Signal Restoration Algorithms Research Articles

Development of a novel signal restoration algorithm to eliminate the distorted components in space charge measurement excited by femtosecond laser irradiation

AbstractFor the space charge measurement method with optical excitation for electrical insulation, the distortion of the excitation laser on the measurement signal and the accumulation of space charge have not been discussed before. Both experiment and simulation results show that three types of distorted components introduced by optical excitation can lead to distortion of the upper interface signal. Further, the factors causing distortion of the measured signal and the formation mechanism are analysed. A virtual electrode potential compensation method and a distorted component extraction method are proposed. Meanwhile, an attenuation restoration and charge conversion correction factor is introduced, leading to a novel signal processing algorithm adapted to space charge optical measurement methods. Compared with the traditional algorithm, the novel algorithm has an error of less than 1% in the calculation of charge and electric field strength, with an increase in accuracy of 47.7% and 9.81%, respectively. By applying the novel restoration algorithm, the comparison shows that the space charge accumulation does not change significantly under laser irradiation, verifying the reliability of the optical excitation. The given algorithm can provide a theoretical and technical foundation for the realisation of the optical measurement method for space charge.

전파 거리에 따른 신호의 감쇠와 분산이 고려된 순시 주파수 추정 알고리즘 및 장거리 전파용 반사파 계측법 시뮬레이터 개발

Time-Frequency domain Reflectometry(TFDR) is used for the purpose of fault detection and evaluating the integrity in cables. TFDR can diagnose live wire in nondestructive. but, the incident signal cannot aviod attenuation and dispersion according to increasing propagation distance, propagation velocity changes with propagation distance. attenuation and dispersion in long distance lead to decresing falut detection performance of cable. therefore, Developing instantaneous frequency Estimation algorithm of signal and signal restoration algorithm in order to determine tendency of propagation velocity for propagation distance, we demonstrate the performance of algorithm by implementing TFDR simulator possible long length.

Signal restoration algorithm for photoacoustic imaging systems.

In a photoacoustic (PA) imaging system, the detectors are bandwidth-limited. Therefore, they capture PA signals with some unwanted ripples. This limitation degrades the resolution/contrast and induces sidelobes and artifacts in the reconstructed images along the axial direction. To compensate for the limited bandwidth effect, we present a PA signal restoration algorithm, where a mask is designed to extract the signals at the absorber positions and remove the unwanted ripples. This restoration improves the axial resolution and contrast in the reconstructed image. The restored PA signals can be considered as the input of the conventional reconstruction algorithms (e.g., Delay-and-sum (DAS) and Delay-multiply-and-sum (DMAS)). To compare the performance of the proposed method, DAS and DMAS reconstruction algorithms were performed with both the initial and restored PA signals on numerical and experimental studies (numerical targets, tungsten wires, and human forearm). The results show that, compared with the initial PA signals, the restored PA signals can improve the axial resolution and contrast by 45% and 16.1 dB, respectively, and suppress background artifacts by 80%.

Sensor Fault Detection and Signal Restoration in Intelligent Vehicles.

This paper presents fault diagnosis logic and signal restoration algorithms for vehicle motion sensors. Because various sensors are equipped to realize automatic operation of the vehicle, defects in these sensors lead to severe safety issues. Therefore, an effective and reliable fault detection and recovery system should be developed. The primary idea of the proposed fault detection system is the conversion of measured wheel speeds into vehicle central axis information and the selection of a reference central axis speed based on this information. Thus, the obtained results are employed to estimate the speed for all wheel sides, which are compared with measured values to identify fault and recover the fault signal. For fault diagnosis logic, a conditional expression is derived with only two variables to distinguish between normal and fault; further, an analytical redundancy structure and a simple diagnostic logic structure are presented. Finally, an off-line test is conducted using test vehicle information to validate the proposed method; it demonstrates that the proposed fault detection and signal restoration algorithm can satisfy the control performance required for each sensor failure.

A Spike Time-Dependent Online Learning Algorithm Derived From Biological Olfaction.

We have developed a spiking neural network (SNN) algorithm for signal restoration and identification based on principles extracted from the mammalian olfactory system and broadly applicable to input from arbitrary sensor arrays. For interpretability and development purposes, we here examine the properties of its initial feedforward projection. Like the full algorithm, this feedforward component is fully spike timing-based, and utilizes online learning based on local synaptic rules such as spike timing-dependent plasticity (STDP). Using an intermediate metric to assess the properties of this initial projection, the feedforward network exhibits high classification performance after few-shot learning without catastrophic forgetting, and includes a none of the above outcome to reflect classifier confidence. We demonstrate online learning performance using a publicly available machine olfaction dataset with challenges including relatively small training sets, variable stimulus concentrations, and 3 years of sensor drift.

