Adaptive Overcomplete Dictionary Learning-Based Sparsity-Promoting Regularization for Full-Waveform Inversion

The total variation (TV) regularization method has been used to solve the ill-posed inverse problem of electrical resistance tomography (ERT), owing to its good ability to preserve edges. However, the quality of the reconstructed images, especially in the flat region, is often degraded by noise. To optimize the regularization term and the regularization factor according to the spatial feature and to improve the resolution of reconstructed images, a spatially adaptive total variation (SATV) regularization method is proposed. A kind of effective spatial feature indicator named difference curvature is used to identify which region is a flat or edge region. According to different spatial features, the SATV regularization method can automatically adjust both the regularization term and regularization factor. At edge regions, the regularization term is approximate to the TV functional to preserve the edges; in flat regions, it is approximate to the first-order Tikhonov (FOT) functional to make the solution stable. Meanwhile, the adaptive regularization factor determined by the spatial feature is used to constrain the regularization strength of the SATV regularization method for different regions. Besides, a numerical scheme is adopted for the implementation of the second derivatives of difference curvature to improve the numerical stability. Several reconstruction image metrics are used to quantitatively evaluate the performance of the reconstructed results. Both simulation and experimental results indicate that, compared with the TV (mean relative error 0.288, mean correlation coefficient 0.627) and FOT (mean relative error 0.295, mean correlation coefficient 0.638) regularization methods, the proposed SATV (mean relative error 0.259, mean correlation coefficient 0.738) regularization method can endure a relatively high level of noise and improve the resolution of reconstructed images.

Full waveform inversion (FWI) is a technique used to estimate subsurface model parameters by minimizing the difference between observed and calculated seismic data. Sparsity-promoting regularization are useful tools for traditional FWI methods to tackle complex subsurface structures. Since the traditional regularization techniques can only impose some fixed priors, it is necessary to develop a regularization strategy to obtain more flexible priors. In this way, we develop a structural sparse representation method that exploits the non-local self-similarity prior of the model, which is achieved by grouping similar patches using graph matching operators and a dynamic group selection strategy. A group-based dictionary is trained with the aim of providing the best sparse representation of complex features and variations in the entire model perturbation. The dynamic selection strategy of the training method can balance computational efficiency and inversion accuracy by constantly updating and retaining groups during the processing. In addition, two loop algorithm framework is utilized to enhance the robustness and the efficiency of the proposed method. Numerical experiments are presented to demonstrate that the proposed method outperforms the total variation regularization method and the adaptive dictionary learning with non-local self-similarity in terms of robustness and resolution. This structural sparsity-promoting regularization is incorporated into the FWI problem through a two-loop algorithm framework, enhancing the robustness and efficiency of FWI results.

To solve the ill-posed problem in electrical impedance tomography (EIT) and overcome the blur effect made by conventional L2 Tikhonov regularization, a new two-step iterative regularization algorithm is applied for the process reconstruction of lung respiration. This algorithm is based on total variation (TV) regularization method, and uses a two-step iterative method with TV denoising operator, so that it can achieve double regularization effect. This algorithm has advantages in both resolution and robustness. Both simulation and experiment results are executed to prove the effectiveness of TV regularization method.

We introduce a total variation (TV) regularization model for synthetic aperture radar (SAR) image despeckling. A dual-formulation-based adaptive TV (ATV) regularization method is applied to solve the TV regularization. The parameter adaptation of the TV regularization is performed based on the noise level estimated via wavelets. The TV-regularization-based image restoration model has a good performance in preserving image sharpness and edges while removing noises, and it is therefore effective for edge preserve SAR image despeckling. Experiments have been carried out using optical images contaminated with artificial speckles first and then SAR images. A despeckling evaluation index (DEI) is designed to assess the effectiveness of edge preserve despeckling on SAR images, which is based on the ratio of the standard deviations of two neighborhood areas of different sizes of a pixel. Experimental results show that the proposed ATV method can effectively suppress SAR image speckles without compromising the edge sharpness of image features according to both subjective visual assessment of image quality and objective evaluation using DEI.

Total variation (TV) regularization method is a typical method to preserve the discontinuities structure in EIT. Isotropic TV and anisotropic TV are two well-known variants of TV. The main differences between them are that the latter tends to distort the reconstructed internal inhomogeneities along the coordinate axis. In this article, we adopt the alternating direction method of multipliers (ADMM) to overcome the non-differentiability of the anisotropic TV and verify the characteristics of anisotropic TV regularization by the tank experiments.

