Deblurring Filter Research Articles

Q-compensated image-domain least-squares reverse time migration through preconditioned point-spread functions

Image-domain least-squares reverse time migration (IDLSRTM) through point-spread functions (PSFs) has been proven to be a feasible approach to improve the spatial resolution and amplitude fidelity of reflection images recovered by reverse time migration (RTM). However, it usually ignores the earth’s Q-effects, which may lead to an unfocused reflection image with an undesired spatial resolution. In this paper, we develop a Q-compensated IDLSRTM approach (denoted as Q-IDLSRTM) through PSFs, in which we use the viscoacoustic wave equation based on the generalized standard linear solid model to simulate inherent subsurface attenuation and the linear inversion to compensate for the amplitude attenuation. The PSFs are estimated by a round of modeling-migration computation and spatial interpolation on the fly. There are two key points in the developed Q-IDLSRTM approach. The first is that we must apply the deblurring filter as a preconditioner to compensate for the attenuation of image amplitude of PSFs and RTM in a viscoacoustic medium, before the iterative solution. The preconditioned PSFs and RTM images can help us to construct a less ill-posed image-domain inverse problem that can produce an improved image quality and a faster convergence rate, compared with the conventional Q-IDLSRTM approach without the deblurring filter. The second key point is that we can impose the L1-norm constraint and total variation regularization on the reflection image to stabilize the solution of the ill-posed inverse problem. Several 2D and 3D experiments verify that the developed approach can achieve better imaging quality in terms of amplitude fidelity and spatial resolution relative to the conventional Q-IDLSRTM and acoustic IDLSRTM approaches.

A tutorial of image-domain least-squares reverse time migration through point-spread functions

Least-squares reverse time migration (LSRTM) has shown great potential to improve the amplitude fidelity and spatial resolution of a reverse time migration (RTM) image. However, the main disadvantage is that it requires significant computational resources for the iterative solution. To ameliorate this problem, the image-domain LSRTM (IDLSRTM) approach through point-spread functions (PSFs) has been proven to be a viable and alternative technique to deconvolve the standard RTM image. In this paper, we develop a tutorial for the numerical implementation of IDLSRTM through PSFs. The Hessian matrix in the standard IDLSRTM approach is estimated through the spatial interpolation of precomputed PSFs on the fly, where the PSFs are computed by one-round forward modeling and migration. However, the resulting IDLSRTM scheme is highly ill-conditioned because of the incomplete acquisition condition, irregular subsurface illumination, and band-limited data. To stabilize inversion and improve the inverted image, we suggest that the PSFs and RTM images should be deblurred by applying a deblurring filter. The deblurring PSFs can reduce the condition number of the standard Hessian matrix and make the inverse problem more well conditioned, thus improving imaging quality and accelerating convergence. Furthermore, the regularization operators should be imposed to produce a reasonable inverted image and avoid the overfitting of the image-matching term. Based on several examples with synthetic and field data, we can conclude two significant points. The first point is that the standard IDLSRTM approach through the conventional PSFs can only recover a reflectivity image similar to the deblurring RTM and nonstationary matching filter (NMF) approaches. The second point is that the deblurring IDLSRTM approach through the deblurring PSFs can retrieve the reflectivity image with higher resolution and better amplitude fidelity than the standard IDLSRTM approach and the standard RTM approach with the deblurring filter or NMF.

Least-squares interferometric migration of microseismic source location with a deblurring filter

Microseismic source locations play an important role in monitoring hydraulic fracturing in unconventional oil and gas exploration. Waveform-based source location methods can reliably and automatically image source locations without phase identification. A widely used and representative waveform-based method is interferometric migration (IM), which can eliminate the excitation-time term and image the source location in space by using correlograms of pairwise receivers. IM can avoid the trade-off between the inversions of excitation time and source location, but provides low-resolution source location images with strong migration artifacts. To improve the spatial resolution, we first developed a least-squares interferometric migration (LSIM). LSIM iteratively minimizes the correlogram residuals using the conjugate-gradient (CG) method. It provides a significant improvement in spatial resolution compared with conventional IM but requires a large number of iterations and high computational costs. To overcome this drawback, we develop an efficient least-squares interferometric migration with a deblurring filter (DLSIM) for high-resolution microseismic source locations. We introduce the Hessian matrix into the microseismic source location problem and approximate the inverse Hessian with a relatively inexpensive deblurring filter. The deblurring filter is applied to the updated gradient matrix in the CG algorithm. It could significantly accelerate the convergence rate of the least-squares inversion and meanwhile, provide a high spatial resolution. We use synthetic and real hydraulic fracturing data to demonstrate the robustness and effectiveness of DLSIM. Data noise, velocity error, and wavelet error are considered in the synthetic tests to simulate actual situations. The inverted results find that DLSIM achieves high-resolution source location images after 5–10 iterations that are equivalent to those of LSIM after approximately 50 iterations. Therefore, DLSIM can dramatically reduce the computational cost owing to its fewer number of iterations compared with LSIM.

