Curvelet-based Method Research Articles

Iterative deblending using unsupervised learning with double-deep neural networks

Simultaneous source acquisition technology can greatly improve seismic acquisition efficiency. However, due to continuous shooting and serious crosstalk noise of the adjacent sources in seismic data, simultaneous source data cannot be directly used in conventional data processing procedures. Therefore, simultaneous source data need to be deblended to obtain the conventional shot record. Under densely sampled sources, we have developed a novel unsupervised deep learning (UDL) method based on the double-deep neural networks for iterative inversion deblending of simultaneous source data. Our UDL, which is mainly composed of the residual neural network (R-net) and the U-net neural network, has excellent nonlinear optimization ability. The total loss function design can optimize our UDL in the correct direction and avoid the problem of overfitting. By minimizing the total loss function, the R-net and U-net branches of the UDL can extract the coherent effective signals of all sources and suppress the crosstalk noise. The most prominent advantage of our UDL method is that it does not require label data, and the training data set does not contain raw unblended data, thus solving the problem of missing training data sets. The examples with two synthetic and one field data set are used to prove the effectiveness of iterative inversion deblending of simultaneous source data based on our UDL method when sources are within a small distance of each other. By comparing our UDL method with the traditional curvelet-based and contourlet-based methods, the superiority of our method in the quality of separation results is demonstrated.

Seismic data recovery using deep targeted denoising priors in an alternating optimization framework

The problem of recovering the complete seismic data from undersampled field-observed data is a long-term challenge. Many recent efforts to address this problem develop model-based recovery methods. However, current model-based methods cannot accurately capture inherent priors of seismic data to obtain optimal recovery results. For this issue, we have developed a novel model-based seismic data recovery method, which integrates a deep learning (DL)-based targeted denoiser into the seismic data recovery model and leverages the deep targeted denoising priors learned by this denoiser to implement high accuracy data recovery. Specifically, we first use operator-splitting technology to decouple the data-consistency term and prior constraint term in a seismic data recovery model, resulting in an alternating optimization scheme composed of a least-squares inversion subtask and a proximal minimization subtask. The DL-based targeted denoiser, a dual-channel deep denoising network (DcDDNet), is then plugged into the alternating optimization scheme as a modular component, according to the mathematical equivalence between the proximal operator and the targeted denoiser. This modular component replaces the formalized proximal minimization subtask and plays the role of an implicit prior in the recovery optimization problem. Finally, the least-squares inversion and deep denoising subtasks in the alternating optimization scheme are iteratively executed to achieve seismic data recovery. Due to the integration of the powerful DcDDNet, this method not only enjoys high flexibility and impressive generalization capability but also has high computational efficiency and excellent performance. Synthetic and field data with regular and irregular undersampling are used to evaluate the recovery capability of this method. The results demonstrate that, compared with the f- x adaptive interpolation and curvelet-based recovery methods, our method has advantages in visual and quality metrics. In addition, this method also is more practical in seismic applications because it works in the time-space domain and can handle spatial aliasing and spectral leakage.

Characterization of drilling-related noise and curvelet-based evaluation of seismic-interferometric reflections for imaging of iron-bearing formations in Pilbara, Western Australia

SUMMARY Here we analyse ambient noise (AN) data generated during drilling of exploration boreholes and recorded using a dense array deployed over one of the numerous shallow iron-ore mineralization targets in the Pilbara region (Western Australia). Drilling and drilling-related operations were reoccurring in a sequence as described by the drillers’ field notes, which created the rare opportunity to analyse AN data in time segments when only one type of technical process was predominantly active. Consequently, most of the recorded AN sources did not overlap in time and space. We extract the recordings in 15-min-long segments matching the time-span of single field-note entry and identify individually acting AN sources associated with specific field operations. The temporal variations of noise spectrograms and AN cross-correlations show dependency on the sequence of a few consecutive field operations and specific frequency–amplitude patterns associated with single field operations. These changes are directly reflected by the events visible in the retrieved virtual-source gathers (VSG), implying significant changes in noise temporal and spatial stationarity. Some VSGs represent the mixed contributions of surface and air waves. To remove the contributions of these arrivals to the reflection imaging, we visually inspect all data and select only field operations acting as stationary-phase sources specifically for the reflection retrieval. This was done for different receiver configurations inside PilbArray, and as a result, we obtain a collection of VSGs containing coherent body-wave reflections. Database of visually inspected VSGs is used to develop and benchmark a semi-automatic curvelet-based method for accurate parametrization of the reflection events retrieved from passive data and to compare the imaging quality of the different field operations. Common-midpoint stacks from manually and automatically selected VSGs show reflectivity consistent with the one obtained from the active-source data and related to the structure hosting shallow iron mineralization. Our results demonstrate the capacity of AN seismic interferometry to retrieve body-wave reflections and image shallow mineralization. They also provide an intermediate step toward automating the passive reflection imaging with similar data sets.

