Seismic impedance inversion plays a crucial role in obtaining underground physical properties and enhancing seismic exploration accuracy. In recent years, semi-supervised methods have significantly improved the efficiency and precision of impedance inversion. However, methods based on convolutional neural networks (CNNs) often struggle to effectively capture long-term dependencies in data, which can negatively impact the results of seismic acoustic impedance inversion for tasks with long-term characteristics. Therefore, this letter proposes a semi-supervised learning acoustic impedance inversion network that integrates the advanced deep learning techniques, including Kolmogorov-Arnold networks (KANs) and convolutional KAN. Through experimental comparisons of acoustic impedance fitting results, we demonstrate that KAN and convolutional KAN exhibit stronger fitting capabilities for long-term acoustic impedance data than traditional linear layers and CNN. This provides a novel method and strategy for establishing the mapping relationship between seismic data and wave impedance. Additionally, testing on the Marmousi2 model shows that the network incorporating these new deep learning methods improves the lateral continuity of the inversion profile and enhances the prediction accuracy in impedance inversion.

Estimating the subsurface impedance properties is an essential process in seismic exploration and reservoir characterization. The accuracy and efficiency of impedance inversion have been greatly improved by semi-supervised methods. However, existing semi-supervised inversion methods treat poststack seismic traces as independent sequential time series, which causes accumulated prediction errors along the time axis and horizontally noncontinuous seismic events. We propose a semi-supervised impedance inversion network. The new contribution includes two perspectives: 1) an attention mechanism is utilized to derive data-adaptive weights from both the time and positional axes, which largely reduces the artifacts in conventional semi-supervised impedance inversions and 2) a super-resolution module is implemented to reconcile the dimensional inconsistency between seismic data and the resultant impedance profile. By testing on the Marmousi2 model, the SEG advanced modeling (SEAM), as well as the field data, we show that the newly added modules can largely reduce the artifacts and improve the prediction accuracy for acoustic impedance.

By using multicomponent and multiwave seismic data, elastic reverse time migration (ERTM) can produce accurate PP and PS images for complex structures. One key of ERTM is to decompose the source- and receiver-side wavefields into pure P- and S-waves with correct amplitudes and phases. Conventional wavefield decomposition methods require to solve either a Poisson’s equation or an additional P-wave equation, increasing the computational cost. To mitigate this issue, we present a novel framework of physical constrained neural network (PCNN) to efficiently implement P- and S-wave separation. The new network includes both fully connected and convolutional blocks for data fitting and takes into account the properties of curl-free P-wave and divergence-free S-wave as a physical constraint. After the training, the proposed PCNN can accurately decompose elastic wavefield and produce pure P- and S-waves with correct phases, amplitudes and physical unit. We then apply the PCNN-based method to multicomponent reverse-time migration, in which a modified dot-product imaging condition is used to calculate PP and PS images. Numerical experiments demonstrate that the proposed PCNN-based workflow can produce accurate PP and PS images while improving the computational efficiency by three orders of magnitude compared to traditional Helmholtz-based decomposition methods.

Seismic noise suppression is an important preprocessing stage for obtaining high-quality seismic signals, which are crucial for seismic exploration. Deep learning methods have achieved excellent results in the field of seismic signal processing. Currently, many researchers have used convolutional neural networks for seismic signal denoising, but few have used Transformer model for related research. We apply the swin transformer model, an improved version of transformer model based on the self-attention mechanism, to denoise two-dimensional seismic data. The swin transformer calculates self-attention within shifted windows, effectively improving information exchange within the different windows. It performs well in suppressing random seismic noise to improve the signal-to-noise ratio.

In seismic exploration, collected traces inevitably appear noise and irregular sampled along the spatial coordinates, which affects seismic inversion and imaging. Seismic data interpolation is modelled by solving an inverse problem with regularization terms in mathematics. But sparse or low-rank priors in model-based methods cannot capture complex information from seismic data. A denoiser learned by convolution neural network (CNN) can be regarded as an implicit prior which helps improving the accuracy of model. For this motivation, we choose an unbiased DnCNN as a blind denoiser, and use a stochastic gradient algorithm to iteratively train the interpolated model, thus using the a priori information implied in the denoiser to interpolate the seismic data. We demonstrate the feasibility of the proposed method through synthetic and field data with comparative experiments, where it has excellent performance with handling interpolation and spatial aliasing.