Signal restoration in intensity-modulated optical OFDM access systems

It is well known that deliberate signal clipping in an intensity-modulated (IM) laser transmitter helps to overcome the optical orthogonal frequency division multiplexing (OFDM) system performance limitation that is related to the signal high peak-to-average power ratio. The amplitude of a clipped OFDM signal has to be optimized in order to minimize the optical power that is required to achieve a specified system performance. However, the signal clipping introduces nonlinear distortion (so-called clipping noise) and leads to a system performance penalty. In this Letter, the performance of the IM optical OFDM system with digital baseband clipping distortion in the transmitter and clipping noise compensation by means of signal restoration in the digital signal processing unit of the system receiver is analytically evaluated. It is demonstrated that the system bit-error ratio can be reduced by more than an order of magnitude, from 10(-3) to 3.5×10(-5), by applying only the first iteration of the signal restoration algorithm proposed in this Letter. The results of the analytical analysis are verified with brute-force numerical simulations based on direct error counting.

Recursive Supervised Estimation of a Markov-Switching GARCH Process in the Short-Time Fourier Transform Domain

In this paper, we introduce a Markov-switching generalized autoregressive conditional heteroscedasticity (GARCH) model for nonstationary processes with time-varying volatility structure in the short-time Fourier transform (STFT) domain. The expansion coefficients in the STFT domain are modeled as a multivariate complex GARCH process with Markov-switching regimes. The GARCH formulation parameterizes the correlation between sequential conditional variances while the Markov chain allows the process to switch between regimes of different GARCH formulations. We obtain a necessary and sufficient condition for the asymptotic wide-sense stationarity of the model, and develop a recursive algorithm for signal restoration in a noisy environment. The conditional variance is estimated by iterating propagation and update steps with regime conditional probabilities, while the model parameters are evaluated a priori from a training data set. Experimental results demonstrate the performance of the proposed algorithm.

A geometrical problem arising in a signal restoration algorithm

Let ℤ2N={0, ..., 2N-1} denote the group of integers modulo 2N, and let L be the space of all real functions of ℤ2N which are supported on {0,...N−1}. The spectral phase of a function f:ℤ2N→ℝ is given by φf(k)=arg $$\hat f(k)$$ for k ∈ ℤ2N, where $$\hat f$$ denotes the discrete Fourier transforms of f. For a fixed s∈L let Ks denote the cone of all f:ℤ2N→ℝ which satisfy φf ≡ φs and let Ms be its linear span. The angle αs between Ms and L determines the convergence rate of the signal restoration from phase algorithm of Levi and Stark [3]. Here we prove the following conjectures of Urieli et al. [7] who verified them for the N≤3 case:

Integral inequality bounding the weighted absolute deviation of an n-dimensional function

The author states and proves an integral inequality that bounds the weighted integrated absolute deviation of a differentiable n-dimensional real function over an interval, relative to any value the function takes within the interval. Examples illustrate the utility of the inequality. In particular, the inequality is shown to be applicable to certain set-theoretic signal restoration algorithms, which project an observed (degraded) signal onto a closed, convex prototype set defined by a linear filter and a suitable bound.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Two new robust nonlinear signal restoration algorithms

