Showing papers on "Noise (signal processing) published in 2014"

Variational Mode Decomposition

Abstract: During the late 1990s, Huang introduced the algorithm called Empirical Mode Decomposition, which is widely used today to recursively decompose a signal into different modes of unknown but separate spectral bands. EMD is known for limitations like sensitivity to noise and sampling. These limitations could only partially be addressed by more mathematical attempts to this decomposition problem, like synchrosqueezing, empirical wavelets or recursive variational decomposition. Here, we propose an entirely non-recursive variational mode decomposition model, where the modes are extracted concurrently. The model looks for an ensemble of modes and their respective center frequencies, such that the modes collectively reproduce the input signal, while each being smooth after demodulation into baseband. In Fourier domain, this corresponds to a narrow-band prior. We show important relations to Wiener filter denoising. Indeed, the proposed method is a generalization of the classic Wiener filter into multiple, adaptive bands. Our model provides a solution to the decomposition problem that is theoretically well founded and still easy to understand. The variational model is efficiently optimized using an alternating direction method of multipliers approach. Preliminary results show attractive performance with respect to existing mode decomposition models. In particular, our proposed model is much more robust to sampling and noise. Finally, we show promising practical decomposition results on a series of artificial and real data.

An approach to fault diagnosis of reciprocating compressor valves using Teager-Kaiser energy operator and deep belief networks

Abstract: This paper presents an approach to implement vibration, pressure, and current signals for fault diagnosis of the valves in reciprocating compressors. Due to the complexity of structure and motion of such compressor, the acquired vibration signal normally involves transient impacts and noise. This causes the useful information to be corrupted and difficulty in accurately diagnosing the faults with traditional methods. To reveal the fault patterns contained in this signal, the Teager-Kaiser energy operation (TKEO) is proposed to estimate the amplitude envelopes. In case of pressure and current, the random noise is removed by using a denoising method based on wavelet transform. Subsequently, statistical measures are extracted from all signals to represent the characteristics of the valve conditions. In order to classify the faults of compressor valves, a new type of learning architecture for deep generative model called deep belief networks (DBNs) is applied. DBN employs a hierarchical structure with multiple stacked restricted Boltzmann machines (RBMs) and works through a greedy layer-by-layer learning algorithm. In pattern recognition research areas, DBN has proved to be very effective and provided with high performance for binary values. However, for implementing DBN to fault diagnosis where most of signals are real-valued, RBM with Bernoulli hidden units and Gaussian visible units is considered in this study. The proposed approach is validated with the signals from a two-stage reciprocating air compressor under different valve conditions. To confirm the superiority of DBN in fault classification, its performance is compared with that of relevant vector machine and back propagation neuron networks. The achieved accuracy indicates that the proposed approach is highly reliable and applicable in fault diagnosis of industrial reciprocating machinery.

System and method for high-sensitivity sensor

Abstract: A sensor unit that includes at least one sensor configured to measure an ambient condition is described. The controller can be configured to receive instructions, to report a notice level when the controller determines that data measured by the at least one sensor fails a report threshold test corresponding to a report threshold value. The controller can also be configured to obtain a plurality of calibration measurements from the at least one sensor during a calibration period and to adjust the threshold based on the calibration measurements. The controller can be configured to compute a first threshold level corresponding to background noise and a second threshold level corresponding to sensor noise, and to compute the report threshold value from the second threshold. In one embodiment, the sensor unit adjusts one or more of the thresholds based on ambient temperature.

Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition

Abstract: Dynamic mode decomposition (DMD) provides a practical means of extracting insightful dynamical information from fluids datasets. Like any data processing technique, DMD’s usefulness is limited by its ability to extract real and accurate dynamical features from noise-corrupted data. Here, we show analytically that DMD is biased to sensor noise, and quantify how this bias depends on the size and noise level of the data. We present three modifications to DMD that can be used to remove this bias: (1) a direct correction of the identified bias using known noise properties, (2) combining the results of performing DMD forwards and backwards in time, and (3) a total least-squares-inspired algorithm. We discuss the relative merits of each algorithm and demonstrate the performance of these modifications on a range of synthetic, numerical, and experimental datasets. We further compare our modified DMD algorithms with other variants proposed in the recent literature.