Adaptive Multiple Subtraction Based on an Accelerating Iterative Curvelet Thresholding Method.

In the seismic exploration, recorded data contain primaries and multiples, where primaries, as signals of interest, can be used to image the subsurface geology. Surface-related multiple elimination (SRME), one important class of multiple attenuation algorithms, operates in two stages, multiple prediction and subtraction. Due to the phase and amplitude errors in the predicted multiples, adaptive multiple subtraction (AMS) is the key step of SRME. The main challenge of this technique resides in removing multiples without distorting primaries. The curvelet-based AMS methods, which exploit the sparsity of primary and multiple in curvelet domain and the misfit between the original and estimated signals in data domain, have shown outstanding performances in real seismic data processing. These methods are realized by using the iterative curvelet thresholding (ICT), which has heavy computation burden since it includes two forward/inverse curvelet transform (CuT) pairs in each iteration. To ameliorate the computational cost, we propose an accelerating ICT method by exploiting the misfit between the original and estimated signals in curvelet domain directly. Since the proposed method only needs do one forward/inverse CuT pair, it is faster than the traditional ICT method. Considering that the error of the predicted multiple is frequency-dependent, we furthermore introduce the joint constraints within different frequency bands to stabilize and improve the multiple attenuation. Synthetic and field examples demonstrate that the proposed method outperforms the traditional ICT method. In addition, the proposed method has shown to be suitable for refining other AMS methods' results, yielding a SNR improvement of 0.5-2.8 dB.

An efficient wavelet and curvelet-based PET image denoising technique.

Positron emission tomography (PET) image denoising is a challenging task due to the presence of noise and low spatial resolution compared with other imaging techniques such as magnetic resonance imaging (MRI) and computed tomography (CT). PET image noise can hamper further processing and analysis, such as segmentation and disease screening. The wavelet transform-based techniques have often been proposed for PET image denoising to handle isotropic (smooth details) features. The curvelet transform-based PET image denoising techniques have the ability to handle multi-scale and multi-directional properties such as edges and curves (anisotropic features) as compared with wavelet transform-based denoising techniques. The wavelet denoising method is not optimal for anisotropic features, whereas the curvelet denoising method sometimes has difficulty in handling isotropic features. In order to handle the weaknesses of individual wavelet and curvelet-based methods, the present research proposes an efficient PET image denoising technique based on the combination of wavelet and curvelet transforms, along with a new adaptive threshold selection to threshold the wavelet coefficients in each subband (except last level low pass (LL) residual). The proposed threshold utilizes the advantages of adaptive threshold taken from BayesShrink along with the neighborhood window concept. The present method was tested on both simulated phantom and clinical PET datasets. Experimental results show that our method has achieved better results than the existing methods such as VisuShrink, BayesShrink, NeighShrink, ModineighShrink, curvelet, and an existing wavelet curvelet-based method with respect to different noise measurement metrics, such as mean squared error (MSE), signal-to-noise ratio (SNR), peak signal-to-noise ratio (PSNR), and image quality index (IQI). Furthermore, notable performance is achieved in the case of medical applications such as gray matter segmentation and precise tumor region identification. Graphical Abstract Block diagram of the proposed method. (a) Steps of the proposed denoising method and (b) image information generated by each step of (a).