Application of hybrid regularization method for tomographic reconstruction of midlatitude ionospheric electron density

Sparse coding allows the representation of complex data as a linear combination of basis sparse vectors (alternatively called atoms or codewords), a collection of which constitutes a dictionary. Dictionary learning is a learning process aimed at finding a small number of optimal basis vectors for a more accurate representation of the original data. The existing dictionary learning methods do not address the inherent uncertainty of the input data in their learning processes. To compensate for the uncertainty, and to obtain a flexible and effective learning system, we introduce a new adaptive fuzzy dictionary learning (AFDL) method for image classification purposes. The new method iteratively alternates between sparse coding based on a given dictionary and an adaptive fuzzy dictionary learning approach to learn (improve) dictionary atoms. The adjustability of the dictionary and coefficients vectors, in this method, provide us a more accurate and straight representation of input data. AFDL was applied on magnetic resonance images from the cancer image archive datasets, for medical image classification of cancer tumors. Finally, the overall experimental results clearly show that our approach outperforms its rival techniques in terms of accuracy, sensitivity, and specificity. Convergence speed in the experimental results shows that AFDL can achieve its acceptable precision in a reasonable time.

High-amplitude noise could interfere with useful seismic signals, affecting our ability in processing and interpreting seismic data. Thus, attenuating seismic noise is an important task in seismic processing. Total variation (TV) has played an important role in many steps of seismic data processing but always neglected the seismic structural information. Directional TV (DTV), however, considers the structural direction of seismic events but tends to cause the staircasing effect on seismic records based on the first-order formulation. Here, we develop a high-order DTV (HDTV) method for seismic denoising. It considers the local structural direction of the seismic data and calculates the higher order derivatives of seismic images to avoid the staircasing effect. We design several synthetic models that are contaminated by various types of random noise to test the denoising ability. The denoising performance of our new method is compared with the first-order DTV, conventional high-order TV, and TV regularization methods from two aspects, i.e., the signal-to-noise ratio and the effective signal leakage degree. Then, the advantages of the proposed method are further validated via several field seismic data sets.

Summary Full-waveform inversion (FWI) is a technique which solves the ill-posed seismic inversion problem of fitting our model data to the measured ones from the field. FWI is capable of providing high-resolution estimates of the model, and of handling wave propagation of arbitrary complexity (visco-elastic, anisotropic); yet, it often fails to retrieve high-contrast geological structures, such as salt. One of the reasons for the FWI failure is that the updates at earlier iterations are too smooth to capture the sharp edges of the salt boundary. We compare several regularization approaches, which promote sharpness of the edges. Minimum gradient support (MGS) regularization focuses the inversion on blocky models, even more than the total variation (TV) does. However, both approaches try to invert undesirable high wavenumbers in the model too early for a model of complex structure. Therefore, we apply the Sobolev space norm as a regularizing term in order to maintain a balance between sharp and smooth updates in FWI. We demonstrate the application of these regularizations on a Marmousi model, enriched by a chunk of salt. The model turns out to be too complex in some parts to retrieve its full velocity distribution, yet the salt shape and contrast are retrieved.

A cascading l0 regularization reconstruction method in nonsubsampled contourlet domain for limited-angle CT

Classical full waveform inversion (FWI) is an unconstrained data fitting/parameter estimation problem where the exact solution of the wave equation is enforced in the objective function, leading to highly non-linear problem prone to cycle skipping. To extend the linear regime of FWI, the wavefield reconstruction inversion (WRI) computes wavefields with wave equation relaxation to foster data fidelity before estimating parameters by minimizing the source residuals the relaxation generated. This wave equation relaxation was first implemented with a penalty method, which requires a dynamic control of the penalty parameter. To overcome this issue, iteratively refined (IR)-WRI replaces the penalty method by the alternating direction method of multipliers (ADMM) in which the Lagrange multipliers provide additional leverages to control the solution accuracy. Furthermore, ADMM provides a suitable framework to equip IR-WRI with bound constraint and hybrid Tikhonov+total variation regularization (BTT). Here, we assess the robustness of BTT-regularized IRWRI against sparse long-offset stationary-recording acquisitions. We show how the blockiness and sparsity-promoting properties of the BTT regularization narrow the null space of the FWI resulting from incomplete illumination and mitigate aliasing artifacts when a few sources and receivers are deployed on regular or random grids.