Exploiting Patch Similarity for SAR Image Processing: The nonlocal paradigm

Abstract: Most current synthetic aperture radar (SAR) systems offer high-resolution images featuring polarimetric, interferometric, multifrequency, multiangle, or multidate information. SAR images, however, suffer from strong fluctuations due to the speckle phenomenon inherent to coherent imagery. Hence, all derived parameters display strong signal-dependent variance, preventing the full exploitation of such a wealth of information. Even with the abundance of despeckling techniques proposed over the last three decades, there is still a pressing need for new methods that can handle this variety of SAR products and efficiently eliminate speckle without sacrificing the spatial resolution. Recently, patch-based filtering has emerged as a highly successful concept in image processing. By exploiting the redundancy between similar patches, it succeeds in suppressing most of the noise with good preservation of texture and thin structures. Extensions of patch-based methods to speckle reduction and joint exploitation of multichannel SAR images (interferometric, polarimetric, or PolInSAR data) have led to the best denoising performance in radar imaging to date. We give a comprehensive survey of patch-based nonlocal filtering of SAR images, focusing on the two main ingredients of the methods: measuring patch similarity and estimating the parameters of interest from a collection of similar patches.

Low-Power, Noise Insensitive Communication Channel using Logarithmic Detector Amplifier (LDA) Demodulator

Abstract: A method is provided for communicating signals at a low power level in an electromagnetic interference (EMI) environment A first device transmits a modulated signal having a first carrier frequency, including the encoded information via a hardwire transmission medium In one aspect, the power level of the modulated signal can be adjusted to minimize power consumption or reduce the generation of EMI The modulated signal may be in one of the following formats: frequency modulation (FM) or phase modulation (PM) to name a few examples A second device including a logarithmic detector amplifier (LDA) demodulator circuit receives the signal, which may be mixed with EMI The LDA demodulator circuit amplifies the modulated signal, without amplifying the EMI, to supply a demodulated baseband signal, which may be an n-ary digital signal, or an audio signal A low-power, noise insensitive communication channel is also provided

Information Transmission Using the Nonlinear Fourier Transform, Part III: Spectrum Modulation

Abstract: Motivated by the looming capacity crunch in fiber-optic networks, information transmission over such systems is revisited. Among numerous distortions, interchannel interference in multiuser wavelength-division multiplexing (WDM) is identified as the seemingly intractable factor limiting the achievable rate at high launch power. However, this distortion and similar ones arising from nonlinearity are primarily due to the use of methods suited for linear systems, namely WDM and linear pulse-train transmission, for the nonlinear optical channel. Exploiting the integrability of the nonlinear Schrodinger (NLS) equation, a nonlinear frequency-division multiplexing (NFDM) scheme is presented, which directly modulates noninteracting signal degrees-of-freedom under NLS propagation. The main distinction between this and previous methods is that NFDM is able to cope with the nonlinearity, and thus, as the signal power or transmission distance is increased, the new method does not suffer from the deterministic crosstalk between signal components, which has degraded the performance of previous approaches. In this paper, emphasis is placed on modulation of the discrete component of the nonlinear Fourier transform of the signal and some simple examples of achievable spectral efficiencies are provided.

Joint Sparse Recovery Method for Compressed Sensing With Structured Dictionary Mismatches

Abstract: In traditional compressed sensing theory, the dic- tionary matrix is given ap riori, whereas in real applications this matrix suffers from random noise and fluctuations. In this paper, we consider a signal model where each column in the dictionary matrix is affected by a structured noise. This formulation is common in direction-of-arrival (DOA) estimation of off-grid targets, encountered in both radar systems and array processing. We propose to use joint sparse signal recovery to solve the com- pressed sensing problem with structured dictionary mismatches and also give an analytical performance bound on this joint sparse recovery. We show that, under mild conditions, the reconstruction error of the original sparse signal is bounded by both the sparsity and the noise level in the measurement model. Moreover, we implement fast first-order algorithms to speed up the computing process. Numerical examples demonstrate the good performance of the proposed algorithm and also show that the joint-sparse recovery method yields a better reconstruction result than existing methods. By implementing the joint sparse recovery method, the accuracy and efficiency of DOA estimation are improved in both passive and active sensing cases.

