Spiking Deconvolution Research Articles

Weak fault detection based on amplification-compression function and sparse spike deconvolution

Weak fault detection is still a hotspot in these years. The key of this work is to enhance the ratio of signal to noise (SNR). Then a new extraction method of weak fault impact based on amplification algorithm is proposed. Since the fault impact is related to bigger derivative, the amplification function combined with the derivative of the vibration signal is used to amplify the amplitude of the impact. Then Sparse Spike Deconvolution (SSD) which has been widely used in earthquake for impact detection is able to extract small impact from the signal processed by amplification function. Then, in order to enhance the periodicity of fault impacts, the compression function is used to compress the amplitude of bigger impacts according to different scales. At last, the experiment result shows that the proposed method is more effective than the common envelope analysis.

Post stack seismic data processing for enhancing subsurface reservoir mapping in the Shushan basin, Western Desert, Egypt

ABSTRACT Reprocessing of seismic reflection data over Nader field in the Egyptian Western Desert, improved the images of the surface structural framework. The appearance of seismic data can be affected by various factors apart from subsurface structure, including data acquisition problems and processing artefacts. Different post-stack processing steps were tested and compared to the original seismic data determine the enhancement of data quality and improvements on imaging the subsurface. The applied post-stack processing sequence increased the seismic data resolution through increasing the signal-to-noise ratio, enhancing faults detection, and reflectors sharpness and continuity. The Time Variant Frequency Filter (TVF) application is found to be better than applying the filter in one time window and provided more detailed frequency contents and in turn better reflectors identification. The Frequency/Wave Number (F/K) filter removed lot of the existing linear noises resulted in more clear images. The Frequency/Distance (F/X) Deconvolution enhanced the data coherency by removing the existing random noises. The Spiking Deconvolution showed remarkable enhancement in compressing the reflectors and increasing their continuity. The reprocessed data interpretation of Abu Roash C member in Nader Filed, Shushan basin, North Western Desert, Egypt, comparing to the original, showed better mapping and faults detection, which highlighted new potential structures that could act as hydrocarbon traps.

Improved DRT Determination Through a Modified Sparse Spike Deconvolution

Impedance spectroscopy is a powerful characterization method to evaluate the performance of electrochemical systems. However, overlapping signals in the resulting impedance spectra oftentimes cause misinterpretation of the data. The distribution of relaxation times (DRT) method overcomes this problem by transferring the impedance data from the frequency domain into the time domain, which yields DRT spectra with an increased resolution. Unfortunately, the determination of the DRT is an ill-posed problem, and appropriate mathematical regularizations become inevitable to find suitable solutions. [1]The Tikhonov algorithm is a widespread algorithm for the determination of the DRT g and is given by [2] min g (|| Z - A ⋅ g || + λ ⋅ ||L ⋅ g ||)where the regularization parameter λ scales the penalty term. Unfortunately, this leads to unlikely spectra due to necessary boundaries. The sparse spike deconvolution is using the known positive distribution function for a ZARC-element. Thus this deconvolution leads to more natural spectra for the determination of the DRT. However, the sparse spike deconvolution has a very limited scope by using one single regularization parameter. Consequently, we replaced the scalar regularization parameter with a vector P and added a new regularization parameter k for the simultaneous minimization of the vector and the norm of the residuals. The minimization function of this method is given by [3]min P (|| Z - A ⋅ G( P ) ⋅ c || ⋅ k + ||ln(1 - P )||)Herein the G is a matrix with multiple impulse functions.Literature: [1] Ivers-Tiffée, E., & Weber, A., J.Ceram. Soc. Jpn. 2017, 125, 4. [2] Gavrilyuk, A. L., Osinkin, D. A., & Bronin, D. I., Russ. J. Electrochem., 2017, 53, 6. [3] Bergmann, T. G., & Schlüter, N., ChemPhysChem, 2022