Current machine learning methods make a positive difference to outlook on data assimilation. In this paper, an efficient assimilation of image sequences that incorporated in a deep neural networks (DNN) framework is put forward. To tackle the motion estimation of fluid, the image model characterizing both the evolution of the tracers and the velocity was considered. Owing to the ability of describing nonlinear physical processes, the output of DNN substitutes deterministic information from physical laws. It will be consistent with observed images by optimizing the network parameters rather than the variable itself. The dimension of the variable to be determined will reduce. The regularized DNN that accounts for the characteristics of the flows was employed to improve the ability of structure preservation. Realistic assimilation of tracers image sequence from the perspective of the oceanic applications shows that the proposed method is robust for extracting velocity field with vortex structures.

Full-waveform inversion (FWI) is an efficient technique for capturing the subsurface physical features by iteratively minimizing the misfit between simulated and observed seismograms. As such a problem is ill-posed, a significant ingredient for a satisfactory solution is to incorporate desirable priors. Most traditional regularized FWI approaches suffer from the non-adaptiveness and sensitivity of regularizers. Deep learning-assisted inversion methods can use pre-trained priors or parametric network priors as regularizers. We develop a novel FWI method based on a physics-constrained iterative algorithm with a learned regularization (FWIPLR). The introduced framework easily enables high-quality inversion by integrating two complementary terms: the physical constraints of the imaging system characterized by its forward model and a priori knowledge of the expected results characterized by a deep convolutional neural network (CNN) based regularizer. In particular, the advanced CNN denoiser, which corresponds to an implicit regularization term, is firstly trained with large-scale natural images and then fine-tuned with small-scale geological images. Such a transfer learning strategy seems appealing as it makes FWIPLR more generic to distinct geological models. To stabilize the optimization, we employ the spectral normalization instead of batch normalization to impose Lipschitz constraint on the networks. We validate the method effectiveness on Marmousi, Overthrust, and 2004 BP models. The comparable results illustrate the ability of FWIPLR for producing high-resolution subsurface structures compared with total variation regularized FWI, conventional denoiser and other CNN denoiser regularized FWI, in particular, when the initial model is inaccurate, data lose low-frequency information or model contains high-contrast media.

Full-waveform inversion (FWI) is a powerful technique for building high-quality subsurface geological structures. It is known to suffer from local minima problems when a good starting model is lost. To obtain a desirable solution, regularization constraints are needed to impose suitable priors, in particular for salt models. Recent studies have allowed cooperating the denoising operator as a specific prior with optimization algorithms to effectively solve various image reconstruction tasks. Inspired by the promising performance of regularization by denoising (RED), we propose a flexible unsupervised learning FWI framework, in which the regularizer is an extensive variant of RED powered by learned gradient for addressing salt models’ inversion. To further mitigate local minima issues, the Wasserstein distance induced by the optimal transport (OT) theory with a new preprocessing transformation is applied as a measure in data domain. Integrating the physical constraints featured by the wave equation and the model priors featured by the deep convolutional neural network (CNN), our method is able to produce measurement consistent and high-resolution results. We experimentally compare the proposed method with the traditional total variation regularized FWI and RED regularized FWI on the well-known geological models. The numerical results demonstrate the effectiveness of our method for handling the inversion task of high-contrast media in the presence of a free-surface case. Moreover, our framework is adaptive to restrict the solutions by leveraging the regularizer with learned gradient, whose training does not need any geological images, thus paving the way to develop FWI algorithms with state-of-the-art deep learning (DL) techniques in interdisciplinary research.

First arrival enhancement can improve the picking accuracy. Traditional seismic interferometry is based on the correlation calculation of multiple iterations to enhance the first arrival. Besides being sensitive to nonuniform Gaussian noise, the correlated and iterative operations causing seismic wavelet deformation with positive sidelobes are the main problems. While the fourth-order cumulant (CUM4) has been introduced into interferometry methods to suppress the coherent Gaussian noise, seismic wavelet deformation still exists. We propose to use the third-order cumulant (CUM3) diagonal slice to extract precise time delay information between different seismic traces. This modification effectively reduces the energy of the positive sidelobes caused by the correlation calculation. To reduce iteration times, we calculate both forward and reverse time delays between each trace and other traces, rather than selecting a single reference trace. This optimization increases the stacking number between receiver points. Experimental results on simulated data not only demonstrate the effective suppression of positive sidelobes, but also show the improvement in the signal-to-noise ratio (SNR). Applications to field data also obtain the first arrival information with high resolution. Moreover, we extend the application of the CUM3 diagonal slice to the extrapolated super-virtual interference (ESVRI) method and also obtain competitive results.