Noisy low-rank matrix completion with general sampling distribution

Abstract: In the present paper we consider the problem of matrix completion with noise for general sampling schemes. Unlike previous works, in our construction we do not need to know or to evaluate the sampling distribution or the variance of the noise. We propose new nuclear-norm penalized estimators, one of them of the ''square-root'' type. We prove that, up to a logarithmic factor, our estimators achieve optimal rates with respect to the estimation error.

Adaptive Double Subspace Signal Detection in Gaussian Background—Part I: Homogeneous Environments

Abstract: In this two-part paper, we consider the problem of adaptive multidimensional/multichannel signal detection in Gaussian noise with unknown covariance matrix. The test data (primary data) is assumed as a collection of sample vectors, arranged as the columns of a rectangular data array. The rows and columns of the signal matrix are both assumed to lie in known subspaces, but with unknown coordinates. Due to this feature of the signal structure, we name this kind of signal as the double subspace signal. Part I of this paper focuses on the adaptive detection in homogeneous environments, while Part II deals with the adaptive detection in partially homogeneous environments. Precisely, in this part, we derive the generalized likelihood ratio test (GLRT), Rao test, Wald test, as well as their two-step variations, in homogeneous environments. Three types of spectral norm tests (SNTs) are also introduced. All these detectors are shown to possess the constant false alarm rate (CFAR) property. Moreover, we discuss the differences between them and show how they work. Another contribution is that we investigate various special cases of these detectors. Remarkably, some of them are well-known existing detectors, while some others are still new. At the stage of performance evaluation, conducted by Monte Carlo simulations, both matched and mismatched signals are dealt with. For each case, more than one scenario is considered.

Phase-sensitive Optical Time Domain Reflectometer Assisted by First-order Raman Amplification for Distributed Vibration Sensing Over >100 km

Abstract: In this study, the authors present an experimental and theoretical description of the use of first order Raman amplification to improve the performance of a Phase-sensitive optical time domain reflectometer (φOTDR) when used for vibration measurements over very long distances. A special emphasis is given to the noise which is carefully characterized and minimized along the setup. A semiconductor optical amplifier and an optical switch are used to greatly decrease the intra-band coherent noise of the setup and balanced detection is used to minimize the effects of RIN transferred from the Raman pumps. The sensor was able to detect vibrations of up to 250 Hz (close to the limits set by the time of flight of light pulses) with a resolution of 10 m in a range of 125 km. To achieve the above performance, no post-processing was required in the φOTDR signal. The evolution of the φOTDR signal along the fiber is also shown to have a good agreement with the theoretical model.

Switching times in long-overlap Josephson junctions subject to thermal fluctuations and non-Gaussian noise sources

Abstract: We investigate the superconducting lifetime of long current-biased Josephson junctions, in the presence of Gaussian and non-Gaussian noise sources. In particular, we analyze the dynamics of a Josephson junction as a function of the noise signal intensity, for different values of the parameters of the system and external driving currents. We find that the mean lifetime of the superconductive state is characterized by nonmonotonic behavior as a function of noise intensity, driving frequency, and junction length. We observe that these nonmonotonic behaviors are connected with the dynamics of the junction phase string during the switching towards the resistive state. An important role is played by the formation and propagation of solitons, with two different dynamical regimes characterizing the dynamics of the phase string. Our analysis allows to evidence the effects of different bias current densities, that is a simple spatially homogeneous distribution and a more realistic inhomogeneous distribution with high current values at the edges. Stochastic resonant activation, noise-enhanced stability, and temporary trapping phenomena are observed in the system investigated.