Local Geometry of Nonconvex Spike Deconvolution From Low-Pass Measurements

Spike deconvolution is the problem of recovering the point sources from their convolution with a known point spread function, which plays a fundamental role in many sensing and imaging applications. In this paper, we investigate the local geometry of recovering the parameters of point sources$\unicode{x2014}$including both amplitudes and locations$\unicode{x2014}$by minimizing a natural nonconvex least-squares loss function measuring the observation residuals. We propose preconditioned variants of gradient descent (GD), where the search direction is scaled via some carefully designed preconditioning matrices. We begin with a simple fixed preconditioner design, which adjusts the learning rates of the locations at a different scale from those of the amplitudes, and show it achieves a linear rate of convergence$\unicode{x2014}$in terms of entrywise errors$\unicode{x2014}$when initialized close to the ground truth, as long as the separation between the true spikes is sufficiently large. However, the convergence rate slows down significantly when the dynamic range of the source amplitudes is large. To bridge this issue, we introduce an adaptive preconditioner design, which compensates for the learning rates of different sources in an iteration-varying manner based on the current estimate. The adaptive design provably leads to an accelerated convergence rate that is independent of the dynamic range, highlighting the benefit of adaptive preconditioning in nonconvex spike deconvolution. Numerical experiments are provided to corroborate the theoretical findings.

Super-resolution with Binary Priors: Theory and Algorithms.

The problem of super-resolution is concerned with the reconstruction of temporally/spatially localized events (or spikes) from samples of their convolution with a low-pass filter. Distinct from prior works which exploit sparsity in appropriate domains in order to solve the resulting ill-posed problem, this paper explores the role of binary priors in super-resolution, where the spike (or source) amplitudes are assumed to be binary-valued. Our study is inspired by the problem of neural spike deconvolution, but also applies to other applications such as symbol detection in hybrid millimeter wave communication systems. This paper makes several theoretical and algorithmic contributions to enable binary super-resolution with very few measurements. Our results show that binary constraints offer much stronger identifiability guarantees than sparsity, allowing us to operate in "extreme compression" regimes, where the number of measurements can be significantly smaller than the sparsity level of the spikes. To ensure exact recovery in this "extreme compression" regime, it becomes necessary to design algorithms that exactly enforce binary constraints without relaxation. In order to overcome the ensuing computational challenges, we consider a first order auto-regressive filter (which appears in neural spike deconvolution), and exploit its special structure. This results in a novel formulation of the super-resolution binary spike recovery in terms of binary search in one dimension. We perform numerical experiments that validate our theory and also show the benefits of binary constraints in neural spike deconvolution from real calcium imaging datasets.

Introducing Alternative Algorithms for the Determination of the Distribution of Relaxation Times

Impedance spectroscopy is a powerful characterization method to evaluate the performance of electrochemical systems. However, overlapping signals in the resulting impedance spectra oftentimes cause misinterpretation of the data. The distribution of relaxation times (DRT) method overcomes this problem by transferring the impedance data from the frequency domain into the time domain, which yields DRT spectra with an increased resolution. Unfortunately, the determination of the DRT is an ill‐posed problem, and appropriate mathematical regularizations become inevitable to find suitable solutions. The Tikhonov algorithm is a widespread method for computing DRT data, but it leads to unlikely spectra due to necessary boundaries. Therefore, we introduce the application of three alternative algorithms (Gold, Richardson Lucy, Sparse Spike) for the determination of stable DRT solutions and compare their performances. As the promising Sparse Spike deconvolution has a limited scope when using one single regularization parameter, we furthermore replaced the scalar regularization parameter with a vector. The resulting method is able to calculate well‐resolved DRT spectra.

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.

Warped mapping–based blind deconvolution for resolution improvement

ABSTRACTOwing to the influence of absorption and scattering, the components of seismic waves, especially those with higher frequencies, always suffer amplitude attenuation and phase distortion during their propagation through the earth. Nonstationary blind deconvolution takes such attenuations into account for prestack seismic data. This not only compensates for attenuation‐induced energy loss but also simultaneously addresses the energy loss associated with the reflectivity series and wavelet. Additionally, nonstationary blind deconvolution can greatly improve the resolution of seismic data. However, prestack nonstationary blind deconvolution is difficult to implement because it is not easy to estimate the attenuation function of prestack seismic data unless the quality factor of the Earth is assumed to be constant. In this regard, we introduced a nonstationary blind deconvolution method for prestack gathering. First, we used warped mapping to calculate the attenuation function of the prestack data. Then, we incorporated the attenuation function into the nonstationary sparse spike deconvolution based on Toeplitz‐sparse matrix factorization for reflectivity series and wavelet estimation. The proposed method is velocity‐independent and can be adapted to the time‐varying Q model. To validate its stability and effectiveness, numerical and real data examples were adopted. The results show that the proposed method provides a straightforward routine for the estimation of prestack reflectivity coefficients for further processing and inversion.