Multidimensional prestack seismic data reconstruction can be viewed as a low-rank tensor completion problem. Recently, the nuclear norm has been widely used as a convex surrogate of the tensor rank function for low-rank tensor recovery and has been successfully applied to 5-D seismic data reconstruction. However, solving the nuclear norm-based relaxed convex problem typically leads to a suboptimal solution of the original rank minimization problem, often degrading the reconstruction performance. In this study, to seek solutions to the aforementioned problems, we established a nonconvex logDet function as a smooth approximation for the tensor rank instead of the convex tensor nuclear norm and applied it to solve the 5-D seismic data reconstruction problem. Thereafter, we propose solving the obtained nonconvex relaxation problem using an alternating direction method of multipliers (ADMMs) algorithm. Numerical experiments of our approach on synthetic 5-D seismic data demonstrated remarkable reconstruction performance compared with the performances of higher-order singular value decomposition (HOSVD), nuclear norm, and parallel matrix factorization (PMF) methods in terms of visual examination and numerical test. We further illustrate the performance of the proposed method using a land data survey.

Full waveform inversion (FWI) has been implemented using deep learning techniques as an analogue recurrent neural network for geophysics. However, the cycle-skipping issue, from which the conventional FWI suffers, troubles the deeplearning aided FWI as well if the least-square loss function is used to measure the misfit between observed and synthetic data. We propose to use a Wasserstein distance loss function combined with a newly designed preprocessing transform, named integration affine scaling, for the inversion. This transform transfers the seismograms into probability densities, and significantly improves the inversion results. Numerical results show that the proposed method outperforms its counterparts in mitigating cycle-skipping, in comparison with other loss functions including the least-square, the absolute, and the quadratic Wasserstein distance losses.

Random noise attenuation is an important step in seismic data processing. Unfortunately, most conventional denoising methods heavily rely on specific prior knowledge and fine-tuning of the parameters. Therefore, they often fail to suppress random noise. Recent works based on supervised learning techniques for seismic noise suppression show outstanding performance. However, this paradigm needs large-scale labeled training datasets that are not available for seismic field data. Inspired by the self-supervised learning, we propose a promising unsupervised learning scheme that aims at suppressing the random noise with only a noisy shot gather. The method is based on a specific$\mathcal {J}$-invariant function and an assumption that the noise is statistical independent while the useful signal exhibits some correlation. To further improve the denoising quality, we integrate the transfer learning strategy. We experimentally demonstrate that the proposed framework faithfully recovers the denoised data on both prestack and poststack synthetic and field data although the pretrained network is trained with the prestack synthetic dataset. The preliminary comparisons with traditional and learning-based approaches indicate the effectiveness and robustness as well.

In this work, we propose a structure sparsity regularization strategy in the framework of 4-D variational data assimilation (4-D Var). In meteorology and oceanography, the number of unknown model variables is far fewer than that of image observations, often leading to solve an underdetermined nonlinear inverse problem. In recent years, the$\ell ^{1}$-norm-based sparsity regularization approach has attracted great attention in the field of 4-D Var because of its data structure preservation and noise suppression. To avoid little underlying physical priors considered, we introduce a widely used dictionary learning (DL) method to adaptively derive an efficient sparse approximation via learning a basis from a given dataset. For our target application of estimating sea surface flows, we consider a DL sparsity constraint on the variable of flow vorticity due to its rich spatial variation related to flows evolution. A novel anisotropic regularization method combined with fluid dynamics characteristics could overcome magnitude underestimation and staircase artifacts appearing in the gradient regularization-based 4-D Var method. The split Bregman iteration with fast convergence property is employed to solve the$\ell ^{1}+\ell ^{2}$nonsmooth minimization problem. The promising fluid flows estimation performance in real test cases (assimilation of image sequences collected from CORIOLIS experimental turntable) demonstrates the efficiency of our approach.