Low-rank approximation based multichannel wiener filter algorithms for noise reduction with application in cochlear implants

Abstract: This paper presents low-rank approximation based multichannel Wiener filter algorithms for noise reduction in speech plus noise scenarios, with application in cochlear implants. In a single speech source scenario, the frequency-domain autocorrelation matrix of the speech signal is often assumed to be a rank-1 matrix, which then allows to derive different rank-1 approximation based noise reduction filters. In practice, however, the rank of the autocorrelation matrix of the speech signal is usually greater than one. Firstly, the link between the different rank-1 approximation based noise reduction filters and the original speech distortion weighted multichannel Wiener filter is investigated when the rank of the autocorrelation matrix of the speech signal is indeed greater than one. Secondly, in low input signal-to-noise-ratio scenarios, due to noise non-stationarity, the estimation of the auto-correlation matrix of the speech signal can be problematic and the noise reduction filters can deliver unpredictable noise reduction performance. An eigenvalue decomposition based filter and a generalized eigenvalue decomposition based filter are introduced that include a more robust rank-1, or more generally rank-R, approximation of the autocorrelation matrix of the speech signal. These noise reduction filters are demonstrated to deliver a better noise reduction performance especially in low input signal-to-noise-ratio scenarios. The filters are especially useful in cochlear implants, where more speech distortion and hence a more aggressive noise reduction can be tolerated.

Fast photonic information processing using semiconductor lasers with delayed optical feedback: Role of phase dynamics

Abstract: Semiconductor lasers subject to delayed optical feedback have recently shown great potential in solving computationally hard tasks. By optically implementing a neuro-inspired computational scheme, called reservoir computing, based on the transient response to optical data injection, high processing speeds have been demonstrated. While previous efforts have focused on signal bandwidths limited by the semiconductor laser's relaxation oscillation frequency, we demonstrate numerically that the much faster phase response makes significantly higher processing speeds attainable. Moreover, this also leads to shorter external cavity lengths facilitating future on-chip implementations. We numerically benchmark our system on a chaotic time-series prediction task considering two different feedback configurations. The results show that a prediction error below 4% can be obtained when the data is processed at 0.25 GSamples/s. In addition, our insight into the phase dynamics of optical injection in a semiconductor laser also provides a clear understanding of the system performance at different pump current levels, even below solitary laser threshold. Considering spontaneous emission noise and noise in the readout layer, we obtain good prediction performance at fast processing speeds for realistic values of the noise strength.

Corrupted Sensing: Novel Guarantees for Separating Structured Signals

Abstract: We study the problem of corrupted sensing, a generalization of compressed sensing in which one aims to recover a signal from a collection of corrupted or unreliable measurements. While an arbitrary signal cannot be recovered in the face of arbitrary corruption, tractable recovery is possible when both signal and corruption are suitably structured. We quantify the relationship between signal recovery and two geometric measures of structure, the Gaussian complexity of a tangent cone, and the Gaussian distance to a subdifferential. We take a convex programming approach to disentangling signal and corruption, analyzing both penalized programs that tradeoff between signal and corruption complexity, and constrained programs that bound the complexity of signal or corruption when prior information is available. In each case, we provide conditions for exact signal recovery from structured corruption and stable signal recovery from structured corruption with added unstructured noise. Our simulations demonstrate close agreement between our theoretical recovery bounds and the sharp phase transitions observed in practice. In addition, we provide new interpretable bounds for the Gaussian complexity of sparse vectors, block-sparse vectors, and low-rank matrices, which lead to sharper guarantees of recovery when combined with our results and those in the literature.