A Novel Multichannel Seismic Deconvolution Method via Structure-Oriented Regularization

Seismic deconvolution is an effective approach to improve the resolution of seismic data and plays an important role in migration imaging, reservoir prediction and other fields. However, conventional deconvolution methods are usually based on sparse-type regularization (e.g., <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{1}$ </tex-math></inline-formula> -norm) and adopt a trace-by-trace inversion strategy to reconstruct the subsurface reflectivity series. Although such methods can improve the resolution of seismic records to a certain extent, the lack of spatial constraint will result in poor spatial continuity in the reconstructed reflectivity. This phenomenon is particularly obvious in regions with complicated geologic structures. For the purpose of overcoming this issue, we have developed a structure-oriented regularization-based multichannel sparse spike deconvolution (SOR-based MSSD) method. This method imposes <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{1}$ </tex-math></inline-formula> -norm regularization on the reflectivity to obtain the high-resolution subsurface reflectivity series and imposes structure-oriented regularization (SOR) on the expected high-resolution seismic data to improve the spatial continuity of the inversion result. First, we construct SOR term based on the local structural orientations which can be estimated from the poststack seismic data. Then, we integrate the seismic data misfit term, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{1}$ </tex-math></inline-formula> -norm constraint term, and the SOR term to formulate the objective function. At last, we use the alternating direction method of multipliers (ADMMs) to efficiently solve the objective function. We compare the SOR-based MSSD with existing methods by using synthetic and field data. Both deconvolution examples illustrate the performance of proposed method in terms of improving the spatial continuity.

De-noising receiver function data using the unsupervised deep learning approach

SUMMARYThe converted wave data (P-to-s or S-to-p), traditionally termed as receiver functions, are often contaminated with noise of different origin that may lead to the erroneous identification of phases and thus influence the interpretations. Here, we utilize an unsupervised deep learning approach called Patchunet to de-noise the converted wave data. We divide the input data into several patches, which are input to the encoder and decoder network to extract some meaningful features. The method de-noises an image patch by patch and utilizes the redundant information on similar patches to obtain the final de-noised results. The method is first tested on a suite of synthetic data contaminated with various amounts of Gaussian and realistic noise and then on the observed data from three permanent seismic stations: HYB (Hyderabad, India), LBTB (Lobatse, Botswana, South Africa) and COR (Corvallis, Oregon, USA). The method works very well even when the signal-to-noise ratio is poor or with the presence of spike noise and deconvolution artifacts. The field data demonstrate the effectiveness of the method for attenuating the random noise especially for the mantle phases, which show significant improvements over conventional receiver function based images.

Direct extraction of signal and noise correlations from two-photon calcium imaging of ensemble neuronal activity.

Neuronal activity correlations are key to understanding how populations of neurons collectively encode information. While two-photon calcium imaging has created a unique opportunity to record the activity of large populations of neurons, existing methods for inferring correlations from these data face several challenges. First, the observations of spiking activity produced by two-photon imaging are temporally blurred and noisy. Secondly, even if the spiking data were perfectly recovered via deconvolution, inferring network-level features from binary spiking data is a challenging task due to the non-linear relation of neuronal spiking to endogenous and exogenous inputs. In this work, we propose a methodology to explicitly model and directly estimate signal and noise correlations from two-photon fluorescence observations, without requiring intermediate spike deconvolution. We provide theoretical guarantees on the performance of the proposed estimator and demonstrate its utility through applications to simulated and experimentally recorded data from the mouse auditory cortex.