Noise present in real gravity data can lead to inaccurate inversion results. Multi-task strategy in deep learning provides a promising method to solve this problem. In this study, a multi-task framework is proposed for simultaneous inversion and denoising of noisy gravity data, in which the denoising task can constrain the inversion task. To extract multi-scale field information for high precision inversion, a novel backbone network, known as the cross-dimensional UNet (CDUNet), is proposed. CDUNet employs cross-dimensional skip-connections to transfer different scale field features, wherein transformation modules are used to convert two dimensional (2D) features extracted from gravity data to 3D features for density model reconstruction. A noisy dataset was synthesized to train the network, which comprised diverse density models having highly random geometric and physical characteristics. The test set evaluations showed that CDUNet and the multi-task framework could integrate well and the inversion accuracy of the network could reach 70.8% over the density perturbation area and 97% over the entire area. The synthetic examples showed that the inverted models characterized by distinct boundaries and relatively accurate values. Finally, the method was validated using real data from the Vinton salt dome in Texas and Louisiana, USA.

Quantitative phase imaging (QPI) is an emerging label-free technique that produces images containing morphological and dynamical information without contrast agents. Unfortunately, the phase is wrapped in most imaging system. Phase unwrapping is the computational process that recovers a more informative image. It is particularly challenging with thick and complex samples such as organoids. Recent works that rely on supervised training show that deep learning is a powerful method to unwrap the phase; however, supervised approaches require large and representative datasets which are difficult to obtain for complex biological samples. Inspired by the concept of deep image priors, we propose a deep-learning-based method that does not need any training set. Our framework relies on an untrained convolutional neural network to accurately unwrap the phase while ensuring the consistency of the measurements. We experimentally demonstrate that the proposed method faithfully recovers the phase of complex samples on both real and simulated data. Our work paves the way to reliable phase imaging of thick and complex samples with QPI.

The data-driven tight frame (DDTF) method is a dictionary learning method which has been used widely in the adaptive sparse representation and the seismic random noise attenuation. In the DDTF method, the thresholding operator setting plays a significant role on balancing the noise removal and preservation of detail information with high frequency. The hard thresholding operator is closely related to the noise variance; however, the noise variance is unknown and unstable which varies spatially. In this letter, we propose a spatially adaptive DDTF (SA-DDTF) method to find an optimal thresholding parameter without knowing the noise variance. The thresholding is determined by the coherence between the dictionary and the reconstruction residual. Furthermore, the thresholding is chosen adaptively for each patch of the seismic data. In case of the synthetic seismic data denoising, we obtain the reconstructed seismic data with a higher signal-to-noise ratio value. Furthermore, compared with the existing random noise reduction methods, the SA-DDTF method performs much better on the amplitude preservation of weak signal when attenuating the blind random noise for field data.

We propose a novel method for robust estimation of multiple local dips in seismic data via signal decomposition. The decomposition is achieved by regularizing each separated component to have a single dip. The single-dip regularization is built based on the fact that piecewise constant dips indicate that local gradient vectors lie on the same directions. The method is formulated as an optimization problem, which is solved in the framework of a block coordinate descent method. The proposed method is robust to random noise and can be used to estimate multiple dips accurately. As the proposed method has clear physical meaning, it is easy to be applied for other tasks, such as random and coherent noise attenuation, signal separation, and so on. We test the feasibility of our method in estimating local dips with synthetic and field data and compare with the structural tensor method and the plane-wave destruction method. Results demonstrated that the proposed method can estimate multiple dips and is more robust to noise than the other two methods. Applications for random noise attenuation, coherent signals separation, and unconformity detection are also tested.

Sparse coding method has been used for seismic denoising, as the data can be sparsely represented by the sparse transform and dictionary learning (DL) methods. DL methods have attracted wide attention because the learned dictionary is adaptive. However, for seismic denoising, the dictionary learned from the noise data is a mix of atoms representing seismic data patterns and atoms representing noise patterns. To make the dictionary contain more atoms to represent seismic data, we consider adding to the dictionary the local and nonlocal similarities of the data via the structured graph and propose a new DL method, namely, the structured graph dictionary learning (SGDL). The atoms of dictionary learned by the SGDL are smooth, which implies smoothness of any signal represented over this dictionary. In addition, in the dictionary domain, we use the nonlocal model, namely, SSC-GSM that connects Gaussian scale mixture (GSM) with simultaneous sparse coding (SSC), to represent the seismic data. We apply the method to the synthetic data and two kinds of field data. Results show that our method can better remove strong noise and retain the seismic weak events also.

