Deconvolution Filter Research Articles

Rock density model of the Southern Benue trough in Nigeria from a synthetic gravity and in-situ density data

ABSTRACT The aim of this study is to identify potential mineral deposits beneath the Southern Benue Trough of Nigeria based on apparent density mapping technique of estimating lateral rock densities from modelled gravity data. In this study, we apply the inverse density deconvolution filter to a short-wavelength gravity component in order to estimate the rock densities for mineral exploration applications and tectonic studies at the Southern Benue Trough in Nigeria. The estimated rock densities vary between 2.50 and 2.74 g/cm3, with minimum density values assigned to volcano-sedimentary deposits along the Cameroon Volcanic Line and maximum density values in the eastern and southern parts associated with mafic igneous rocks. Our gravity and density maps reveal the geometry of dominant geological structures within the study area. The density map highlights carbonate-hosted metallic elements with varying intercalations. Some of these identified mineralized zones coincide with locations of past and present producing mines. Intermediate and mafic igneous rocks as well as highly compacted and volcano-sedimentary rocks are mapped as rock-forming minerals for a mineral exploration. Hence, the obtained model of mineral-bearing rocks mainly demonstrates mechanisms of tectonic events, patterns of deformation regimes, and mineral prospectivity map of the study area.

Fuzzy Entropy-Assisted Deconvolution Method and Its Application for Bearing Fault Diagnosis.

Vibration signal analysis is an important means for bearing fault diagnosis. Affected by the vibration of other machine parts, external noise and the vibration transmission path, the impulses induced by a bearing defect in the measured vibrations are very weak. Blind deconvolution (BD) methods can counteract the effect of the transmission path and enhance the fault impulses. Most BD methods highlight fault features of the filtered signals by impulse-featured objective functions (OFs). However, residual noise in the filtered signals has not been well tackled. To overcome this problem, a fuzzy entropy-assisted deconvolution (FEAD) method is proposed. First, FEAD takes advantage of the high noise sensitivity of fuzzy entropy (FuzzyEn) and constructs a weighted FuzzyEn-kurtosis OF to enhance the fault impulses while suppressing noise interference. Then, the PSO algorithm is used to iteratively solve the optimal inverse deconvolution filter. Finally, envelope spectrum analysis is performed on the filtered signal to realize bearing fault diagnosis. The feasibility of FEAD was first verified by the bearing fault simulation signals at constant and variable speeds. The bearing test signals from Case Western Reserve University (CWRU), the railway wheelset and the test bench validated the good performance of FEAD in fault feature enhancement. A comparison with and quantitative results for the other state-of-the-art BD methods indicated the superiority of the proposed method.

Approximate deconvolution discretisation

A new strategy is presented for the construction of high-order spatial discretisations extracted from a lower-order basic discretisation. The key consideration is that any spatial discretisation of a derivative of a solution can be expressed as the exact differentiation of a corresponding ‘filtered’ solution. Hence, each numerical discretisation method may be directly linked to a unique spatial filter, expressing the truncation error of the basic method. By approximately deconvolving the implied filter of the basic numerical discretisation an augmented high-order method can be obtained. In fact, adopting a deconvolution of the implied filter of suitable higher order enables the formulation of a new spatial discretisation method of correspondingly higher order. This construction is illustrated for finite difference (FD) discretisation schemes, solving partial differential equations in fluid mechanics. Knowing the implied filter of the basic discretisation, one can derive a corresponding higher order method by approximately eliminating the implied spatial filter to a certain desired order. We use deconvolution to compensate for the implied filter. This corresponds to a ‘sharpening’ of numerical solution features before the application of the basic FD method. The combination will be referred to as Approximate Deconvolution Discretisation (ADD). The accuracy of the deconvolved FD scheme depends on the order of approximation of the deconvolution filter. We present the ‘sharpening’ of several well-known FD operators for first- and second-order derivatives and quantify the achieved accuracy in terms of the modified wavenumber spectrum. Examples include high-order extensions up to new schemes with spectral accuracy. The practicality of the deconvolved FD schemes is illustrated in various ways: (i) by investigation of exactly solvable advection and diffusion problems, (ii) by tracking the evolution of the numerical solution to the Taylor-Green vortex problem and (iii) by showing that ADD yields spectral accuracy for the Burgers equation and for double-jet flow of an incompressible fluid.

