Autoregressive Moving Average Filter Research Articles

GACP: graph neural networks with ARMA filters and a parallel CNN for hyperspectral image classification

ABSTRACT In recent years, the use of convolutional neural networks (CNNs) and graph neural networks (GNNs) to identify hyperspectral images (HSIs) has achieved excellent results, and such methods are widely used in agricultural remote sensing, geological exploration, and marine remote sensing. Although many generalization classification algorithms are designed for the purpose of learning a small number of samples, there is often a problem of a low utilization rate of position information in the empty spectral domain. Based on this, a GNN with an autoregressive moving average (ARMA)-based smoothing filter samples the node information in the null spectral domain and then captures the spatial information at the pixel level via spatial feature convolution; then, the null spectral domain position information lost by the CNN is located by a coordinate attention (CA) mechanism. Finally, autoregressive, spatial convolution, and CA mechanisms are combined into multiscale features to enhance the learning capacity of the network for tiny samples. Experiments conducted on the widely used Indian Pines (IP) dataset, the Botswana (BS) dataset, Houton 2013 (H2013), and the WHU-Hi-HongHu (WHU) benchmark HSI dataset demonstrate that the proposed GACP technique can perform classification work with good accuracy even with a small number of training examples.

Application of linear filter and moment equation for parametric rolling in irregular longitudinal waves

Parametric rolling is one of the dangerous dynamic phenomena. In order to discuss the safety of a vessel when a dangerous phenomenon occurs, it is important to estimate the probability of certain dynamical behavior of the ship with respect to a certain threshold level. In this paper, the moment values are obtained by solving the moment equations. Since the stochastic differential equation(SDE) is needed to obtain the moment equations, the Autoregressive Moving Average(ARMA) filter is used. The effective wave is modeled by using the 6th-order ARMA filter. In addition, the parametric excitation process is modeled by using a non-memory transformation obtained from the relationship between GM and wave elevation. The resulting system of equations is represented by the 8th-order It\^o stochastic differential equation, which consists of a second-order SDE for the ship motion and a 6th-order SDE for the effective wave. This system has nonlinear components. Therefore, the cumulant neglect closure method is used as higher-order moments need to be truncated. Furthermore, the probability density function of roll angle is determined by using moment values obtained from the SDE and the moment equation. Here, two types of the probability density function are suggested and have a good agreement.

Semi-Supervised Locality Preserving Dense Graph Neural Network With ARMA Filters and Context-Aware Learning for Hyperspectral Image Classification

The application of graph convolutional networks (GCNs) to hyperspectral image (HSI) classification is a heavily researched topic. However, GCNs are based on spectral filters, which are computationally costly and fail to suppress noise effectively. In addition, the current GCN-based methods are prone to oversmoothing (the representation of each node tends to be congruent) problems. To circumvent these problems, a novel semi-supervised locality-preserving dense graph neural network (GNN) with autoregressive moving average (ARMA) filters and context-aware learning (DARMA-CAL) is proposed for HSI classification. In this work, we introduce the ARMA filter instead of a spectral filter to apply to GNNs. The ARMA filter can better capture the global graph structure and is more robust to noise. More importantly, the ARMA filter can simplify calculations compared with the spectral filter. In addition, we show that the ARMA filter can be approximated by a recursive method. Furthermore, we propose a dense structure, which not only implements the ARMA filter in the structure, but is also locality-preserving. Finally, we design a layerwise context-aware learning mechanism to extract the useful local information generated by each layer of the dense ARMA network. The experimental results on three real HSI datasets show that DARMA-CAL outperforms the compared state-of-the-art methods.

Graph Neural Networks With Convolutional ARMA Filters.