Multichannel sparse spike deconvolution based on dynamic time warping

Multichannel sparse spike deconvolution based on dynamic time warping

Sparse optimization on measures with over-parameterized gradient descent

Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks training. We show that this problem can be solved by discretizing the measure and running non-convex gradient descent on the positions and weights of the particles. For measures on a d-dimensional manifold and under some non-degeneracy assumptions, this leads to a global optimization algorithm with a complexity scaling as $$\log (1/\epsilon )$$ in the desired accuracy $$\epsilon $$ , instead of $$\epsilon ^{-d}$$ for convex methods. The key theoretical tools are a local convergence analysis in Wasserstein space and an analysis of a perturbed mirror descent in the space of measures. Our bounds involve quantities that are exponential in d which is unavoidable under our assumptions.

On the Stable Resolution Limit of Total Variation Regularization for Spike Deconvolution

The stability of spike deconvolution, which aims at recovering point sources from their convolution with a point spread function (PSF), is known to be related to the separation between those sources. When the observations are noisy, it is critical to ensure support stability, where the deconvolution does not lead to spurious, or oppositely, missing estimates of the point sources. In this paper, we study the resolution limit of stably recovering the support of two closely located point sources using the Beurling-LASSO estimator, which is a convex optimization approach based on total variation regularization. We establish a sufficient separation criterion between the sources, depending only on the PSF, above which the Beurling-LASSO estimator is guaranteed to return a stable estimate of the point sources, with the same number of estimated elements as that of the ground truth. Our result highlights the impact of PSF on the resolution limit in the noisy setting, which was not evident in previous studies of the noiseless setting. Towards the end, we show that the same resolution limit applies to resolving two close-located sources in conjunction of other well-separated sources.

Problems with the standard vibroseis deconvolution: some practical solutions

In conventional vibroseis data processing, the recorded sweep is correlated with the recorded trace, assuming that the estimated groundforce is equal to the sweep, but it is demonstrated that due to the non-linearity associated with the vibrator system, the true groundforce and the recorded sweep are not the same. Further, while processing, it is assumed that the zero phase Klauder wavelet is convolved with the Earth’s reflectivity, completely ignoring the fact that the far-field velocity is basically proportional to the time-derivative of the groundforce, hence on real data, it is not possible to achieve an ideal zero-phase wavelet. Additionally, the Earth’s low-pass filtering generates a mixed-phase signal, which is not suitable for conventional deconvolution. We demonstrate that the recorded sweep contaminates the traces with harmonic noise and recommend a pre-determined sweep for cross-correlation. Further, to avoid minimum-phase violation issue, we endorse the frequency domain sweep deconvolution method (FDSD). Our results on synthetic as well as real seismic data, generated after FDSD, show significant improvement in resolution and noise suppression, as compared to the cross-correlated one. It was also shown that the predictive deconvolution combined with FDSD should be used to generate deconvolved seismic sections, and the spiking deconvolution should be avoided.

A Sparse Spike Deconvolution Algorithm Based on a Recurrent Neural Network and the Iterative Shrinkage-Thresholding Algorithm

Conventional sparse spike deconvolution algorithms that are based on the iterative shrinkage-thresholding algorithm (ISTA) are widely used. The aim of this type of algorithm is to obtain accurate seismic wavelets. When this is not fulfilled, the processing stops being optimum. Using a recurrent neural network (RNN) as deep learning method and applying backpropagation to ISTA, we have developed an RNN-like ISTA as an alternative sparse spike deconvolution algorithm. The algorithm is tested with both synthetic and real seismic data. The algorithm first builds a training dataset from existing well-logs seismic data and then extracts wavelets from those seismic data for further processing. Based on the extracted wavelets, the new method uses ISTA to calculate the reflection coefficients. Next, inspired by the backpropagation through time (BPTT) algorithm, backward error correction is performed on the wavelets while using the errors between the calculated reflection coefficients and the reflection coefficients corresponding to the training dataset. Finally, after performing backward correction over multiple iterations, a set of acceptable seismic wavelets is obtained, which is then used to deduce the sequence of reflection coefficients of the real data. The new algorithm improves the accuracy of the deconvolution results by reducing the effect of wrong seismic wavelets that are given by conventional ISTA. In this study, we account for the mechanism and the derivation of the proposed algorithm, and verify its effectiveness through experimentation using theoretical and real data.