We have introduced a new decomposition method for seismic data, termed complex variational mode decomposition (VMD), and we have also designed a new filtering technique for random noise attenuation in seismic data by applying the VMD on constant-frequency slices in the frequency-offset (f -x) domain. The motivation behind this paper is to overcome the potential low performance of empirical mode decomposition (EMD) for energy preservation of the steeply dipping events when used for noise attenuation, and low resolution when used for signal decomposition. The VMD is proposed to decompose a signal into an ensemble of band-limited modes. For seismic data consisting of linear events, the constant-frequency slices of its f -x spectrum are exactly band-limited. The noise attenuation algorithm is summarized as follows. First, the Fourier transform is applied on the time axis of the 2-D seismic data. Next, the VMD is applied on each frequency slice of the f -x spectrum and the decomposed modes are combined to obtain the filtered frequency slice. Finally, an inverse Fourier transform is applied on the frequency axis of the f -x spectrum to obtain the denoised result. The resulting VMD-based noise attenuation method is equivalent to applying a Wiener filter on each decomposed mode, which is achieved during the decomposition progress. We also applied 2-D VMD on 3-D seismic data for denoising. Numerical results show that the proposed VMD-based method achieves a higher denoising quality than both the f -x deconvolution method and the EMD-based denoising method, especially for preserving the steep slopes.

In this paper, we present a novel method for assimilating geometric information from observed images. Image assimilation technology fully utilizes structural information from the dynamics of the images to retrieve the state of a system and thus to better predict its evolution. Level-set method describing the evolution of the geometry shapes of a given system is taken into account to include the dynamics of the images. This method takes advantage of Lagrangian information in an Eulerian numerical framework. In our numerical experiments, we apply this state-of-the-art technique to a pollutant transport problem, to calibrate the initial contours of pollutants and to identify diffusion coefficients of the model. It can be shown a potential approach for oil spills, because topological merging and breaking of oil slicks are well defined and easily performed by this proposed approach. Numerical results show that the proposed method is visibly efficient compared with the classical method based on the concentration map when the concentration measurements and the background fields are not well available.

SUMMARY In spite of numerous works studying file replication strategies on distributed systems, data management policies remain mostly handled by manual operators or very basic algorithms on production grids. Among other causes, this situation is due to the lack of models taking job reliability into account. In this paper, we study file replication using new metrics to evaluate the reliability of distributed storage configurations. A stateful storage availability model is introduced to cope with the inability of the stateless model to account for the commonsense intuition that limiting the number of storage hosts involved in the execution of an application improves reliability. We describe the job success probability and the brittleness entropy, a metric describing the uncertainty of the job failure rate associated to a storage configuration. Results, obtained on synthetic data and on traces extracted from the European Grid Infrastructure, show that the stateful model is more accurate than the stateless on real data, and that it can describe the consequences of limiting the number of storage hosts on application reliability. These findings open the door to the design of new file replication strategies taking storage availability into account. Copyright © 2014 John Wiley & Sons, Ltd.

Bandpass filtering is a common way to estimate ground-roll noise on land seismic data, because of the relatively low-frequency content of ground roll. However, there is usually a frequency overlap between ground roll and the desired seismic reflections that prevents bandpass filtering alone from effectively removing ground roll without also harming the desired reflections. We apply a bandpass filter with a relatively high upper bound to provide an initial imperfect separation of ground roll and reflection signal. We then apply a technique called “local orthogonalization” to improve the separation. The procedure is easily implemented, since it involves only bandpass filtering and a regularized division of the initial signal and noise estimates. We demonstrate the effectiveness of the method on an open-source set of field data.

We propose a new iterative reweighted algorithm with iterative support detection (referred to as RISD) to improve the decoding performance for compressed sensing (CS). The support detection from previous iterations can be interpreted as extracting “prior information” that allows for different reweighting strategies within and without the detected support. The proposed RISD method achieves better sparsity-measurement tradeoff than both classicalL1algorithms and iteratively reweighted algorithms.