Segmentation of gastric cancer from microscopic biopsy images using deep learning approach

In Computer vision for microscopy image analysis applications, object segmentation, classification, and structure localization are essential processes for many biological researchers across the globe. The proposed method is significant as it provides automated cancer diagnosis. The manual interpretation of microscopic biopsy for cancer diagnosis is subjective, time-consuming, and dependent on pathologists’ interpretations, degree of skill. An automated cancer diagnosis is required to address these constraints. In this work, A deep learning-based architecture, namely enhanced EMD convolution neural networks (EECNNs) for object segmentation is proposed for microscopy images. The multiple IMFs give detailed frequency components of an image for feature extraction. This improves the performance significantly as compared to the previous works of feature extraction. The presented network is utilized for the segmentation of nuclei and cells in microscopy. The network uses multi-resolution deconvolution filters to train at several levels of an input image, it links the intervening layers for improved localization and context and provides the outcome. The additional convolution layers, which skip the max-pooling function, allow the network to train for varying input intensities and object dimensions while making it adaptable to noisy data. Here, we have compared the experimental results of the proposed method on widely accessible data sets which demonstrate that the proposed method provides superior results in terms of Accuracy of 0.9445, Specificity of 0.9256, Sensitivity of 0.9245, MCC of 0.9654, and BCR of 0.9250.

Deep network-based maximum correlated kurtosis deconvolution: A novel deep deconvolution for bearing fault diagnosis

Deconvolution methods (DMs) which can adaptively design the filter for the feature extraction is the most effective tool to counteract the effect of the transmission path. Convolutional sparse filter (CSF) as a new deconvolution mode, which transfers the complicated numeric calculation to the simple feature learning for the optimization and solution of the deconvolution filter coefficient using neural network, has a remarkable superiority especially under the heavy noise condition compared with the traditional DMs. Yet, the problems of the filter length selection and the sensibility to random interference largely confine its application. Motived by this, a novel deep network-based maximum correlated kurtosis deconvolution (MCKD-DeNet) is proposed in this paper. Firstly, according to the multiple-inputs way of the neural network, a filter initialization is designed using the Hanning window. With different filters guided by the initialization, a serial of filtered signals is input to learn the fault feature. Secondly, correlated kurtosis, which can simultaneously evaluate the periodicity and impulsiveness of the signal, is chosen as the new cost function to train the neural network. And the input period is estimated between the layers by calculating the autocorrelation of the most informative filtered signal. Subsequently, the component with most fault information is locked as the output of MCKD-DeNet using the proposed dimension reduction method based on the correlation coefficient. Finally, compared with previous CSF and improved maximum correlated kurtosis deconvolution, the proposed MCKD-DeNet is verified to have the performance superiority by simulated signal with different noise levels and interference as well as experimental data collected from wind turbine experiment bench with bearing fault.

Outlier Denoising Using a Novel Statistics-Based Mask Strategy for Compressive Sensing

Denoising is always an important step in seismic processing, in order to produce high-quality data for subsequent imaging and inversion. Different types of noise can be suppressed using targeted denoising methods. For outlier noise with singular amplitudes, many classical denoising methods suffer from signal leakage. To mitigate this issue, we developed a statistics-based mask method and incorporated it into the compressive sensing (CS) framework, in order to remove outlier noise. A statistical analysis for seismic data amplitudes was first used to identify the locations of traces containing outlier noise. Then, the outlier trace locations were compared with a mask matrix generated by jitter sampling, and we replaced the sampled traces of the jitter mask that had the outlier noise with their nearby unsampled traces. The optimized sampling matrix enabled us to effectively identify and remove outliers. This optimized mask strategy converts an outlier denoising problem into a data reconstruction problem. Finally, a sparsely constrained inverse problem was solved using a soft-threshold iteration solver to recover signals at the null locations. The feasibility and adaptability of the proposed method were demonstrated through numerical experiments for synthetic and field data. The results showed that the proposed method outperformed the conventional f-x deconvolution and median filter method, and could accurately suppress outlier noise and recover missed expected signals.