Signal restoration is a well-known problem is many scientific fields such as image processing and geophysics. Here, we process a signal to enhance its quality in order to uncover features about the original or system input signal z that are not apparent in the noisy and distorted output of the system, u. Once the model is specified, the signal restoration problem is then to find a signal z” that is as close as possible to the original one subject to a suitable optimality criterion. The assumed givens are the output u, system model h, and any a priori knowledge about the solution in the form of constraints. Various methods that relied on different criteria showed attractive results in well-defined situations. Minimum meansquare error, maximum entropy, maximum likelihood, and maximum a posteriori probability are a few criteria that have proven useful. Here, regularization theory is used to tackle the problem. Especially, the stabilizing functional approach is considered [ 1,2 ] . The problem is formulated as the constrained minimization of a certain stabilizing functional a( z, P) [1,2]. The choice of the stabilizing functional or criterion based on the problem at hand is still an open question. In a recent paper [l] , Karayiannis and Venetsanopoulos investigated the choice of a stabilizing functional in the case of 2-D ill-posed inverse problems. These authors emphasized the use of a certain class of quadratic functionals as stabilizing functionals. The use of global nonquadratic functionals was discouraged due to several problems. One main problem is the justification of the choice of a particular nonquadratic functional [l] . Recently, a step toward reducing the set of nonquadratic functionals to an optimal class of functionals useful in speech and image compression, cluster analysis, and pattern classification was presented by Jones [ 31. The considered functionals satisfy an orthogonality condition similar to that enjoyed by linear projections in Hilbert space. The concept of directed orthogonality is known as the correlation matching property in speech analysis and as expected value matching within the space of probability densities [ 41. Jones demonstrates that the Itakura-Saito distortion measure (ISD) of communication theory and the Kullback-Leilber distance measure ( KLM ) of statistics are the only functionals in the smooth Ali-Silvey-Csiszar class and the class of regular ratio distortion measures, respectively, to obey the directed orthogonality principle. Therefore, our focus in this paper is to investigate further these two functionals, i.e., Qisn and RkLM. In Section II, a regularized solution for the ill-posed inverse problem of signal restoration is developed through the use of the stabilizing function approach that uses the entropic stabilizing functionals &, and !l kLM, respectively. These functionals are minimized subject to a mean-squared-error constraint equation. This produces two iterative schemes, called the ISD and KLM algorithms, through which the signal is obtained. In Section III, the derived iterative algorithms are shown to be theoretically sound, leading to a unique, robust solution. In Section IV, examples that demonstrate the restoration achieved by the new methods in several signal-to-noise-ratio (SNR) environments are presented. Finally, we note that this work is an extension of that presented in [ 61.

Data acquisition and digital filtering in analytical isotachophoresis

Voltage-to-frequency conversion (VFC) or 12-bit integrating analog-to-digital conversion with data bunching/averaging during 50 ms is suggested as the optimum data acquisition technique in isotachophoresis. Computer simulation of digital filtering of the conductivity and UV signal in analytical isotachophoresis in the time domain with Savitzky—Golay filtering, commonly used in chromatography, leads to unwanted oscillations at the stepwise change of the signal at the zone-to-zone boundary. If it is really necessary to remove noise prior to further signal evaluation, a rectangular moving average filter is preferred. In that case, a signal restoration algorithm should be applied to the filtered signal.

Convergence issues for iterative deconvolution signal restoration algorithms

The factors that affect the convergence of various iterative deconvolution algorithms will be presented. Topics covered will include the mathematical basis for convergence, how convergence is affected by the type of algorithm used, the class of data being deconvolved, its noise characteristics, and how distortions and errors in the system function affect convergence. Also discussed are some methods on how convergence can be enhanced. Test data are used to support conclusions.

An efficient algorithm for MR image reconstruction without low spatial frequencies

It is demonstrated that if the image to be reconstructed is known to have some zero-valued pixels, the dynamic ranges can be better used by disregarding the largest signals and using signal restoration methods. Low-frequency and high-frequency signals are related, using the knowledge that some pixels are zero, by a set of linear equations in which the number of equations is equal to the number of zero pixels, and the number of unknowns is equal to the number of low-frequency signal samples rejected. An improved Fourier transform (FT), magnetic resonance (MR) imaging method based on a least-square-error (LSE) technique, and an efficient algorithm for signal restoration when the low-frequency components are discarded are presented. In this method, the regions of support in both the image domain and the frequency domain can have arbitrary shapes, and all zero pixels in the image domain can be taken into account. The algorithm has been tested on simulated and experimental data with acceptable results.

A class of iterative signal restoration algorithms

A class of iterative signal restoration algorithms is derived based on a representation theorem for the generalized inverse of a matrix. These algorithms exhibit a first or higher order of convergence, and some of them consist of an online and an offline computational part. The conditions for convergence, the rate of convergence of these algorithms, and the computational load required to achieve the same restoration results are derived. An iterative algorithm is also presented which exhibits a higher rate of convergence than the standard quadratic algorithm with no extra computational load. These algorithms can be applied to the restoration of signals of any dimensionality. The presented approach unifies a large number of iterative restoration algorithms. Based on the convergence properties of these algorithms, combined algorithms are proposed that incorporate a priori knowledge about the solution in the form of constraints and converge faster than previously published algorithms.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>