Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Least‐squares migration has been shown to improve image quality compared to the conventional migration method, but its computational cost is often too high to be practical. In this paper, we develop two numerical schemes to implement least‐squares migration with the reverse time migration method and the blended source processing technique to increase computation efficiency. By iterative migration of supergathers, which consist in a sum of many phase‐encoded shots, the image quality is enhanced and the crosstalk noise associated with the encoded shots is reduced. Numerical tests on 2D HESS VTI data show that the multisource least‐squares reverse time migration (LSRTM) algorithm suppresses migration artefacts, balances the amplitudes, improves image resolution and reduces crosstalk noise associated with the blended shot gathers. For this example, the multisource LSRTM is about three times faster than the conventional RTM method. For the 3D example of the SEG/EAGE salt model, with a comparable computational cost, multisource LSRTM produces images with more accurate amplitudes, better spatial resolution and fewer migration artefacts compared to conventional RTM. The empirical results suggest that multisource LSRTM can produce more accurate reflectivity images than conventional RTM does with a similar or less computational cost. The caveat is that the LSRTM image is sensitive to large errors in the migration velocity model.

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Multi‐source least‐squares reverse time migration

Introduction to Inverse Problems in Imaging

Hyperspectral image (HSI) denoising is challenging not only because of the difficulty in preserving both spectral and spatial structures simultaneously, but also due to the requirement of removing various noises, which are often mixed together. In this paper, we present a nonconvex low rank matrix approximation (NonLRMA) model and the corresponding HSI denoising method by reformulating the approximation problem using nonconvex regularizer instead of the traditional nuclear norm, resulting in a tighter approximation of the original sparsity-regularised rank function. NonLRMA aims to decompose the degraded HSI, represented in the form of a matrix, into a low rank component and a sparse term with a more robust and less biased formulation. In addition, we develop an iterative algorithm based on the augmented Lagrangian multipliers method and derive the closed-form solution of the resulting subproblems benefiting from the special property of the nonconvex surrogate function. We prove that our iterative optimization converges easily. Extensive experiments on both simulated and real HSIs indicate that our approach can not only suppress noise in both severely and slightly noised bands but also preserve large-scale image structures and small-scale details well. Comparisons against state-of-the-art LRMA-based HSI denoising approaches show our superior performance.

Denoising of Hyperspectral Images Using Nonconvex Low Rank Matrix Approximation

Nowadays, a large amount of information has to be transmitted or processed. This implies high-power processing, large memory density, and increased energy consumption. In several applications, such as imaging, radar, speech recognition, and data acquisition, the signals involved can be considered sparse or compressive in some domain. The compressive sensing theory could be a proper candidate to deal with these constraints. It can be used to recover sparse or compressive signals with fewer measurements than the traditional methods. Two problems must be addressed by compressive sensing theory: design of the measurement matrix and development of an efficient sparse recovery algorithm. These algorithms are usually classified into three categories: convex relaxation, non-convex optimization techniques, and greedy algorithms. This paper intends to supply a comprehensive study and a state-of-the-art review of these algorithms to researchers who wish to develop and use them. Moreover, a wide range of compressive sensing theory applications is summarized and some open research challenges are presented.

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A Review of Sparse Recovery Algorithms

Introduction.- Regularization Theory and Recent Developments.- Nonstandard Regularization and Advanced Optimization Theory and Methods.- Numerical Inversion in Geoscience and Quantitative Remote Sensing.

Optimization and regularization for computational inverse problems and applications

The staggered-grid finite-difference (FD) method is widely used in numerical simulation of the wave equation. With stability conditions, grid dispersion often exists because of the discretization of the time and the spatial derivatives in thewave equation. Therefore, suppressing grid dispersion is a key problem for the staggered-grid FD schemes. To reduce the grid dispersion, the traditional method uses high-order staggered-grid schemes in the space domain. However, the wave is propagated in the time and space domain simultaneously. Therefore, some researchers proposed to derive staggered-grid FD schemes based on the time-space domain dispersion relationship. However, such methods were restricted to low frequencies and special angles of propagation. We have developed a regularizing technique to tackle the ill-conditioned property of the symmetric linear system and to stably provide approximate solutions of the FD coefficients for acoustic-wave equations. Dispersion analysis and seismic numerical simulations determined that the proposed method satisfies the dispersion relationship over a much wider range of frequencies and angles of propagation and can ensure FD coefficients being solved via a well-posed linear system and hence improve the forward modeling precision.

/pdf/seismic-modeling-by-optimizing-regularized-staggered-grid-hmmr31gjnx.pdf

Seismic modeling by optimizing regularized staggered-grid finite-difference operators using a time-space-domain dispersion-relationship-preserving method

SUMMARY

Due to the influence of variations in landform, geophysical data acquisition is usually subsampled. Reconstruction of the seismic wavefield from subsampled data is an ill-posed inverse problem. Compressive sensing (CS) can be used to recover the original geophysical data from the subsampled data. In this paper, we consider the wavefield reconstruction problem as a CS and propose a piecewise random subsampling scheme based on the wavelet transform. The proposed sampling scheme overcomes the disadvantages of uncontrolled random sampling. In computation, an l1-norm constrained trust region method is developed to solve the CS problem. Numerical results demonstrate that the proposed sampling technique and the trust region approach are robust in solving the ill-posed CS problem and can greatly improve the quality of wavefield recovery.

/pdf/recovery-of-seismic-wavefields-based-on-compressive-sensing-3acyuq73kt.pdf

Recovery of seismic wavefields based on compressive sensing by an l1‐norm constrained trust region method and the piecewise random subsampling

Seismic fault detection using an encoder–decoder convolutional neural network with a small training set

Restoration of seismic data as an ill-posed inverse problem means to recover the complete wavefields from sub-sampled data. Since seismic data are typically sparse in the curvelet domain, this problem can be solved based on the compressive sensing theory. Meanwhile three major problems are modelling, sampling and solving methods. We first construct l 0 and l 1 minimization models and then develop fast projected gradient methods to solve the restoration problem. For seismic data interpolation/restoration, the regular sub-sampled data will generate coherence aliasing in the frequency domain, while the random sub-sampling cannot control the largest sampling gap. Therefore, we consider a new sampling technique in this article which is based on the controlled piecewise random sub-sampling scheme. Numerical simulations are made and compared with the iterative soft thresholding method and the spectral gradient-projection method. It reveals that the proposed algorithms have the advantages of high precision, robus...

/pdf/a-review-on-restoration-of-seismic-wavefields-based-on-52h12hka5y.pdf

Changchun Yang

Papers

Optimization and regularization for computational inverse problems and applications

Seismic modeling by optimizing regularized staggered-grid finite-difference operators using a time-space-domain dispersion-relationship-preserving method

Recovery of seismic wavefields based on compressive sensing by an l1‐norm constrained trust region method and the piecewise random subsampling

Seismic fault detection using an encoder–decoder convolutional neural network with a small training set

A review on restoration of seismic wavefields based on regularization and compressive sensing