Popular graph neural networks implement convolution operations on graphs based on polynomial spectral filters. In this paper, we propose a novel graph convolutional layer inspired by the auto-regressive moving average (ARMA) filter that, compared to polynomial ones, provides a more flexible frequency response, is more robust to noise, and better captures the global graph structure. We propose a graph neural network implementation of the ARMA filter with a recursive and distributed formulation, obtaining a convolutional layer that is efficient to train, localized in the node space, and can be transferred to new graphs at test time. We perform a spectral analysis to study the filtering effect of the proposed ARMA layer and report experiments on four downstream tasks: semi-supervised node classification, graph signal classification, graph classification, and graph regression. Results show that the proposed ARMA layer brings significant improvements over graph neural networks based on polynomial filters.

Supervised Single Channel Speech Enhancement Based on Dual-Tree Complex Wavelet Transforms and Nonnegative Matrix Factorization Using the Joint Learning Process and Subband Smooth Ratio Mask

In this paper, we propose a novel speech enhancement method based on dual-tree complex wavelet transforms (DTCWT) and nonnegative matrix factorization (NMF) that exploits the subband smooth ratio mask (ssRM) through a joint learning process. The discrete wavelet packet transform (DWPT) suffers the absence of shift invariance, due to downsampling after the filtering process, resulting in a reconstructed signal with significant noise. The redundant stationary wavelet transform (SWT) can solve this shift invariance problem. In this respect, we use efficient DTCWT with a shift invariance property and limited redundancy and calculate the ratio masks (RMs) between the clean training speech and noisy speech (i.e., training noise mixed with clean speech). We also compute RMs between the noise and noisy speech and then learn both RMs with their corresponding clean training clean speech and noise. The auto-regressive moving average (ARMA) filtering process is applied before NMF in previously generated matrices for smooth decomposition. An ssRM is proposed to exploit the advantage of the joint use of the standard ratio mask (sRM) and square root ratio mask (srRM). In short, the DTCWT produces a set of subband signals employing the time-domain signal. Subsequently, the framing scheme is applied to each subband signal to form matrices and calculates the RMs before concatenation with the previously generated matrices. The ARMA filter is implemented in the nonnegative matrix, which is formed by considering the absolute value. Through ssRM, speech components are detected using NMF in each newly formed matrix. Finally, the enhanced speech signal is obtained via the inverse DTCWT (IDTCWT). The performances are evaluated by considering an IEEE corpus, the GRID audio-visual corpus, and different types of noises. The proposed approach significantly improves objective speech quality and intelligibility and outperforms the conventional STFT-NMF, DWPT-NMF, and DNN-IRM methods.

Filter Design for Autoregressive Moving Average Graph Filters

In the field of signal processing on graphs, graph filters play a crucial role in processing the spectrum of graph signals. This paper proposes two different strategies for designing autoregressive moving average (ARMA) graph filters on both directed and undirected graphs. The first approach is inspired by Prony's method, which considers a modified error between the modeled and the desired frequency response. The second technique is based on an iterative approach, which finds the filter coefficients by iteratively minimizing the true error (instead of the modified error) between the modeled and the desired frequency response. The performance of the proposed algorithms is evaluated and compared with finite impulse response (FIR) graph filters, on both synthetic and real data. The obtained results show that ARMA filters outperform FIR filters in terms of approximation accuracy and they are suitable for graph signal interpolation, compression, and prediction.

ARMA order model detection using minimum of Kurtosis: application on seismic data

The objective of this study is to find the order and coefficients of non-low-phase causal filters for ARMA (auto regressive moving average) filter model, using the Kurtosis minimization criterion. This method is based on the Kurtosis calculation of the treated sample at the input level and its identification at the output of the ARMA model. For this purpose, the order and coefficients of the AR (auto regressive) part are identified using the Yule-Walker algorithm at order two and then extended to order four. To obtain the MA (moving average) part, the AR components are calculated at first from the ARMA filter by deconvolution. Then, spectrally equivalent and minimum phase (SEMP) MA filter is identified using the Durbin algorithm at second and fourth order. Finally, the correct filter is found when the Kurtosis value of the output ARMA filter reconstituted is the closest to the Kurtosis of introduced signal. The proposed method is then tested on simulated processes and applied to real seismic data to perform blind deconvolution and obtain the reflectivity coefficients of subsoil studied.