Vibration Diagnosis and Optimization of Industrial Robot Based on TPA and EMD Methods

This paper proposed method that combined transmission path analysis (TPA) and empirical mode decomposition (EMD) envelope analysis to solve the vibration problem of an industrial robot. Firstly, the deconvolution filter time-domain TPA method is proposed to trace the source along with the time variation. Secondly, the TPA method positioned the main source of robotic vibration under typically different working conditions. Thirdly, independent vibration testing of the Rotate Vector (RV) reducer is conducted under different loads and speeds, which are key components of an industrial robot. The method of EMD and Hilbert envelope was used to extract the fault feature of the RV reducer. Finally, the structural problems of the RV reducer were summarized. The vibration performance of industrial robots was improved through the RV reducer optimization. From the whole industrial robot to the local RV Reducer and then to the internal microstructure of the reducer, the source of defect information is traced accurately. Experimental results showed that the TPA and EMD hybrid methods were more accurate and efficient than traditional time-frequency analysis methods to solve industrial robot vibration problems.

CFFsBD: A Candidate Fault Frequencies-Based Blind Deconvolution for Rolling Element Bearings Fault Feature Enhancement

The repetitive transient impulses are typical symptoms of rolling bearing faults. The indicator of second-order cyclostationarity (ICS2)-based blind deconvolution (CYCBD) maximizing the cyclostationary behavior of the excitation source proves to be an effective method for enhancing the periodic cyclostationarity component caused by bearing defect. However, the deviation of the fault characteristic frequency—a common phenomenon easily caused by roller creep or measurement systems, etc., can lead to the collapse of this method in practical applications. Additionally, this method is prone to induce the generation of pseudo-cyclostationary components under the guidance of an inappropriate cyclic frequency. Thus, this work proposes a candidate fault frequencies (CFFs)-based blind deconvolution, abbreviated as CFFsBD, for fault feature enhancement of bearings. This idea comes from the concept of CFFs—a collection of frequencies most likely to be associated with bearing fault that can be identified by mining the local time–frequency features of the signal to be analyzed. A new indicator constructed by using CFFs to replace the cycle frequencies in ICS2 is utilized as the criterion to guide the solution of the deconvolution filter. This new indicator is a generalized version of ICS2, and thus, CYCBD can be considered a special case of the proposed CFFsBD. The performance of the CFFsBD is demonstrated by the analysis of simulated and experimental signals of faulty bearings. The results highlight the robustness and stability of the proposed CFFsBD in extracting fault-induced cyclostationary symptoms.

Decomposing stress wave interference in a cylindrical wooden medium using an inverse deconvolution filter.

Excitation of an embedded waveguide in the cross section plane of a cylindrical structure produces Rayleigh modes propagating primarily in circumferential regions of the propagating medium. In many applications, this region is critical to the overall strength of the structure. Using the through-transmission technique, the Rayleigh mode in cylindrical symmetry produces clockwise and counterclockwise trajectories that interfere with each other at the receiver, producing a composite energy response in the temporal domain that hinders the accurate mode characterization. This work presents a decomposition algorithm consisting of three processing steps: (1) analytical continuous wavelet transforms of the raw waveform; (2) frequency polynomial approximation of the inverse point spread function using L2 norm optimization; and (3) derivation of the inverse deconvolution filter via the dual derivative operator. This work demonstrates the mathematical formulation and algorithm implementation with numerical and empirical validations. The proposed decomposition filter can achieve the overall time and energy estimation accuracy with a relative root mean square error of 0.07. Its broader impact will enhance the parametric estimation of the diagnostic stress wave for material characterization.