2-D and 3-D Q-Compensated Image-Domain Least-Squares Reverse Time Migration Through the Hybrid Point Spread Functions and the Hybrid Deblurring Filter

Image-domain least-squares reverse time migration (IDLSRTM) through point spread functions (PSFs) is a suitable compromise between image quality and computational efficiency for inversion-based imaging tools. However, the conventional IDLSRTM method in acoustic approximation does not account for the subsurface attenuation effects, which may result in the unfocused migration image in attenuated geological environments. To incorporate the attenuation effects and improve the image quality, we develop a Q-compensated IDLSRTM method by using the hybrid PSFs rather than the acoustic PSFs as the blurring functions to deconvolve the adjoint migration image. These hybrid PSFs are estimated by a combination of computation between the viscoacoustic Born modeling and acoustic reverse time migration (RTM) using a series of uniform point scatterers. To further improve the quality of inverted images, we have applied a hybrid deblurring filter to the hybrid PSFs and acoustic RTM image, before the iterative inversion. Through some numerical examples of synthetic and field data, we have demonstrated that the proposed Q-IDLSRTM method combined with the hybrid PSFs and the hybrid deblurring filter can compensate for the attenuation effects and provide seismic images with improved spatial resolution and balanced image amplitudes. Relative to the conventional IDLSRTM methods through acoustic and hybrid PSFs, the proposed method can provide migration images with higher image resolution and better-balanced image amplitudes.

Least-Squares Reverse Time Migration With Curvelet-Domain Preconditioning Operators

Least-squares reverse time migration (LSRTM) is an amplitude-preserving seismic imaging technique that aims at finding the subsurface reflectivity model. It is often performed iteratively using an inversion algorithm, such as the conjugate gradient method. Such an implementation requires a huge amount of calculation as it may converge slowly. Preconditioning plays a crucial role in seismic inverse problems. In this study, we propose a novel preconditioning method for LSRTM. The proposed method estimates a new guided curvelet-domain deblurring filter for one-step LSRTM and preconditioned LSRTM. Then, the filter is applied to migrated images and gradients in LSRTM. Such a deblurring filter acts as a curvelet-domain local linear approximation of the least-squares functional inverse Hessian, which can improve the image quality and accelerate the convergence. Numerical tests on the synthetic model and a field data example demonstrate that the preconditioning operator can effectively accelerate the convergence of LSRTM. One-step LSRTM can obtain comparable image quality to that of conventional iterative LSRTM with only a single iteration. The comparison of the convergence curves demonstrates that the curvelet-domain preconditioning operators accelerate the convergence of LSRTM. Furthermore, the preconditioned LSRTM achieves better image quality than the conventional LSRTM. We compare preconditioning operators based on diagonal and local linear approximations. The preconditioning operator based on the local linear approximation has more robust performance and more stable convergence curves than the diagonal-based approximation.

Migration of viscoacoustic data using acoustic reverse time migration with hybrid deblurring filters

Viscoacoustic migration can significantly compensate for the amplitude loss and phase distortion in migration images computed from highly attenuated data. However, solving the viscoacoustic wave equation requires a significant amount of storage space and computation time, especially for least-squares migration methods. To mitigate this problem, we used acoustic reverse time migration (RTM) instead of viscoacoustic migration to migrate the viscoacoustic data and then we correct the amplitude and phase distortion by hybrid deblurring filters in the image domain. Numerical tests on synthetic and field data demonstrate that acoustic RTM combined with hybrid deblurring filters can compensate for the attenuation effects and produce images with high resolution and balanced amplitudes. This procedure requires less than one-third of the storage space and is [Formula: see text] times faster compared with the viscoacoustic migration, but at the cost of mildly reduced accuracy. Here, [Formula: see text] represents the number of iterations used for least-squares migration method. This method can be extended to 3D migration at even a greater cost saving.

