Research on a deconvolution algorithm for laser-induced fluorescence diagnosis based on the maximum entropy principle

Laser-induced fluorescence(LIF)spectroscopy is employed for plasma diagnosis,necessitating the utilization of deconvolution algorithms to isolate the Doppler effect from the raw spectral signal.However,direct deconvolution becomes invalid in the presence of noise as it leads to infinite amplification of high-frequency noise components.To address this issue,we propose a deconvolution algorithm based on the maximum entropy principle.We validate the effectiveness of the proposed algorithm by utilizing simulated LIF spectra at various noise levels(signal-to-noise ratio,SNR=20–80 d B)and measured LIF spectra with Xe as the working fluid.In the typical measured spectrum(SNR=26.23 d B)experiment,compared with the Gaussian filter and the Richardson–Lucy(R-L)algorithm,the proposed algorithm demonstrates an increase in SNR of 1.39 d B and 4.66 d B,respectively,along with a reduction in the root-meansquare error(RMSE)of 35%and 64%,respectively.Additionally,there is a decrease in the spectral angle(SA)of 0.05 and 0.11,respectively.In the high-quality spectrum(SNR=43.96 d B)experiment,the results show that the running time of the proposed algorithm is reduced by about98%compared with the R-L iterative algorithm.Moreover,the maximum entropy algorithm avoids parameter optimization settings and is more suitable for automatic implementation.In conclusion,the proposed algorithm can accurately resolve Doppler spectrum details while effectively suppressing noise,thus highlighting its advantage in LIF spectral deconvolution applications.

Cryo-EM combined with image deconvolution to determine ZIF-8 crystal structure

Metal–organic frameworks(MOFs) are crystalline porous materials with tunable properties, exhibiting great potential in gas adsorption, separation and catalysis.[1,2]It is challenging to visualize MOFs with transmission electron microscopy(TEM) due to their inherent instability under electron beam irradiation. Here, we employ cryo-electron microscopy(cryoEM) to capture images of MOF ZIF-8, revealing inverted-space structural information at a resolution of up to about 1.7A and enhancing its critical electron dose to around 20 e^(-)/A^(2). In addition, it is confirmed by electron-beam irradiation experiments that the high voltage could effectively mitigate the radiolysis, and the structure of ZIF-8 is more stable along the [100] direction under electron beam irradiation. Meanwhile, since the high-resolution electron microscope images are modulated by contrast transfer function(CTF) and it is difficult to determine the positions corresponding to the atomic columns directly from the images. We employ image deconvolution to eliminate the impact of CTF and obtain the structural images of ZIF-8. As a result, the heavy atom Zn and the organic imidazole ring within the organic framework can be distinguished from structural images.

Study of inter-well interference in shale gas reservoirs by a robust production data analysis method based on deconvolution

In order to overcome the defects that the analysis of multi-well typical curves of shale gas reservoirs is rarely applied to engineering,this study proposes a robust production data analysis method based on deconvolution,which is used for multi-well inter-well interference research.In this study,a multi-well conceptual trilinear seepage model for multi-stage fractured horizontal wells was established,and its Laplace solutions under two different outer boundary conditions were obtained.Then,an improved pressure deconvolution algorithm was used to normalize the scattered production data.Furthermore,the typical curve fitting was carried out using the production data and the seepage model solution.Finally,some reservoir parameters and fracturing parameters were interpreted,and the intensity of inter-well interference was compared.The effectiveness of the method was verified by analyzing the production dynamic data of six shale gas wells in Duvernay area.The results showed that the fitting effect of typical curves was greatly improved due to the mutual restriction between deconvolution calculation parameter debugging and seepage model parameter debugging.Besides,by using the morphological characteristics of the log-log typical curves and the time corresponding to the intersection point of the log-log typical curves of two models under different outer boundary conditions,the strength of the interference between wells on the same well platform was well judged.This work can provide a reference for the optimization of well spacing and hydraulic fracturing measures for shale gas wells.

Enhancing the vertical resolution of lunar penetrating radar data using predictive deconvolution

The Yutu-2 rover onboard the Chang’E-4 mission performed the first lunar penetrating radar detection on the farside of the Moon.The high-frequency channel presented us with many unprecedented details of the subsurface structures within a depth of approximately 50 m.However,it was still difficult to identify finer layers from the cluttered reflections and scattering waves.We applied deconvolution to improve the vertical resolution of the radar profile by extending the limited bandwidth associated with the emissive radar pulse.To overcome the challenges arising from the mixed-phase wavelets and the problematic amplification of noise,we performed predictive deconvolution to remove the minimum-phase components from the Chang’E-4 dataset,followed by a comprehensive phase rotation to rectify phase anomalies in the radar image.Subsequently,we implemented irreversible migration filtering to mitigate the noise and diminutive clutter echoes amplified by deconvolution.The processed data showed evident enhancement of the vertical resolution with a widened bandwidth in the frequency domain and better signal clarity in the time domain,providing us with more undisputed details of subsurface structures near the Chang’E-4 landing site.