In this paper, we apply compressed sensing (CS) to video compression. CS techniques exploit the observation that one needs much fewer random measurements than given by the Shannon-Nyquist sampling theory to recover an object if this object is compressible (i.e., sparse in the spatial domain or in a transform domain). In the CS framework, we can achieve sensing, compression, and denoising simultaneously. We propose a fast and simple online encoding by the application of pseudorandom downsampling of the 2-D fast Fourier transform to video frames. For offline decoding, we apply a modification of the recently proposed approximate message passing (AMP) algorithm. The AMP method has been derived using the statistical concept of “state evolution,” and it has been shown to considerably accelerate the convergence rate in special CS-decoding applications. We shall prove that the AMP method can be rewritten as a forward-backward splitting algorithm. This new representation enables us to give conditions that ensure convergence of the AMP method and to modify the algorithm in order to achieve higher robustness. The success of reconstruction methods for video decoding also essentially depends on the chosen transform, where sparsity of the video signals is assumed. We propose incorporating the 3-D dual-tree complex wavelet transform that possesses sufficiently good directional selectivity while being computationally less expensive and less redundant than other directional 3-D wavelet transforms.

In this paper, we first analyze impact of the distribution of sparse signals on reconstruction quality in compressive sensing through experimental results and heuristic analysis. We suggest that trinary/binary sparse signals are one of the most difficult signals to reconstruct in terms of error bounds. We then show that by incorporating linear or non-linear mapping prior to sensing, significant improvement in the recovery performance can be achieved.

Transform-based denoising methods are popularly used in image and signal processing, including seismic data processing. However, they often suffer from unwanted artifacts, e.g., nonsmooth edges and pesudo-Gibbs phenomena. A total variation (TV) minimization technique has the ability to suppress these artifacts, particularly in the vicinity of discontinuities. In this letter, we employ the almost optimal sparse transform for seismic data, i.e., curvelet transform, to represent and denoise seismic cubes, combining a projected TV technique as a postprocessing method, in order to reduce unwanted nonsmooth artifacts caused by the curvelet transform. We shrink seismic noise via retaining the significant curvelet coefficients, but for the small ones under a given threshold, we modify them by searching for the minimization of their TV values, instead of setting them to zeros, i.e., TV-combined curvelets with adjustment of small curvelet coefficients by TV minimization. We prove its validity in seismic denoising by comparing with existing methods, including curvelets, TV denoising, and TV-combined curvelets with adjustment of large curvelet coefficients by TV minimization. Numerical experiments show that seismic noise is effectively suppressed by the present technique and that nonsmooth artifacts caused by the curvelet transform are also reduced significantly.

We propose a compressive video sensing scheme based on user attention model (UAM) for real video sequences acquisition. In this work, for every group of consecutive video frames, we set the first frame as reference frame and build a UAM with visual rhythm analysis (VRA) to automatically determine region-of-interest (ROI) for non-reference frames. The determined ROI usually has significant movement and attracts more attention. Each frame of the video sequence is divided into non-overlapping blocks of 16 × 16 pixel size. Compressive video sampling is conducted in a block-by-block manner on each frame through a single operator and in a whole region manner on the ROIs through a different operator. Our video reconstruction algorithm involves alternating direction l1- norm minimization algorithm (ADM) for the frame difference of non-ROI blocks and minimum total-variance (TV) method for the ROIs. Experimental results showed that our method could significantly enhance the quality of reconstructed video and reduce the errors accumulated during the reconstruction.

Sparse representation of seismic data is a crucial step for seismic forward modeling and seismic processing such as coherent noise separation, imaging, and sparsity-promoting data recovery. In this letter, a new locally adaptive wavelet transform, called easy-path wavelet transform (EPWT), is applied for the sparse representation of seismic data. The EPWT is an adaptive geometric wavelet transform that works along a series of special pathways through the input data and exploits the local correlations of the data. The transform consists of two steps: reorganizing the data following the pathways according to the data values and then applying a 1-D wavelet transform along the pathways. This leads to a very sparse wavelet representation. In comparison to conventional wavelets, the EPWT concentrates most of the energy of signals at smooth scales and needs less significant wavelet coefficients to represent signals. Numerical experiments show that the new method is really superior over the conventional wavelets and curvelets in terms of sparse representation and compression of seismic data.

