An inverse problem of reconstructing the time-dependent coefficient in a one-dimensional hyperbolic equation

In this paper, for the first time the inverse problem of reconstructing the time-dependent potential (TDP) and displacement distribution in the hyperbolic problem with periodic boundary conditions (BCs) and nonlocal initial supplemented by over-determination measurement is numerically investigated. Though the inverse problem under consideration is ill-posed by being unstable to noise in the input data, it has a unique solution. The Crank–Nicolson-finite difference method (CN-FDM) along with the Tikhonov regularization (TR) is applied for calculating an accurate and stable numerical solution. The programming language MATLAB built-in lsqnonlin is used to solve the obtained nonlinear minimization problem. The simulated noisy input data can be inverted by both analytical and numerically simulated. The obtained results show that they are accurate and stable. The stability analysis is performed by using Fourier series.

Online Signal Denoising Using Adaptive Stochastic Resonance in Parallel Array and its Application to Acoustic Emission Signals

Signal denoising has been significantly explored in various engineering disciplines. In particular, structural health monitoring applications generally aim to detect weak anomaly responses (including acoustic emission) generated by incipient damage, which are easily buried in noise. Among various approaches, stochastic resonance (SR) has been widely adopted for weak signal detection. While many advancements have been focused on identifying useful information from the frequency domain by optimizing parameters in a post-processing environment to activate SR, it often requires detailed information about the original signal a priori, which is hardly assessed from signals overwhelmed by noise. This research presents a novel online signal denoising strategy by utilizing SR in a parallel array of bistable systems. The original noisy input with additionally applied noise is adaptively scaled, so that the total noise level matches the optimal level that is analytically predicted from a generalized model to robustly enhance signal denoising performance for a wide range of input amplitudes that are often not known in advance. Thus, without sophisticated post-processing procedures, the scaling factor is straightforwardly determined by the analytically estimated optimal noise level and the ambient noise level, which is one of the few quantities that can be reliably assessed from noisy signals in practice. Along with numerical investigations that demonstrate the operational principle and the effectiveness of the proposed strategy, experimental validation of denoising acoustic emission signals by employing a bistable Duffing circuit system exemplifies the promising potential of implementing the new approach for enhancing online signal denoising in practice.

Smoothing Skeleton Avatar Visualizations Using Signal Processing Technology

Movements of a person can be recorded with a mobile camera and visualized as sequences of stick figures for assessments in health and elderly care, physio-therapy, and sports. However, since the visualizations flicker due to noisy input data, the visualizations themselves and even whole assessment applications are not trusted in general. The present paper evaluates different filters for smoothing the movement visualizations but keeping their validity for a visual physio-therapeutic assessment. It evaluates variants of moving average, high-pass, and Kalman filters with different parameters. Moreover, it presents a framework for the quantitative evaluation of smoothness and validity. As these two criteria are contradicting, the framework also allows to weight them differently and to automatically find the correspondingly best-fitting filter and its parameters. Different filters can be recommended for different weightings of smoothness and validity. The evaluation framework is applicable in more general contexts and with more filters than the three filters assessed. However, as a practical result of this work, a suitable filter for stick figure visualizations in a mobile application for assessing movement quality could be selected and used in a mobile app. The application is now more trustworthy and used by medical and sports experts, and end customers alike.

Noise2Grad: Extract Image Noise to Denoise

In many image denoising tasks, the difficulty of collecting noisy/clean image pairs limits the application of supervised CNNs. We consider such a case in which paired data and noise statistics are not accessible, but unpaired noisy and clean images are easy to collect. To form the necessary supervision, our strategy is to extract the noise from the noisy image to synthesize new data. To ease the interference of the image background, we use a noise removal module to aid noise extraction. The noise removal module first roughly removes noise from the noisy image, which is equivalent to excluding much background information. A noise approximation module can therefore easily extract a new noise map from the removed noise to match the gradient of the noisy input. This noise map is added to a random clean image to synthesize a new data pair, which is then fed back to the noise removal module to correct the noise removal process. These two modules cooperate to extract noise finely. After convergence, the noise removal module can remove noise without damaging other background details, so we use it as our final denoising network. Experiments show that the denoising performance of the proposed method is competitive with other supervised CNNs.

Synaptic Plasticity in Memristive Artificial Synapses and Their Robustness Against Noisy Inputs

Emerging brain-inspired neuromorphic computing paradigms require devices that can emulate the complete functionality of biological synapses upon different neuronal activities in order to process big data flows in an efficient and cognitive manner while being robust against any noisy input. The memristive device has been proposed as a promising candidate for emulating artificial synapses due to their complex multilevel and dynamical plastic behaviors. In this work, we exploit ultrastable analog BiFeO3 (BFO)-based memristive devices for experimentally demonstrating that BFO artificial synapses support various long-term plastic functions, i.e., spike timing-dependent plasticity (STDP), cycle number-dependent plasticity (CNDP), and spiking rate-dependent plasticity (SRDP). The study on the impact of electrical stimuli in terms of pulse width and amplitude on STDP behaviors shows that their learning windows possess a wide range of timescale configurability, which can be a function of applied waveform. Moreover, beyond SRDP, the systematical and comparative study on generalized frequency-dependent plasticity (FDP) is carried out, which reveals for the first time that the ratio modulation between pulse width and pulse interval time within one spike cycle can result in both synaptic potentiation and depression effect within the same firing frequency. The impact of intrinsic neuronal noise on the STDP function of a single BFO artificial synapse can be neglected because thermal noise is two orders of magnitude smaller than the writing voltage and because the cycle-to-cycle variation of the current–voltage characteristics of a single BFO artificial synapses is small. However, extrinsic voltage fluctuations, e.g., in neural networks, cause a noisy input into the artificial synapses of the neural network. Here, the impact of extrinsic neuronal noise on the STDP function of a single BFO artificial synapse is analyzed in order to understand the robustness of plastic behavior in memristive artificial synapses against extrinsic noisy input.

Robustness of a dynamical systems model with a plastic self-organising vector field to noisy input signals

We investigate the robustness with respect to random stimuli of a dynamical system with a plastic self-organising vector field, previously proposed as a conceptual model of a cognitive system and inspired by the self-organised plasticity of the brain. This model of a novel type consists of an ordinary differential equation subjected to the time-dependent “sensory” input, whose time-evolving solution is the vector field of another ordinary differential equation governing the observed behaviour of the system, which in the brain would be neural firings. It is shown that the individual solutions of both these differential equations depend continuously over finite time intervals on the input signals. In addition, under suitable uniformity assumptions, it is shown that the non-autonomous pullback attractor and forward omega limit set of the given two-tier system depend upper semi-continuously on the input signal. The analysis holds for both deterministic and noisy input signals, in the latter case in a pathwise sense.