Deblurring,artifact-free optical coherence tomography with deconvolution-random phase modulation

Deconvolution is a commonly employed technique for enhancing image quality in optical imaging methods.Unfortu-nately,its application in optical coherence tomography(OCT)is often hindered by sensitivity to noise,which leads to ad-ditive ringing artifacts.These artifacts considerably degrade the quality of deconvolved images,thereby limiting its effect-iveness in OCT imaging.In this study,we propose a framework that integrates numerical random phase masks into the deconvolution process,effectively eliminating these artifacts and enhancing image clarity.The optimized joint operation of an iterative Richardson-Lucy deconvolution and numerical synthesis of random phase masks(RPM),termed as De-conv-RPM,enables a 2.5-fold reduction in full width at half-maximum(FWHM).We demonstrate that the Deconv-RPM method significantly enhances image clarity,allowing for the discernment of previously unresolved cellular-level details in nonkeratinized epithelial cells ex vivo and moving blood cells in vivo.

Blind Deconvolution Method Based on Precondition Conjugate Gradients

In seismic data processing, blind deconvolution is a key technology. Introduced in this paper is a flow of one kind of blind deconvolution. The optimal precondition conjugate gradients (PCG) in Kyrlov subspace is also used to improve the stability of the algorithm. The computation amount is greatly decreased.

Prestack nonstationary deconvolution based on variable-step sampling in the radial trace domain

The conventional nonstationary convolutional model assumes that the seismic signal is recorded at normal incidence. Raw shot gathers are far from this assumption because of the effects of offsets. Because of such problems, we propose a novel prestack nonstationary deconvolution approach. We introduce the radial trace （RT） transform to the nonstationary deconvolution, we estimate the nonstationary deconvolution factor with hyperbolic smoothing based on variable-step sampling （VSS） in the RT domain, and we obtain the high-resolution prestack nonstationary deconvolution data. The RT transform maps the shot record from the offset and traveltime coordinates to those of apparent velocity and traveltime. The ray paths of the traces in the RT better satisfy the assumptions of the convolutional model. The proposed method combines the advantages of stationary deconvolution and inverse Q filtering, without prior information for Q. The nonstationary deconvolution in the RT domain is more suitable than that in the space-time （XT） domain for prestack data because it is the generalized extension of normal incidence. Tests with synthetic and real data demonstrate that the proposed method is more effective in compensating for large-offset and deep data.

Nonstationary sparsity-constrained seismic deconvolution

The Robinson convolution model is mainly restricted by three inappropriate assumptions, i.e., statistically white reflectivity, minimum-phase wavelet, and stationarity. Modern reflectivity inversion methods（e.g., sparsity-constrained deconvolution） generally attempt to suppress the problems associated with the first two assumptions but often ignore that seismic traces are nonstationary signals, which undermines the basic assumption of unchanging wavelet in reflectivity inversion. Through tests on reflectivity series, we confirm the effects of nonstationarity on reflectivity estimation and the loss of significant information, especially in deep layers. To overcome the problems caused by nonstationarity, we propose a nonstationary convolutional model, and then use the attenuation curve in log spectra to detect and correct the influences of nonstationarity. We use Gabor deconvolution to handle nonstationarity and sparsity-constrained deconvolution to separating reflectivity and wavelet. The combination of the two deconvolution methods effectively handles nonstationarity and greatly reduces the problems associated with the unreasonable assumptions regarding reflectivity and wavelet. Using marine seismic data, we show that correcting nonstationarity helps recover subtle reflectivity information and enhances the characterization of details with respect to the geological record.

Experimental analysis and application of sparsity constrained deconvolution

Sparsity constrained deconvolution can improve the resolution of band-limited seismic data compared to conventional deconvolution. However, such deconvolution methods result in nonunique solutions and suppress weak reflections. The Cauchy function, modified Cauchy function, and Huber function are commonly used constraint criteria in sparse deconvolution. We used numerical experiments to analyze the ability of sparsity constrained deconvolution to restore reflectivity sequences and protect weak reflections under different constraint criteria. The experimental results demonstrate that the performance of sparsity constrained deconvolution depends on the agreement between the constraint criteria and the probability distribution of the reflectivity sequences; furthermore, the modified Cauchy- constrained criterion protects the weak reflections better than the other criteria. Based on the model experiments, the probability distribution of the reflectivity sequences of carbonate and clastic formations is statistically analyzed by using well-logging data and then the modified Cauchy-constrained deconvolution is applied to real seismic data much improving the resolution.

