.net/projects/libpsht.

A numerically efficient method of modeling interdigitated electrodes for capacitive film sensing

Interdigitated electrodes represent a commonly used planar structure when it comes to implementing capacitive sensors. The electric field decays strongly in the surface normal direction of the electrode arrangement. This can be used to estimate the thickness of dielectric films residing on the electrodes. A simple example for an application would be the detection of the build-up of biofilms. The exact expressions for the capacitance are relatively complex and can be provided in closed form only for the case without a cover layer. In this contribution we present an efficient modeling approach based on a physically motivated approximation of the charge distribution on the electrodes. Establishing a closed-form spectral domain representation of the associated electric potential distribution allows a numerically highly efficient calculation of the capacitance utilizing the FFT algorithm. In contrast to previous works, additional cover layers can be easily included in the model, which allows studying the aforementioned sensing effect.

A Robust Method for the Computation of Green's Functions in Stratified Media

Closed-form Green's functions for unbounded planar stratified media are derived in terms of cylindrical and spherical waves. The methodology is based on a two-level approximation of the spectral-domain representation of Green's functions. This robust, efficient, and fully numerical approach does not call for an analytical extraction of ldquoproblematicrdquo behaviors, such as the quasi-static terms and the surface wave poles, prior to the spectrum fitting. Instead, the spatial-domain Green's functions derived in this paper provide an accurate description of both the near-field singularity in the vicinity of the source and the far-field dominant behavior of the surface waves.

HYBRID RADIATIONB MODES OF MICROWAVE INTEGRATED CIRCUIT (MIC) LINES-THEORY AND APPLICATION

Spectral domain approach for continuous spectrum of wide class of microwave integrated circuit (MIC) lines is proposed. The continuous spectrum is treated as a continuum of so called hybrid radiation modes. They are the limits of volume modes of line in which lower and/or upper shieldings are moved to infinity. In the preliminary part of analysis a convenient classification of MIC lines into one-side opened and two-sides opened lines is introduced. The spectral domain representation of hybrid radiation modes is discussed in detail and boundary conditions for visible and invisible parts of spectrum are formulated. The normalization conditions in spectral domain are also proposed for both classes of lines. In the next part of paper an iterative approach in spectral domain is proposed for hr modes of one-side opened line. The boundary conditions for hybrid radiation modes are combined with spectral domain approach and the second order equation is formulated for unknown spectral amplitudes of electric or magnetic fields in visible part of spectrum. Two schemes of iteration are presented and they both lead to solutions classified as hybrid EH (y) and HE (y) modes. In the case of two-sides opened lines the solution is a sum of two partial solutions corresponding to symmetrical and unsymmetrical sources distributions. Each partial solution can be found by the iterative procedure proposed for one-side opened lines. The efficiency of proposed procedure was verified for the case of hybrid radiation modes of microstrip line. The results of calculations of amplitudes and phases of spectral amplitudes in visible spectrum part for examplary hybrid radiation modes are shown. As an example of an application of the hybrid radiation modes concept, the advanced cavity model of rectangular patch antenna is proposed. This model allows to calculate the parameters with acceptable precision nearly ten times faster than professional full-wave design tools. In the

BROADBAND SPATIOTEMPORAL DIFFERENTIAL-OPERATOR REPRESENTATIONS FOR VELOCITY-DEPENDENT SCATTERING

A novel approach based on spatiotemporal differential- operators is developed here for broadband, velocity-dependent scattering. Unlike the spectral-domain representations, the new method facilitates a compact formulation for scattering by arbitrary excitation signals, in the presence of moving objects. In free space (vacuum), relativistically exact formulas are developed. After developing the general theory, analysis of relativistically exact free-space scattering by cylinders, and a half-plane, are examined. For cylinders the analysis shows that in the far field pulses are located on circles in the co-moving reference-frame where the object is at-rest. In other reference frames this feature is valid only as an approximation. These results apply also to the diffractive part of the half-plane scattered field. The geometrical-optics contribution is associated with plane-waves and obeys the appropriate transformations. The various zones for these fields in an arbitrary reference-frame are analyzed.

1/f noise synthesis model in discrete-time for circuit simulation

Flicker noise, popularly known as 1/f noise is a commonly observed phenomenon in semiconductor devices. To incorporate 1/f noise in circuit simulations, models are required to synthesize such noise in discrete time. This paper proposes a model based on the fact that 1/f processes belong to the class of statistically self-similar random processes. The model generates 1/f noise in the time domain (TD) with a simple white noise input and is parameterized by a quantity whose value can be adjusted to reflect the desired 1/f parameter, that is, the slope of the 1/f spectrum. It thus differs from most of the earlier modeling approaches, which were confined to the spectral domain. To verify fit between the model and actual 1/f noise measurements, experiments were conducted using discrete devices such as a PIN photodiode at various bias conditions and sampling frequencies. The noise synthesized by the model was found to provide a good match to the measurements. Furthermore, it is demonstrated that the proposed 1/f noise model can also be incorporated in circuit simulations as a noise current or noise voltage source, which was not feasible earlier with the conventional spectral domain representation. To validate the inclusion of 1/f noise in circuits as TD current or voltage, simulations were carried out on a CMOS ring oscillator and the clock jitter due to 1/f noise was investigated.