Elimination of Side Lobe Ghost Peak Using Wiener Deconvolution Filter in OFDR

Ghost peaks refer to these peaks on backscattering trace measured by a reflectometer similar to Fresnel reflection peaks appearing at the position of non-reflection events in optical fiber or optical waveguide networks testing, which will cause ambiguity in the interpretation of reflection events on backscattering trace. We present a simple and effective method to eliminate side lobe ghost peaks in optical frequency domain reflectometry (OFDR) using a Wiener deconvolution filter. An OFDR system usually contains a main interferometer that is used to measure backscattering trace of fiber umber test (FUT) and an auxiliary interferometer that is used to measure the phase of tunable laser source (TLS) to compensate tuning nonlinearity. Multi-peaks in the spectrum of TLS and reflections in the auxiliary interferometer will generate side lobes on point spread function (PSF) of OFDR system, which will cause ghost peaks on FUT trace. By performing a Wiener deconvolution filtering on the auxiliary interferometer, we can obtain the PSF of an auxiliary interferometer, which is used as a convolution kernel to perform a Wiener deconvolution filtering on FUT trace from the main interferometer. Comparing the main interferometer spatial signal before and after deconvolution filtering, the peak amplitude whose reduction higher than threshold is identified to a ghost peak and is eliminated. By this ghost peak elimination method, we can acquire a pure FUT trace by an OFDR using a low-cost distributed feedback (DFB) TLS with a 26 m test length and an mm level spatial resolution.

Breaking down Polyblur: Fast Blind Correction of Small Anisotropic Blurs

Polyblur is a two stage blind deblurring technique for removing small-sized blurs, like small camera shake or the lens point-spread function, proposed in 2021 by Delbracio et al. First, the blur is modeled with a zero-mean anisotropic Gaussian kernel whose parameters are rapidly estimated from the oriented blurry image gradients. Second, a sharp estimate is obtained by applying an approximate deconvolution filter, which is designed as a polynomial function of the estimated blurring kernel. Since in practice true blurs are not exactly Gaussian filters, the residual blur is gradually removed by repeating this two-stage procedure. Because it relies only on simple image manipulations, Polyblur is a quick blind deblurring technique, running in a fraction of a second on a smartphone. In this presentation, we analyze its key ingredients, showcase several use cases on real images, and provide Numpy and Pytorch implementations.

Digital twin approach for on-load tap changers using data-driven dynamic model updating and optimization-based operating condition estimation

On-load tap changers (OLTCs), which are found in power transformers, are mechanically operating components. The vibration signal of an OLTC can provide effective observed data for estimation of the mechanical state transition and a faulty operating condition. Data-driven methods (e.g., deep learning, machine learning) and physics-based methods (e.g., the finite element method, the lumped parameter model) for health-state estimation require sufficient prior knowledge – such as various observed data about fault states, modeling information (including geometry, material properties), and operating conditions – to build a valid digital twin approach. However, prior knowledge for various OLTCs and transformer models is hard to obtain. To begin to address the shortcomings of existing methods, this study proposes a digital twin approach for OLTCs using 1) pre-processing of the vibration signal, 2) data-driven dynamic model updating, and 3) optimization-based operating condition estimation. First, the time–frequency domain features are extracted from the reference signal using a minimum entropy deconvolution (MED) filter, to extract the impulsive vibration signal from OLTC operation. The initial operating conditions that arise from tap changing and diverter switching are assumed as impulsive force using extracted features. The dynamic model is driven by the numerical algorithm for subspace state-space system identification (N4SID), the reference signal, and the excitation impulse force. Next, the phase and magnitude modulation are updated to estimate uncertain operating condition and refine the dynamic model using optimization-based parameter tuning. Analysis results from the proposed digital twin approach are demonstrated for both a numerical and experimental example to verify the effectiveness of the proposed approach. In the numerical case study, i) the simplified physics-based modelling and ii) the joint-input state estimation method were compared with the proposed method. In the experimental case study, the proposed method was applied to an OLTC vibration signal of both inactive and active power transformers. The inflection points in the Dynamic Resistance Measurement (DRM) graph show synchronization with the experimental results of the estimated excitation forces derived using the proposed method.

Comparison of methods for end-to-end co-optimization of optical systems and image processing with commercial lens design software.