Runtime Estimation of the Number of Active Devices in IEEE 802.15.4 Slotted CSMA/CA Networks with Deferred Transmission and No Acknowledgment Using ARMA Filters

We propose a novel method for estimating the number of active devices in an IEEE 802.15.4 network. Here, we consider an IEEE 802.15.4 network with a star topology where active devices transmit data frames using slotted carrier sense multiple access with collision avoidance (CSMA/CA) medium access control (MAC) protocol without acknowledgment. In our proposed method, a personal area network (PAN) coordinator of a network counts the number of events that a transmission occurs and the number of events that two consecutive slots are idle in a superframe duration, and the PAN coordinator broadcasts the information through a beacon frame. Each device can count the number of slots that each device is in the backoff procedure and the number of the first clear channel assessment (CCA) that each device performs whenever it performs the first CCA after the backoff procedure. Then, each device estimates the number of active devices in the network based on these counted numbers and the information from PAN coordinator with the help of an autoregressive moving average (ARMA) filter. We evaluate the performance of our proposed ARMA‐based estimation method via simulations where active devices transmit data frames in IEEE 802.15.4 slotted CSMA/CA networks. Simulation results show that our proposed method gives estimation errors of the number of active devices less than 4.501% when the actual number of active devices is varying from 5 to 80. We compare our proposed method with the conventional method in terms of the average and standard deviation for the estimated number of active devices. The simulation results show that our proposed estimation method is more accurate than the conventional method.

Time series estimation of gas sensor baseline drift using ARMA and Kalman based models

Purpose – The purpose of this paper is to present a novel and simple prediction model of long-term metal oxide semiconductor (MOS) gas sensor baseline, and it brings some new perspectives for sensor drift. MOS gas sensors, which play a very important role in electronic nose (e-nose), constantly change with the fluctuation of environmental temperature and humidity (i.e. drift). Therefore, it is very meaningful to realize the long-term time series estimation of sensor signal for drift compensation. Design/methodology/approach – In the proposed sensor baseline drift prediction model, auto-regressive moving average (ARMA) and Kalman filter models are used. The basic idea is to build the ARMA and Kalman models on the short-term sensor signal collected in a short period (one month) by an e-nose and aim at realizing the long-term time series prediction in a year using the obtained model. Findings – Experimental results demonstrate that the proposed approach based on ARMA and Kalman filter is very effective in time series prediction of sensor baseline signal in e-nose. Originality/value – Though ARMA and Kalman filter are well-known models in signal processing, this paper, at the first time, brings a new perspective for sensor drift prediction problem based on the two typical models.

Distributed Autoregressive Moving Average Graph Filters

We introduce the concept of autoregressive moving average (ARMA) filters on a graph and show how they can be implemented in a distributed fashion. Our graph filter design philosophy is independent of the particular graph, meaning that the filter coefficients are derived irrespective of the graph. In contrast to finite-impulse response (FIR) graph filters, ARMA graph filters are robust against changes in the signal and/or graph. In addition, when time-varying signals are considered, we prove that the proposed graph filters behave as ARMA filters in the graph domain and, depending on the implementation, as first or higher ARMA filters in the time domain.

Robust Features for Speech Recognition using Temporal Filtering Technique in the Presence of Impulsive Noise

In this paper we introduce a robust feature extractor, dubbed as Modified Function Cepstral Coefficients (MODFCC), based on gammachirp filterbank, Relative Spectral (RASTA) and Autoregressive Moving-Average (ARMA) filter. The goal of this work is to improve the robustness of speech recognition systems in additive noise and real-time reverberant environments. In speech recognition systems Mel-Frequency Cepstral Coefficients (MFCC), RASTA and ARMA Frequency Cepstral Coefficients (RASTA- MFCC and ARMA-MFCC) are the three main techniques used. It will be shown in this paper that it presents some modifications to the original MFCC method. In our work the effectiveness of proposed changes to MFCC were tested and compared against the original RASTA-MFCC and ARMA-MFCC features. The prosodic features such as jitter and shimmer are added to baseline spectral features. The above-mentioned techniques were tested with impulsive signals under various noisy conditions within AURORA databases. Index Terms—Auditory filter, impulsive noise, MFCC, RASTA filter, ARMA filter, HMM\GMM.