Multiparameter deblurring filter and its application to elastic migration and inversion

Different types of model parameters, such as the P- and S-wave velocities, can be coupled to one another in multiparameter seismic inversion. This coupling effect is not taken into account by the conventional approximation to the Hessian inverse for a single type of parameter, and so it can lead to a slow rate of convergence by an iterative inversion method. To solve this problem, we have developed a multiparameter deblurring filter that approximates the Hessian inverse. This filter takes into account the coupling between different parameters by using stationary local filters to approximate the submatrices of the Hessian inverse for the different types of parameters. The filters are calculated by matching the reference multiparameter migration images to their reference reflectivity models. Numerical tests with elastic migration and inversion indicate that the multiparameter deblurring filter not only reduces the footprint noise, balances the amplitude, and increases the resolution of the elastic migration images, but it also mitigates the crosstalk artifacts caused by the coupling effect. When used as a preconditioner, it also accelerates the convergence rate for elastic inversion.

Zero-offset sections with a deblurring filter in the time domain

The conventional common-midpoint stack is not equivalent to the zero-offset section due to the existence of velocity uncertainty. To obtain a zero-offset reflection section that preserves most reflections and diffractions, we have developed a velocity-independent workflow for reconstructing a high-quality zero-offset reflection section from prestack data with a deblurring filter. This workflow constructs a migration image volume by prestack time migration using a series of constant-velocity models. A deblurring filter for each constant-velocity model is applied to each time-migration image to get a deblurred image volume. To preserve all events in the image volume, each deblurred image panel is demigrated and then summed over the velocity axis. Compared with the workflow without a deblurring filter, the composite zero-offset reflection section has higher resolution and fewer migration artifacts. We evaluate applications of our method to synthetic and field data to validate its effectiveness.

Q-least-squares reverse time migration with viscoacoustic deblurring filters

Viscoacoustic least-squares reverse time migration, also denoted as Q-LSRTM, linearly inverts for the subsurface reflectivity model from lossy data. Compared with conventional migration methods, it can compensate for the amplitude loss in the migrated images due to strong subsurface attenuation and can produce reflectors that are accurately positioned in depth. However, the adjoint [Formula: see text] propagators used for backward propagating the residual data are also attenuative. Thus, the inverted images from [Formula: see text]-LSRTM with a small number of iterations are often observed to have lower resolution when compared with the benchmark acoustic LSRTM images from acoustic data. To increase the resolution and accelerate the convergence of [Formula: see text]-LSRTM, we used viscoacoustic deblurring filters as a preconditioner for [Formula: see text]-LSRTM. These filters can be estimated by matching a simulated migration image to its reference reflectivity model. Numerical tests on synthetic and field data demonstrate that [Formula: see text]-LSRTM combined with viscoacoustic deblurring filters can produce images with higher resolution and more balanced amplitudes than images from acoustic RTM, acoustic LSRTM, and [Formula: see text]-LSRTM when there is strong attenuation in the background medium. Our preconditioning method is also shown to improve the convergence rate of [Formula: see text]-LSRTM by more than 30% in some cases and significantly compensate for the lossy artifacts in RTM images.

Comparisons Of Restored Blurred-Noisy Dental Images Using Wiener Filter And Lucy-Richardson Technique.

This paper attempts to compare dental images (grayscale/truecolor) degraded with blur and noise using different de-blurring filters. The image is degraded by the combination of Gaussian/Average blur and Salt & Pepper /Speckle / Poisson / Gaussian noise for different values of PSF. All the degraded images are then restored using Wiener Filter, Lucy Richardson Filter technique. Restoration by Wiener filter takes place for different values of estimated NSR and restoration by Lucy-Richardson for different iterations. The restored images are then compared on the basis of SNR, MSE and PSNR values. This comparison are made to find which filter technique removes which combination of blur and noise on what value of PSF with high PSNR/SNR and low MSE value.

Improved image reconstruction of low-resolution multichannel phase contrast angiography.

In low-resolution phase contrast magnetic resonance angiography, the maximum intensity projected channel images will be blurred with consequent loss of vascular details. The channel images are enhanced using a stabilized deblurring filter, applied to each channel prior to combining the individual channel images. The stabilized deblurring is obtained by the addition of a nonlocal regularization term to the reverse heat equation, referred to as nonlocally stabilized reverse diffusion filter. Unlike reverse diffusion filter, which is highly unstable and blows up noise, nonlocal stabilization enhances intensity projected parallel images uniformly. Application to multichannel vessel enhancement is illustrated using both volunteer data and simulated multichannel angiograms. Robustness of the filter applied to volunteer datasets is shown using statistically validated improvement in flow quantification. Improved performance in terms of preserving vascular structures and phased array reconstruction in both simulated and real data is demonstrated using structureness measure and contrast ratio.