We compare three different methods to co-optimize hybrid optical/digital imaging systems with a commercial lens design software: conventional optimization based on spot diagram minimization, optimization of a surrogate criterion based on a priori equalization of modulation transfer functions (MTFs), and minimization of the mean square error (MSE) between the ideal sharp image and the image restored by a unique deconvolution filter. To implement the latter method, we integrate - for the first time to our knowledge - MSE optimization to the software Synopsys CodeV. Taking as an application example the design of a Cooke triplet having good image quality everywhere in the field of view (FoV), we show that it is possible, by leveraging deconvolution during the optimization process, to adapt the spatial distribution of imaging performance to a prescribed goal. We also demonstrate the superiority of MSE co-optimization over the other methods, both in terms of quantitative and visual image quality.

THE DIRECT-INVERSION DECONVOLUTION AND ITS APPLICATION IN SEISMIC DATA

Seismic traces are generated by the convolution of reflectivity and seismic wavelet. Due to limited frequency bandwidth, reflectivity can not be resolved easily. Deconvolution is a method to increase the frequency bandwidth and gives seismic data higher resolution, which makes it easier to analyze. Deconvolution is a common method in the seismic data processing. The mathematical definition of deconvolution is an inverse process of convolution, but the computation of deconvolution uses convolution in its process (Wiener deconvolution). We explained a method that is direct from the mathematical definition. We refer to it as direct-inversion deconvolution. The direct-inversion deconvolution process involves the matrix operation between seismic trace and wavelet instead of the deconvolution filter. By applying the direct-inversion deconvolution, the produced (or deconvolved) seismic trace shows a better result with higher resolution, regardless of the wavelet’s phase. Finally, we performed a phase rotation experiment, and the deconvolution result shows no seismic phase alteration. In comparison, we also perform spiking deconvolution in synthetic data experiments. This method is applied to The North Sea Volve Data Village seismic data, and more thin layers are significantly detected. Finally, it turns out that direct-inversion deconvolution gives a higher resolution to seismic data.

Maximum correntropy criterion-based blind deconvolution and its application for bearing fault detection

The distortion of signal caused by transmission path always brings great difficulties to feature extraction for bearing fault diagnosis. It is thus an important work to eliminate the influence of transmission path and recover impulsive features. A novel method called maximum correntropy criterion-based blind deconvolution (MCCBD) is presented in this paper and the strong analytical connection which holds for MOMEDA and MCCBD is revealed. Maximum correntropy criterion (MCC) is used as an objective function to reduce the influence of outliers and the coefficients of the optimal deconvolution filter can be obtained. Moreover, the proposed method adopts an autocorrentropy-based strategy to automatically evaluate the impulse period, hence it can enhance the fault impulses buried by noise without any prior knowledge. Finally, the superiority of MCCBD is exhibited by comparing with some existing methods on the simulated signal and two experimental datasets.

Machine learning-based vertical resolution enhancement considering the seismic attenuation

The vertical resolution of seismic data is important for the interpretation of geologic features at a fine scale. To improve the resolution of seismic data, spectral enhancement has progressed mainly due to one-dimensional (1D) convolutional models and deconvolution filters; however, recent studies have applied machine learning (ML) algorithms. To generate successful outcome using ML techniques, it is important to reflect the features of target data in the training stage of the ML model. One of main features of seismic field data is a non-stationary wavelet over time due to the change of frequency content as the wavelet passes through specific regions, such as a gas reservoir. However, since conventional methods are generally based on a 1D convolutional model, which assumes that the propagating wavelet is stationary, they show low performance for the parts where the frequency content of the wavelet is significantly changed. In this study, we developed a spectral enhancement algorithm using ML techniques, which can be applied to a seismic trace with different frequency contents over time. We showed that sparse spike inversion results of all target data, rather than just well log data, can be useful to obtain information on the reflectivity series for generating a training data set. To verify the performance of the new algorithm, we compared the spectrally enhanced results from the ML model trained by stationary wavelets and time-variant wavelets and confirmed that the latter wavelets provided better results. In addition, we proposed a quality control (QC) method for verifying the spectrally enhanced results. • We developed a spectral enhancement ML algorithm consider the seismic attenuation. • The ML model trained by time-variant wavelets yielded better results for the area with seismic attenuation. • The results obtained by the ML were verified the validity by our proposed QC method only using seismic data.