Compression of head-related transfer function using autoregressive-moving-average models and Legendre polynomials

Head-related transfer functions (HRTFs) are generally large datasets, which can be an important constraint for embedded real-time applications. A method is proposed here to reduce redundancy and compress the datasets. In this method, HRTFs are first compressed by conversion into autoregressive-moving-average (ARMA) filters whose coefficients are calculated using Prony's method. Such filters are specified by a few coefficients which can generate the full head-related impulse responses (HRIRs). Next, Legendre polynomials (LPs) are used to compress the ARMA filter coefficients. LPs are derived on the sphere and form an orthonormal basis set for spherical functions. Higher-order LPs capture increasingly fine spatial details. The number of LPs needed to represent an HRTF, therefore, is indicative of its spatial complexity. The results indicate that compression ratios can exceed 98% while maintaining a spectral error of less than 4 dB in the recovered HRTFs.

Estimation of thermal deformation in machine tools using the hybrid autoregressive moving-average - neural network model

A hybrid model, which is composed of an autoregressive moving-average (ARMA) filter and a feedforward neural network (FNN), is proposed to increase prediction accuracy and to reduce learning time for the estimation of thermal deformations in a machine tool. The ARMA filter is used to yield state variables which establish the relationship between the present and past states of thermal deformations for the reservation of the influences of past temperatures and deformation. Otherwise, the quantity of FNN inputs is very vast because of the data needed for the non-linear system. These state variables, which are estimated by past measured temperatures and past estimated deformation, serve as inputs of the FNN. The algorithms of this hybrid model are presented and verified by the experimental results; also, the prediction accuracy is compared with the ARMA and FNN independently for the same learning iterations.

Engineering the nonlinear phase shift with multistage autoregressive moving-average optical filters

We propose and demonstrate the application of concepts from digital filter design in order to optimize artificial optical resonant structures to produce a nearly ideal nonlinear phase shift response. Multistage autoregressive moving average (ARMA) optical filters (ring-resonator-based Mach-Zehnder interferometer lattices) are designed and studied. The filter group delay is used as a measure instead of finesse or quality factor to study the nonlinear sensitivity for multiple resonances. The nonlinearity of a four-stage ARMA filter is 17 times higher than that of the intrinsic material of the same group delay. We demonstrate that the nonlinear sensitivity can be increased within constant bandwidth by allocating more in-band phase or by using higher-order filter structures and that the nonlinear sensitivity enhancement improves with increasing group delay. We also investigate methods to precompensate the nonlinear response to reduce the occurrence of optical bistabilities. The effect of optical loss, including linear absorption and two-photon absorption, is discussed in postanalysis. In addition, we discuss how the improvement in nonlinear response scales with respect to various filter parameters.

Adaptive spectral analysis of cutaneous electrogastric signals using autoregressive moving average modelling

The recording of the human gastric myoelectrical activity by means of cutaneous electrodes is called electrogastrography (EGG). It provides a noninvasive method of studying electrogastric behaviour. The normal frequency of the gastric signal is about 0.05 Hz. However, sudden changes of its frequency have been observed and are generally considered to be related to gastric motility disorders. Thus, spectral analysis, especially online spectral analysis, can serve as a valuable tool for practical purposes. The paper presents a new method of the adaptive spectral analysis of cutaneous electrogastric signals using autoregressive moving average (ARMA) modelling. It is based on an adaptive ARMA filter and provides both time and frequency information of the signal. Its performance is investigated in comparison with the conventional FFT-based periodogram method. Its properties in tracking time-varying instantaneous frequencies are shown. Its applications to the running spectral analysis of cutaneous electrogastric signals are presented. The proposed adaptive ARMA spectral analysis method is easy to implement and is efficient in computations. The results presented in the paper show that this new method provides a better performance and is very useful for the online monitoring of cutaneous electrogastric signals.