Adaptive step-size fast iterative shrinkage-thresholding algorithm and sparse-spike deconvolution

The standard Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) adopts a search approach consisting of linear increases to determine the step size of the internal gradient. If the input of the initial step-size is not accurate, the convergence of FISTA may be restricted when the linear search scheme is applied. To overcome this problem, we tentatively reduce the step size before each iteration to then obtain the most suitable step-size using a linear search approach. To ensure the convergence of the algorithm, we introduce the step size for the previous and subsequent iterations during the calculation process. This has allowed us sparse-spike deconvolution based on an adaptive step size algorithm (ASFISTA), which to a certain extent solves the problem of the degree of convergence of the standard method. In this paper we first present the new algorithm and then we test its convergence. In order to check the effectiveness of the modified algorithm, we use both the standard FISTA method and the improved ASFISTA method to conduct sparse spike deconvolution on a theoretical model. Finally, we carry out a similar analysis aimed at the recovery of the sparse real signal.

Non-Negative Orthogonal Greedy Algorithms

Orthogonal greedy algorithms are popular sparse signal reconstruction algorithms. Their principle is to select atoms one by one. A series of unconstrained least-square subproblems of gradually increasing size is solved to compute the approximation coefficients, which is efficiently performed using a fast recursive update scheme. When dealing with non-negative sparse signal reconstruction, a series of non-negative least-squares subproblems have to be solved. Fast implementation becomes tricky since each subproblem does not have a closed-form solution anymore. Recently, non-negative extensions of the classical orthogonal matching pursuit and orthogonal least squares algorithms were proposed, using slow ( i.e. , non-recursive) or recursive but inexact implementations. In this paper, we revisit these algorithms in a unified way. We define a class of non-negative orthogonal greedy algorithms and exhibit their structural properties. We propose a fast and exact implementation based on the active-set resolution of non-negative least-squares and exploiting warm start initializations. The algorithms are assessed in terms of accuracy and computational complexity for a sparse spike deconvolution problem. We also present an application to near-infrared spectra decomposition.

Techniques and methods of seismic data processing in active volcanic areas: some applications to multichannel seismic profiles (Gulf of Naples, Southern Tyrrhenian sea, Italy)

The techniques of seismic surveying, especially reflection seismic, considerably varied during last year’s. The contribution to this variation mainly came from the oil industry, which has developed the geophysical methods for oil searching. The basic techniques of seismic exploration consist of the generation of seismic waves artificially in the ground (source) and of the measurement of the requested times to cover the source-receiver path. Seismic data processing of three multichannel seismic profiles located in the Gulf of Naples for an overall length of 150 kilometers is herein presented. The techniques of seismic processing used for the elaboration of the seismic data are up-to-date. Some of them are based on complex mathematical models, allowing obtaining good velocity analysis for the production of stacked sections, ready to be interpreted. In this paper the procedures of processing of multichannel seismic data starting from the field data are shown. Sketch diagrams of the elaboration processes applied during several phases of the whole processing have been constructed. The used software are the Promax2D (Landmark Ltd.) and the Seismic Unix (Colorado School of Mines). The steps of the seismic data processes included the pre-processing, the sorting, the velocity analysis, the normal move-out (NMO), the stacking, the band-pass filtering, the multiple removals, the predictive de-convolution and the spiking de-convolution.

A nonstationary sparse spike deconvolution with anelastic attenuation

Seismic wavelet estimation and deconvolution are essential for high-resolution seismic processing. Because of the influence of absorption and scattering, the frequency and phase of the seismic wavelet change with time during wave propagation, leading to a time-varying seismic wavelet. To obtain reflectivity coefficients with more accurate relative amplitudes, we should compute a nonstationary deconvolution of this seismogram, which might be difficult to solve. We have extended sparse spike deconvolution via Toeplitz-sparse matrix factorization to a nonstationary sparse spike deconvolution approach with anelastic attenuation. We do this by separating our model into subproblems in each of which the wavelet estimation problem is solved by the classic sparse optimization algorithms. We find numerical examples that illustrate the parameter setting, noisy seismogram, and the estimation error of the [Formula: see text] value to validate the effectiveness of our extended approach. More importantly, taking advantage of the high accuracy of the estimated [Formula: see text] value, we obtain better performance than with the stationary Toeplitz-sparse spike deconvolution approach in real seismic data.