In this letter, we apply a new sampling theory named compressed sensing (CS) for aerospace remote sensing to reduce data acquisition and imaging cost. We can only record directly single or multiple pixels while need not the use of additional compression step to improve the problems of power consumption, data storage, and transmission, without degrading spatial resolution and quality of pictures. The CS remote sensing includes two steps: encoding imaging and decoding recovery. A noiselet-transform-based single-pixel imaging and a random Fourier-sampling-based multipixel imaging are alternatively used for encoding, and an iterative curvelet thresholding method is used for decoding. The new sensing mechanism shifts onboard imaging cost to offline decoding recovery. It would lead to new instruments with less storage space, less power consumption, and smaller size than currently used charged coupled device cameras, which would match effective needs particularly for probes sent very far away. Numerical experiments on potential applications for Chinese Chang'e-1 lunar probe are presented.

Recently, a new framework named compressed sensing (CS) for the simultaneous sampling and compression of signals has been applied for panoramic-view imaging in aerospace remote sensing. By CS, it is possible for us to take superresolution photographs using only one or a few pixels rather than a million pixels by conventional digital cameras. However, the most popular approach of satellite/airborne remote sensing is line-scan imaging instead of panoramic-view imaging. In this letter, we propose a single-pixel imaging system for line-scan onboard cameras by applying compressive-scanning matrices in a sensing step and a two-step iterative curvelet thresholding method in an offline decoding step, which converges faster than previous single-step iterative thresholding methods. Numerical experiments show good performance of the proposed method for remote sensing. Results indicate the need to design practical single-pixel remote sensing instruments involving less storage space, less power consumption, and smaller size than the currently used charged-coupled-device cameras.

When we take photos, we often get blurred pictures because of hand shake, motion, insufficient light, unsuited focal length, or other disturbances. Recently, a compressed-sensing (CS) theorem which provides a new sampling theory for data acquisition has been applied for medical and astronomic imaging. The CS makes it possible to take superresolution photos using only one or a few pixels, rather than million pixels, with a conventional digital camera. Here, we further consider a so-called CS deblurring problem: Can we still obtain clear pictures from highly incomplete measurements when blurring disturbances occur? A decoding algorithm based on Poisson singular integral and iterative curvelet thresholding is proposed to correct the deblurring problem with surprisingly incomplete measurements. It permits one to design robust and practical compressed-imaging instruments involving less imaging time, less storage space, less power consumption, smaller size, and cheaper than currently used charged coupled device cameras, which effectively match the needs, particularly for probes sent very far away. It essentially shifts the onboard imaging cost to an offline recovery computational cost. Potential applications in aerospace remote sensing of the Chinese Chang'e-1 lunar probe are presented.

Denoising is always a challenging problem in natural imaging and geophysical data processing. In this paper, we consider the denoising of texture images using a nonlinear reaction-diffusion equation and directional wavelet frames. In our model, a curvelet shrinkage is used for regularization of the diffusion process to preserve important features in the diffusion smoothing and a wave atom shrinkage is used as the reaction in order to preserve and enhance interesting oriented textures. We derive a digital reaction-diffusion filter that lives on graphs and show convergence of the corresponding iteration process. Experimental results and comparisons show very good performance of the proposed model for texture-preserving denoising.

In this paper, a diffusion-based curvelet shrinkage is proposed for discontinuity-preserving denoising using a combination of a new tight frame of curvelets with a nonlinear diffusion scheme. In order to suppress the pseudo-Gibbs and curvelet-like artifacts, the conventional shrinkage results are further processed by a projected total variation diffusion, in which only the insignificant curvelet coefficients or high-frequency part of the signal are changed by use of a constrained projection. Numerical experiments from piecewise-smooth to textured images show good performances of the proposed method to recover the shape of edges and important detailed components, in comparison to some existing methods.

Detection and target tracking have an application to many scientific problems. The approach developed in this paper is motivated by the applications of detection and tracking characteristic deformable structures in geophysical fluids. We develop an integrated detection and tracking method of geophysical fluids based on a discrete curvelet representation of the information characterizing the targets. Curvelets are in some sense geometric wavelets, allowing an optimal sparse representation of two-dimensional piecewise continuous objects with C2-singularities. The proposed approach first identifies a consistent vortex by a curvelet-based gradient-vector-flow snake and then establishes the motion correspondence of the snaxels between successive time frames by a constructed so-called semi-T or comp-T multiscale motion-estimation method based on the geometric wavelets. Furthermore, a combination of total-variation regularization and cycle-spinning techniques effectively removes false matches and improves significantly the estimation. Numerical experiments at each stage demonstrate the performance of the proposed tracking methodology for temporal oceanographic satellite image sequences corrupted by noise, with weak edges and submitted to large deformations, in comparison to conventional methods