Improved H∞ deconvolution filter design for Lur’e singular Markovian jump systems based on sector bounded condition

This paper investigates the deconvolution filter for Lur’e time-varying delays singular Markovian jump systems. Firstly, by establishing mode-dependent Lyapunov–Krasovskill functional and considering sector bounded conditions, stochastic stability conditions and H∞ performance index are obtained for Lur’e singular Markovian jump systems. Secondly, both regularity and impulse-freeness are acquired by singular value decomposition technique. Thirdly, deconvolution filter is realized by virtue of linear matrix inequalities. Ultimately, the utility of this present method is validated by a numerical example and an oil catalytic cracking process.

Improving image contrast and accuracy in velocity estimation by convolution filters for intracardiac blood flow imaging

In this study, the point spread function (PSF) of an ultrasound imaging system was estimated and used as a reference signal in a filtering method for improvement of image quality. The PSF of the imaging system was estimated from measured echo signals from an imaging target. Convolution filters (including deconvolution) were used for improvement of image contrast and spatial resolution. Furthermore, the accuracy in estimation of velocity vectors was evaluated for investigation of the impact of the proposed filters on velocity estimation. In the phantom experiment, contrast of the B-mode image was improved from 76.4 dB to 81.1 dB and 77.8 dB using the convolution and deconvolution filters, respectively. Also, the two-dimensional (2D) velocity distribution in the phantom was estimated by the block matching method, and the bias error (BE) in the estimated lateral velocity was reduced from −19.7% to 2.16% and 2.29% using the convolution and the deconvolution filters, respectively.

Fault diagnosis of a planetary gearbox by D norm-based time synchronous averaging (DTSA) with roughly estimated phase information under an encoder-less operating condition

Minimum entropy deconvolution (MED) filter is widely used to extract fault-related impulse features from noisy vibration signals for fault diagnosis of a gearbox. However, the MED process is vulnerable to abrupt environmental and operational noise, as disturbance components can be extracted instead of fault-related features. To mitigate this issue, time-synchronous averaging (TSA) can be employed to reduce the remaining noise of the MED-filtered signal further. However, TSA requires accurately resampled vibration signals with the aid of an additional encoder system, which could be unavailable in the actual field. Although a typical phase estimation method can be employed, the phase estimation accuracy cannot be precise enough for TSA. In addition, TSA cannot fundamentally recover the fault-related features if the conventional MED filter is undesirably optimized to extract a single dominant impulse feature while eliminating fault-related features. To overcome these challenges, this paper proposes the novel use of D norms for TSA (DTSA). It was found in this paper that D norms, which encapsulate results from multiple MED filters, are amplified at every fault position with margins equal to the length of the MED filter, enabling Dnorm-based TSA (DTSA) by alleviating the slight phase error from vibration signals under an encoder-less condition. In addition, D norms contain all of the fault-related features from the measured signal and thus prevent undesirable eliminations of fault-related features as opposed to the conventional MED process. It was found in this paper that case studies involving an analytic simulation and a 2-kW planetary gearbox testbed indicate that the proposed method outperforms the conventional MED process under a slightly varying speed condition even without an encoder.

Autocorrelation energy and aquila optimizer for MED filtering of sound signal to detect bearing defect in Francis turbine

This paper presents a method to detect the bearing defects in Francis turbine by minimal entropy deconvolution (MED) filter making use of a sound signal. As the outputs of MED are mainly influenced by the filter length hence its appropriate selection is very necessary to recover a single random pulse in case of a weak faulty signal. The optimal filter length selection is done by Aquila optimizer adaptively which uses the autocorrelation energy as its fitness function. Experimentation done on defective bearings of Francis turbine suggested that the proposed method exposes periodic impulses effectively in case of a weak faulty signal or when the fault signal is embedded within the noise or interferences from other parts of Francis turbine. The proposed fault identification method has been compared with other models of MED such as particle swarm optimization -MED and maximum correlated kurtosis deconvolution. Results obtained reveals that the proposed method is superior in identifying the faulty signal embedded with heavy noise.