An improved predictive deconvolution based on maximization of non-Gaussianity

The predictive deconvolution algorithm （PD）, which is based on second-order statistics, assumes that the primaries and the multiples are implicitly orthogonal. However, the seismic data usually do not satisfy this assumption in practice. Since the seismic data （primaries and multiples） have a non-Gaussian distribution, in this paper we present an improved predictive deconvolution algorithm （IPD） by maximizing the non-Gaussianity of the recovered primaries. Applications of the IPD method on synthetic and real seismic datasets show that the proposed method obtains promising results.

Least-Squares及Galerkin谱元方法求解环形区域内的泊松方程

为研究基于Least-Squares变分及Galerkin变分两种形式的谱元方法的求解特性,推导了极坐标系中采用两种变分方法求解环形区域内Poisson方程时对应的弱解形式,采用Chebyshev多项式构造插值基函数进行空间离散,得到两种谱元方法对应的代数方程组,由此分析了系数矩阵结构的特点。数值计算结果显示:Least-Squares谱元方法为实现方程的降阶而引入新的求解变量,使得代数方程组形式更为复杂,但边界条件的处理比Galerkin谱元方法更为简单;两种谱元方法均能求解极坐标系中的Poisson方程且能获得高精度的数值解,二者绝对误差分布基本一致;固定单元内的插值阶数时,增加单元数可减小数值误差,且表现出代数精度的特点,误差降低速度较慢,而固定单元数时,在一定范围内数值误差随插值阶数的增加而减小的速度更快,表现出谱精度的特点;单元内插值阶数较高时,代数方程组系数矩阵的条件数急剧增多,方程组呈现病态,数值误差增大,这一特点限制了单元内插值阶数的取值。研究内容对深入了解两种谱元方法在极坐标系中求解Poisson方程时的特点、进一步采用相关分裂算法求解实际流动问题具有参考价值。

Potential risks of spectrum whitening deconvolution——compared with well-driven deconvolution

Deconvolution is widely used to increase the resolution of seismic data. To compare the resolution ability of conventional spectrum whitening deconvolution to thin layers with that of welldriven deconvolution, a complex sedimentary geological model was designed, and then the simulated seismic data were processed respectively by each of the two methods. The amplitude spectrum of seismic data was almost white after spectrum whitening, but the wavelet resolution was low. The amplitude spectrum after well-driven deconvolution deviated from white spectrum, but the wavelet resolution was high. Further analysis showed that if an actual reflectivity series could not well satisfy the hypothesis of white spectrum, spectrum whitening deconvolution had a potential risk of wavelet distortion, which might lead to a pitfall in high resolution seismic data interpretation. On the other hand, the wavelet after well- driven deconvolution had higher resolution both in the time and frequency domains. It is favorable for high resolution seismic interpretation and reservoir prediction.

A predictive deconvolution method for non-white-noise refl ectivity

Conventional predictive deconvolution assumes that the reflection coefficients of the earth conform to an uncorrelated white noise sequence. The Wiener-Hopf (WH) equation is constructed to solve the filter and eliminate the correlated components of the seismic records, attenuate multiples, and improve seismic resolution. However, in practice, the primary refl ectivity series of fi eld data rarely satisfy the white noise sequence assumption, with the result that the correlated components of the primary reflectivity series are also eliminated by traditional deconvolution. This results in signal distortion. To solve this problem, we have proposed an improved method for deconvolution. First, we estimated the wavelet correlation from seismic records using the spectrum-modeling method. Second, this wavelet autocorrelation was used to construct a new autocorrelation function which contains the correlated components caused by the existence of multiples and avoids the correlated components of the primary reflectivity series. Finally, the new autocorrelation function was brought into the WH equation, and the predictive fi lter operator was calculated for deconvolution. In this paper, we have applied this new method to simulated and field data processing, and we have compared its performance with that of traditional predictive deconvolution. Our results show that the new method can adapt to non-white refl ectivity series without changing the statistical characteristics of the primary reflection coefficient series. Compared with traditional predictive deconvolution, the new method reduces processing noise and improves fidelity, all while maintaining the ability to attenuate multiples and enhance seismic resolution.

Regularized least-squares migration of simultaneous-source seismic data with adaptive singular spectrum analysis

Simultaneous-source acquisition has been recog- nized as an economic and efficient acquisition method, but the direct imaging of the simultaneous-source data produces migration artifacts because of the interference of adjacent sources. To overcome this problem, we propose the regularized least-squares reverse time migration method （RLSRTM） using the singular spectrum analysis technique that imposes sparseness constraints on the inverted model. Additionally, the difference spectrum theory of singular values is presented so that RLSRTM can be implemented adaptively to eliminate the migration artifacts. With numerical tests on a fiat layer model and a Marmousi model, we validate the superior imaging quality, efficiency and convergence of RLSRTM compared with LSRTM when dealing with simultaneoussource data, incomplete data and noisy data.