High-dimensional estimation with geometric constraints

Abstract: Consider measuring an n-dimensional vector x through the inner product with several measurement vectors, a_1, a_2, ..., a_m. It is common in both signal processing and statistics to assume the linear response model y_i = + e_i, where e_i is a noise term. However, in practice the precise relationship between the signal x and the observations y_i may not follow the linear model, and in some cases it may not even be known. To address this challenge, in this paper we propose a general model where it is only assumed that each observation y_i may depend on a_i only through . We do not assume that the dependence is known. This is a form of the semiparametric single index model, and it includes the linear model as well as many forms of the generalized linear model as special cases. We further assume that the signal x has some structure, and we formulate this as a general assumption that x belongs to some known (but arbitrary) feasible set K. We carefully detail the benefit of using the signal structure to improve estimation. The theory is based on the mean width of K, a geometric parameter which can be used to understand its effective dimension in estimation problems. We determine a simple, efficient two-step procedure for estimating the signal based on this model -- a linear estimation followed by metric projection onto K. We give general conditions under which the estimator is minimax optimal up to a constant. This leads to the intriguing conclusion that in the high noise regime, an unknown non-linearity in the observations does not significantly reduce one's ability to determine the signal, even when the non-linearity may be non-invertible. Our results may be specialized to understand the effect of non-linearities in compressed sensing.

Spike-threshold adaptation predicted by membrane potential dynamics in vivo.

Abstract: Neurons encode information in sequences of spikes, which are triggered when their membrane potential crosses a threshold. In vivo, the spiking threshold displays large variability suggesting that threshold dynamics have a profound influence on how the combined input of a neuron is encoded in the spiking. Threshold variability could be explained by adaptation to the membrane potential. However, it could also be the case that most threshold variability reflects noise and processes other than threshold adaptation. Here, we investigated threshold variation in auditory neurons responses recorded in vivo in barn owls. We found that spike threshold is quantitatively predicted by a model in which the threshold adapts, tracking the membrane potential at a short timescale. As a result, in these neurons, slow voltage fluctuations do not contribute to spiking because they are filtered by threshold adaptation. More importantly, these neurons can only respond to input spikes arriving together on a millisecond timescale. These results demonstrate that fast adaptation to the membrane potential captures spike threshold variability in vivo.

Brain Signal Variability is Parametrically Modifiable

Abstract: Moment-to-moment brain signal variability is a ubiquitous neural characteristic, yet remains poorly understood. Evidence indicates that heightened signal variability can index and aid efficient neural function, but it is not known whether signal variability responds to precise levels of environmental demand, or instead whether variability is relatively static. Using multivariate modeling of functional magnetic resonance imaging-based parametric face processing data, we show here that within-person signal variability level responds to incremental adjustments in task difficulty, in a manner entirely distinct from results produced by examining mean brain signals. Using mixed modeling, we also linked parametric modulations in signal variability with modulations in task performance. We found that difficulty-related reductions in signal variability predicted reduced accuracy and longer reaction times within-person; mean signal changes were not predictive. We further probed the various differences between signal variance and signal means by examining all voxels, subjects, and conditions; this analysis of over 2 million data points failed to reveal any notable relations between voxel variances and means. Our results suggest that brain signal variability provides a systematic task-driven signal of interest from which we can understand the dynamic function of the human brain, and in a way that mean signals cannot capture.

Quantum Neural Network-Based EEG Filtering for a Brain–Computer Interface

Abstract: A novel neural information processing architecture inspired by quantum mechanics and incorporating the well-known Schrodinger wave equation is proposed in this paper. The proposed architecture referred to as recurrent quantum neural network (RQNN) can characterize a nonstationary stochastic signal as time-varying wave packets. A robust unsupervised learning algorithm enables the RQNN to effectively capture the statistical behavior of the input signal and facilitates the estimation of signal embedded in noise with unknown characteristics. The results from a number of benchmark tests show that simple signals such as dc, staircase dc, and sinusoidal signals embedded within high noise can be accurately filtered and particle swarm optimization can be employed to select model parameters. The RQNN filtering procedure is applied in a two-class motor imagery-based brain-computer interface where the objective was to filter electroencephalogram (EEG) signals before feature extraction and classification to increase signal separability. A two-step inner-outer fivefold cross-validation approach is utilized to select the algorithm parameters subject-specifically for nine subjects. It is shown that the subject-specific RQNN EEG filtering significantly improves brain-computer interface performance compared to using only the raw EEG or Savitzky-Golay filtered EEG across multiple sessions.