Alignment parameter calibration for IMU using the Taguchi method for image deblurring

Inertial measurement units (IMUs) utilized in smartphones can be used to detect camera motion during exposure, in order to improve image quality degraded with blur through long hand-held exposure. Based on the captured camera motion, blur in images can be removed when an appropriate deblurring filter is used. However, two research issues have not been addressed: (a) the calibration of alignment parameters for the IMU has not been addressed. When inappropriate alignment parameters are used for the IMU, the camera motion would not be captured accurately and the deblurring effectiveness can be downgraded. (b) Also selection of an appropriate deblurring filter correlated with the image quality has still not been addressed. Without the use of an appropriate deblurring filter, the image quality could not be optimal. This paper proposes a systematic method, namely the Taguchi method, which is a robust and systematic approach for designing reliable and high-precision devices, in order to perform the alignment parameter calibration for the IMU and filter selection. The Taguchi method conducts a small number of systematic experiments based on orthogonal arrays. It studies the impact of the alignment parameters and appropriate deblurring filter, which attempts to perform an effective deblurring. Several widely adopted image quality metrics are used to evaluate the deblurred images generated by the proposed Taguchi method. Experimental results show that the quality of deblurred images achieved by the proposed Taguchi method is better than those obtained by deblurring methods which are not involved with the alignment parameter calibration and filter selection. Also, much less computational effort is required by the Taguchi method when comparing with the commonly used optimization methods for determining alignment parameters and deblurring filter.

Integration of image de-blurring in an aerial Mono-SLAM

In this article, we discuss the possibility of integrating image de-blurring techniques in an aerial simultaneous localization and mapping by a single camera (monocular simultaneous localization and mapping (Mono-SLAM)). We use an integrated aerial virtual environment together with a six-degree-of-freedom aircraft flight simulator to show the effectiveness of the approach to generate three-dimensional flight trajectories via integration of image de-blurring in the associated loop of the Mono-SLAM. The objective is to increase the overall performance of a flying mission over an unknown area by means of a vision-only method. The integrated aerial virtual environment produces and collects real-time pictures from a nadir-looking vision sensor mounted on the vehicle. Our MATLAB GUI-based toolbox helps user to investigate an offline Mono-SLAM with a predefined de-blurring method integrated with an estimator which extracts navigational parameters. The system efficient architecture allows effective virtual experiments in a completely unknown environment, without using preloaded maps or predefined features. Simulation outcomes demonstrate the feasibility of navigation of aerial robots in inaccessible environments. Different case studies support the conclusion; nonetheless, we observe a number of nonlinearities from de-blurring filters even for a general aviation aircraft.

Application of digital tomosynthesis (DTS) of optimal deblurring filters for dental X-ray imaging

Digital tomosynthesis (DTS) is a limited-angle tomographic technique that provides some of the tomographic benefits of computed tomography (CT) but at reduced dose and cost. Thus, the potential for application of DTS to dental X-ray imaging seems promising. As a continuation of our dental radiography R&D, we developed an effective DTS reconstruction algorithm and implemented it in conjunction with a commercial dental CT system for potential use in dental implant placement. The reconstruction algorithm employed a backprojection filtering (BPF) method based upon optimal deblurring filters to suppress effectively both the blur artifacts originating from the out-focus planes and the high-frequency noise. To verify the usefulness of the reconstruction algorithm, we performed systematic simulation works and evaluated the image characteristics. We also performed experimental works in which DTS images of enhanced anatomical resolution were successfully obtained by using the algorithm and were promising to our ongoing applications to dental X-ray imaging. In this paper, our approach to the development of the DTS reconstruction algorithm and the results are described in detail.

스트랩다운 적외선 영상센서를 위한 관성센서 기반 강인최소자승 움직임 훼손영상 복원 기법

This paper proposes a new robust motion deblurring filter using the inertial sensor measurements for strapdown image IR applications. With taking the PSF measurement error into account, the motion blurred image is modeled by the linear uncertain state space equation with the noise corrupted measurement matrix and the stochastic parameter uncertainty. This motivates us to solve the motion deblurring problem based on the recently developed robust least squares estimation theory. In order to suppress the ringing effect on the deblurred image, the robust least squares estimator is slightly modified by adoping the ridge-regression concept. Through the computer simulations using the actual IR scenes, it is demonstrated that the proposed algorithm shows superior and reliable motion deblurring performance even in the presence of time-varying motion artifact.