Nonstationary inversion-based directional deconvolution of airgun array signature

Airgun arrays are widely used in marine seismic exploration because signatures excited by airgun arrays have high energy and high-peak bubble ratio, whereas the considerable length and width of the array and ghost reflections make the airgun array signature directional. As a result, the relation of the reflection amplitude with the incident and azimuth angles is variable. This means that the directivity of the airgun array results in a nonstationary wavelet and distorts the relation of the amplitude variation with the incident and azimuth angles. To remove the directivity effect, we propose a nonstationary inversion-based directional deconvolution. At fi rst, the signature as a function of take-off angle and azimuth angle is calculated using the spatial configuration of the airgun array and the near-field signatures. Then, based on the velocity model, the time-variant take-off angles are estimated and directional fi lters are designed using the take-off angles. Finally, the directivity-dependent signatures are shaped to the signature right below the airgun array using nonstationary inversion in the directional deconvolution.

SELF-TUNING WEIGHTED MEASUREMENT FUSION WHITE NOISE DECONVOLUTION ESTIMATOR

For the multi-sensor linear discrete time-invariant stochastic systems with correlated measurement noises and unknown noise statistics,an on-line noise statistics estimator is obtained using the correlation method.Substituting it into the optimal weighted fusion steady-state white noise deconvolution estimator based on the Kalman filtering,a self-tuning weighted measurement fusion white noise deconvolution estimator is presented.By the Dynamic Error System Analysis(DESA) method,it proved that the self-tuning fusion white noise deconvolution estimator converges to the steady-state optimal fusion white noise deconvolution estimator in a realization.Therefore,it has the asymptotically global optimality.A simulation example for the tracking system with 3 sensors and the Bernoulli-Gaussian input white noise shows its effectiveness.

H-infinity deconvolution filtering:a Krein space approach in state-space setting

This note is concerned with the H-infinity deconvolution filtering problem for linear time-varying discretetime systems described by state space models, The H-infinity deconvolution filter is derived by proposing a new approach in Krein space. With the new approach, it is clearly shown that the central deconvolution filter in an H-infinity setting is the same as the one in an H2 setting associated with one constructed stochastic state-space model. This insight allows us to calculate the complicated H-infinity deconvolution filter in an intuitive and simple way. The deconvolution filter is calculated by performing Riccati equation with the same order as that of the original system.

Single Point Positioning with Sequential Least-Squares Filter and Estimated Real-Time Stochastic Model

To obtain higher accurate position estimates, the stochastic model is estimated by using residual of observations, hence, the stochastic model describes the noise and bias in measurements more realistically. By using GPS data and broadcast ephemeris, the numerical results indicating the accurate position estimates at sub-meter level are obtainable.

Multichannel deconvolution with spatial refl ection regularization

Seismic deconvolution plays an important role in the seismic characterization of thin-layer structures and seismic resolution enhancement.However,the trace-by-trace processing strategy is applied and ignores the spatial connection along seismic traces,which gives the deconvolved result strong ambiguity and poor spatial continuity.To alleviate this issue,we developed a structurally constrained deconvolution algorithm.The proposed method extracts the refl ection structure characterization from the raw seismic data and introduces it to the multichannel deconvolution algorithm as a spatial refl ection regularization.Benefi ting from the introduction of the reflection regularization,the proposed method enhances the stability and spatial continuity of conventional deconvolution methods.Synthetic and field data examples confi rm the correctness and feasibility of the proposed method.

A New Fast Iterative Blind Deconvolution Algorithm

Successful blind image deconvolution algorithms require the exact estimation of the Point Spread Function size, PSF. In the absence of any priori information about the imagery system and the true image, this estimation is normally done by trial and error experimentation, until an acceptable restored image quality is obtained. This paper, presents an exact estimation of the PSF size, which yields the optimum restored image quality for both noisy and noiseless images. It is based on evaluating the detail energy of the wave packet decomposition of the blurred image. The minimum detail energies occur at the optimum PSF size. Having accurately estimated the PSF, the paper also proposes a fast double updating algorithm for improving the quality of the restored image. This is achieved by the least squares minimization of a system of linear equations that minimizes some error functions derived from the blurred image. Moreover, a technique is also proposed to improve the sharpness of the deconvolved images, by constrained maximization of some of the detail wavelet packet energies. Simulation results of several examples have verified that the proposed technique manages to yield a sharper image with higher PSNR than classical approaches.