ABSTRACTThis study newly demonstrates a compressed sensing (CS)-based reconstruction scheme for computed tomography (CT) with a translational trajectory. CT with a translational trajectory has many potential applications in the field of non-destructive testing (NDT) and medicine. For example, in the X-ray inspection of a large civil engineering structure, the movements of the source and detector are strictly limited, and a simple straight CT trajectory is preferable. This method could also be applied in X-ray inspection lines in factories and airports. In the medical field, this method would complement the tomosynthesis in mammography. When using a translational trajectory, the dispersion of the fan- or cone-beam creates projection data with the angular information of the sample object. However, the angular information inevitably becomes insufficient when using a translational trajectory, which degrades the reconstruction accuracy. In this case, CS is considered suitable for reconstruction because it has been successfully used for reconstructions from sparse-view and limited-angle data. For reconstruction from the translational trajectory projection, a new concept of directional difference (DD) regularization was proposed. An algorithm was developed based on the alternating direction method of multipliers (ADMM) algorithm to solve the regularization problem. Numerical reconstruction experiments from noisy projection data were conducted and the results were compared with those from other reconstruction methods. The convergence performance of the total variation (TV), DD, and mixed TV-DD regularization methods were examined. The proposed DD and TV-DD methods showed better performance than the TV only regularization. Reconstruction from Monte-Carlo simulated projection data was also demonstrated.

Regularization plays a crucial role in reliably utilizing imaging systems for scientific and medical investigations. It helps to stabilize the process of computationally undoing any degradation caused by physical limitations of the imaging process. In the past decades, total variation regularization played a dominant role in the literature. Two forms of total variation regularizations, namely the first-order and the second-order total variation (TV-1 and TV-2) have been widely used. TV-1 has a disadvantage: it reconstructs images in the form of piece-wise constants when the noise and/or under-sampling is severe, while TV-2 reconstructs natural-looking images under such scenarios. On the other hand, TV-1 can recover sharp jumps better than TV-2. Two forms of generalizations, namely Hessian-Schatten norm (HSN) regularization, and total generalized variation (TGV) regularization, have been proposed and have become significant developments in the area of regularization for imaging inverse problems owing to their performance. While the strength of TGV is that it can combine the advantages of TV-1 and TV-2, HSN has better structure-preserving property. Here, we develop a novel regularization for image recovery that combines the strengths of TGV and HSN. We achieve this by restricting the maximization space in the dual form of HSN in the same way that TGV is obtained from TV-2. We call the new regularization the generalized Hessian-Schatten norm regularization (GHSN). We develop a novel computational method for image reconstruction using the new form of regularization based on the well-known framework called the alternating direction method of multipliers (ADMM). We demonstrate the strength of the GHSN using some reconstruction examples.

Full Waveform Inversion (FWI) is an iterative inversion method whose purpose is to retrieve high-resolution models of subsurface physical parameters. Because FWI relies on the solution of a non-linear ill-posed inverse problem, uncertainty estimation is a crucial issue in practical applications, both in seismology and exploration seismic. While uncertainty assessment is a strongly desired feature for FWI, it remains a challenging problem. In this presentation, we investigate uncertainty estimation within the framework provided by ensemble data-assimilation strategies. We combine the Ensemble Transform Kalman Filter and FWI. We review the concepts underlying our ETKF-FWI method, discuss its limitations and appeals for uncertainty estimation, and illustrate it on a 2D multiparameter inversion of an exploration scale field dataset.

Multibeam imaging sonar provides detailed information that has proven crucial in various applications like cognitive robots, navigation, and inspection. However, because of hardware limitations of multibeam imaging sonar, the captured image with controlled frequency suffers from the dispersion and attenuation with respect to specified material. To integrate more information, a more accurate description about the same scene can be obtained via a technique known as image fusion. Currently, total variation regularization method provides an efficient way to achieve this task on gradient domain. In this paper, we propose a new problem formulation with l₁-total variation model for multibeam sonar image fusion. An alternative minimization method is proposed, which can integrate dual-frequency imaging sonar image into an enhanced one. To the authors’ best knowledge, this is the first study concerning multibeam sonar image fusion. Experimental results on a real world dataset illustrate the effectiveness and efficiency of the proposed algorithm.