관성센서를 이용한 스트랩다운 탐색기 훼손영상 복원기법

본 논문에서는 스트랩다운 영상탐색기 개발을 위해 각속도계 정보를 이용한 실용적인 움직임 훼손영상 복원 필터링 기법을 제안한다. 각속도계 편향오차가 움직임 훼손을 기술하기 위한 점확산 함수 파라미터의 불확실성으로 작용한다는 점에 착안하여, 이를 놈 제한조건을 만족하는 파라미터 불확실성으로 가정한 후 움직임 훼손 영상을 불확정 선형 상태 공간 방정식으로 모델링한다. 각속도계 편향오차에 의한 파라미터 불확실성 행렬이 놈 제한 조건을 만족한다는 가정 하에, 순환 선형 강인 칼만필터에 기반한 움직임 훼손영상 복원필터가 설계된다. 실제 IR 영상을 이용하여 제안된 영상훼손 복원 필터가 각속도계 편향 오차가 존재하는 상황에서도 신뢰할만한 영상복원 성능을 제공함을 확인한다. This paper proposes a practical linear recursive robust motion deblurring filter using the inertial sensor measurements for strapdown image seekers. The angular rate information obtained from the gyro mounted on the missile is used to define the PSF(point spread function). Since the gyro output contains a unknown but bounded bias error. the motion blur image model can be expressed as the linear uncertain system. In consequence, the motion deblurring problem can be cast into the robust Kalman filtering which provides reliable state estimates even in the presence of the parametric uncertainty due to the gyro bias. Through the computer simulations using the actual IR scenes, it is verified that the proposed algorithm guarantees the robust motion deblurring performance.

Least-squares migration of multisource data with a deblurring filter

Least-squares migration (LSM) has been shown to be able to produce high-quality migration images, but its computational cost is considered to be too high for practical imaging. We have developed a multisource least-squares migration algorithm (MLSM) to increase the computational efficiency by using the blended sources processing technique. To expedite convergence, a multisource deblurring filter is used as a preconditioner to reduce the data residual. This MLSM algorithm is applicable with Kirchhoff migration, wave-equation migration, or reverse time migration, and the gain in computational efficiency depends on the choice of migration method. Numerical results with Kirchhoff LSM on the 2D SEG/EAGE salt model show that an accurate image is obtained by migrating a supergather of 320 phase-encoded shots. When the encoding functions are the same for every iteration, the input/output cost of MLSM is reduced by 320 times. Empirical results show that the crosstalk noise introduced by blended sources is more effectively reduced when the encoding functions are changed at every iteration. The analysis of signal-to-noise ratio (S/N) suggests that not too many iterations are needed to enhance the S/N to an acceptable level. Therefore, when implemented with wave-equation migration or reverse time migration methods, the MLSM algorithm can be more efficient than the conventional migration method.

Fast least-squares migration with a deblurring filter

Least-squares migration (LSM) is a linearized waveform inversion for estimating a subsurface reflectivity model that, relative to conventional migration, improves spatial resolution of migration images. The cost, however, is high because LSM typically requires 10 or more iterations, which is at least 20 times more than the CPU cost of conventional migration. To alleviate this expense, we offer a deblurring filter that can be used in a regularization scheme or a preconditioning scheme to give acceptable LSM images with less than one-third the cost of the standard LSM method. Our results in applying deblurred LSM to synthetic data and field data support this claim. In particular, a Marmousi2 model test shows that the data residual for preconditioned deblurred LSM decreases rapidly in the first iteration, which is equivalent to 10 or more iterations of LSM. Empirical results suggest that regularized deblurred LSM after three iterations is equivalent to about 10 iterations of LSM. Applying deblurred LSM to 2D marine data gives a higher-resolution image compared to those from migration or LSM with three iterations. These results suggest that LSM combined with a deblurring filter allows LSM to be a fast, practical tool for improved imaging of complicated structures.

Motion adaptive deblurring filter for LCD

Motion blurring on liquid crystal display (LCD) was modeled by the original image convoluted with a point spread function (PSF). An intensity independent PSF was first deduced by statistical approximation. Based on the PSF, a motion adaptive deblurring filter was proposed to restore the original image. The simulation of motion blurred and deblurred natural images were presented. The results indicate that the proposed deblurring filter can significantly reduce the visible blurring artifact on LCD, which has a simple one-dimensional structure and can be integrated into other video processing algorithms, e.g. frame rate doubling, to further improve the image quality.

Edge-Detected Guided Morphological Filter for Image Sharpening

A new edge-guided morphological filter is proposed to sharpen digital images. This is done by detecting the positions of the edges and then applying a class of morphological filtering. Motivated by the success of threshold decomposition, gradient-based operators are used to detect the locations of the edges. A morphological filter is used to sharpen these detected edges. Experimental results demonstrate that the performance of these detected edge deblurring filters is superior to that of other sharpener-type filters.