ARMA implementation of diffraction operators with inverse-root singularities

The integral of a time-domain diffraction operator which has an integrable inverse-root singularity and an infinite tail is numerically differentiated to get a truncated digital form of the operator. This truncated difference operator effectively simulates the singularity but is computationally inefficient and produces a convolutional truncation ghost. The authors therefore use a least-squares method to model an equivalent autoregressive moving-average (ARMA) filter on the difference operator. The recursive convolution of the ARMA filter with a wavelet has no truncation ghost and an error below 1% of the peak diffraction amplitude. Design and application of the ARMA filter reduces computer (CPU) time by 42% over that repaired with direct convolution. A combination of filter design at a coarse spatial sampling, angular interpolation of filter coefficients to a finer sampling, and recursive application reduces CPU time by 83% over direct convolution or 80% over Fourier convolution, which also has truncation error.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Application of Autoregressive Moving Average Parametric Modeling in Magnetic Resonance Image Reconstruction

The modeling of data is an alternative to conventional use of the fast Fourier transform (FFT) algorithm in the reconstruction of magnetic resonance (MR) images. The application of the FFT leads to artifacts and resolution loss in the image associated with the effective window on the experimentally-truncated phase encoded MR data. The transient error modeling method treats the MR data as a subset of the transient response of an infinite impulse filter (H(z) = B(z)IA(z)). Thus, the data are approximated by a deterministic autoregressive moving average (ARMA) model. The algorithm for calculating the filter coefficients is described. It is demonstrated that using the filter coefficients to reconstruct the image removes the truncation artifacts and improves the resolution. However, determining the autoregressive (AR) portion of the ARMA filter by algorithms that minimize the forward and backward prediction errors (e.g., Burg) leads to significant image degradation. The moving average (MA) portion is determined by a computationally efficient method of solving a finite difference equation with initial values. Special features of the MR data are incorporated into the transient error model. The sensitivity to noise and the choice of the best model order are discussed. MR images formed using versions of the transient error reconstruction (TERE) method and the conventional FFT algorithm are compared using data from a phantom and a human subject. Finally, the computational requirements of the algorithm are addressed.

Statistical design of nearly linear-phase ARMA filters

This paper proposes a method for statistical design of approximately linear-phase autoregressive-moving average (ARMA) digital filters. The key idea of our method is that a time-delayed ARMA filter is used to approximate a high-order FIR filter that meets the prescribed amplitude spectrum sufficiently well. Computer simulations show that the resulting ARMA low-pass, bandpass, and high-pass filters not only meet the prescribed amplitude response specification well, but yield excellent linear phase with much lower order and smaller delay compared to the associated FIR filters.

Design of ARMA digital filters by pole-zero decomposition

A new technique for design of digital filters is presented in this paper. The technique exploits the spectral approximation property of autoregressive modeling to reduce ripple at the edges of the transition band in the filter response. An autoregressive model approximates a given spectrum better at the peaks than at the Valleys. Spectral information around the transition band is transformed into peaks by splitting the given squared-magnitude frequency response into two component spectra. This splitting is accomplished using a pole-zero decomposition technique, which in turn uses the properties of the derivative of phase spectrum of minimum phase filters. One of the component spectra corresponds nearly to the response of an all-pole filter, and the other component spectrum corresponds nearly to the response of an all-zero filter. Each of these corresponends spectra can be represented by a small number of coefficients using autoregressive modeling. The resulting two sets of autoregressive coefficients determine poles and zeros of the autoregressive moving average (ARMA) digital filter. Ripple characteristics in the response of the ARMA filter can be controlled by appropriately choosing the number of poles and zeros. It is shown that a wide variety of magnitude frequency response characteristics can be approximated by an ARMA filter of low order using this technique. The technique does not work well in cases where spectral approximation by autoregressive modeling is poor. Such cases arise when the component spectra have very large dynamic range.