High-precision seismic data reconstruction with multi-domain sparsity constraints based on curvelet and high-resolution Radon transforms

In recent years, the sparsity-promoting reconstruction method based on the compressed sensing theory has been rapidly developed and applied to seismic data reconstruction. Many achievements have been made toward providing high-quality reconstruction by using undersampled data. However, the problem of insufficient reconstruction in null traces still hinders us a lot in practical applications, especially for complex seismic data. Aiming to solve this problem, we made full use of the sparsity characteristics of seismic data in multiple sparse transform domains and jointly reconstructed seismic data to realize the complementary advantages of multiple sparse transforms; As such, we propose a high-precision seismic data recovery method with multi-domain sparsity constraints based on curvelet and high-resolution Radon transforms. Numerical examples by synthetic and real data showed that the new approach can achieve a better reconstruction result than the commonly used curvelet-based recovery method. Integrated with the curvelet transform to develop new recovery method, the high-resolution Radon transform has more advantages than the conventional Radon transform for overcoming the shortcomings associated with the insufficient reconstruction of high-amplitude events. At the same time, the method is also applicable for developing new reconstruction methods by combining other sparse transforms depending on the characteristics of seismic data. The reconstruction method with multi-domain sparsity constraints can easily be extended to three-dimensional situation.

A curvelet-based method to determine wave directions from nautical X-band radar images

A new method to determine wave directions from nautical X-band images is proposed. The signatures of ocean waves show obvious scale and directional characteristics in nautical X-band radar images. Curvelet transform (CT) possesses very high scale and directional sensitivities. Therefore, it has good capability to analyze ocean wave fields. The radar images are decomposed at different scales, in different directions, and at different positions by CT, and curvelet coefficients are obtained. Given to the scale and directional characteristics of surface waves, the information of ocean waves is centralized in the curvelet coefficients of certain directions and at certain scales. Therefore, the wave orientations can be determined. The 180 ambiguity is removed by calculating crosscorrelation coefficients (CCCs) between continuous collected images. The proposed method is verified by the dataset collected on the Northwest coast of the Zhangzi Island in the Yellow Sea of China from March to April 2009.

Breast cancer diagnosis in digitized mammograms using curvelet moments

Background: Feature extraction is a key issue in designing a computer aided diagnosis system. Recent researches on breast cancer diagnosis have reported the effectiveness of multiscale transforms (wavelets and curvelets) for mammogram analysis and have shown the superiority of curvelet transform. However, the curse of dimensionality problem arises when using the curvelet coefficients and therefore a reduction method is required to extract a reduced set of discriminative features.Methods: This paper deals with this problem and proposes a feature extraction method based on curvelet transform and moment theory for mammogram description. First, we performed discrete curvelet transform and we computed the four first-order moments from curvelet coefficients distribution. Hence, two feature sets can be obtained: moments from each band and moments from each level. In this work, both sets are studied. Then, the t-test ranking technique was applied to select the best features from each set. Finally, a k-nearest neighbor classifier was used to distinguish between normal and abnormal breast tissues and to classify tumors as malignant or benign. Experiments were performed on 252 mammograms from the Mammographic Image Analysis Society (mini-MIAS) database using the leave-one-out cross validation as well as on 11553 mammograms from the Digital Database for Screening Mammography (DDSM) database using 2×5-fold cross validation.Results: Experimental results prove the effectiveness and the superiority of curvelet moments for mammogram analysis. Indeed, results on the mini-MIAS database show that curvelet moments yield an accuracy of 91.27% (resp. 81.35 %) with 10 (resp. 8) features for abnormality (resp. malignancy) detection. In addition, empirical comparisons of the proposed method against state-of-the-art curvelet-based methods on the DDSM database show that the suggested method does not only lead to a more reduced feature set, but it also statistically outperforms all the compared methods in terms of accuracy.Conclusions: In summary, curvelet moments are an efficient and effective way to extract a reduced set of discriminative features for breast cancer diagnosis.

Analysis of effect of cycle spinning on wavelet- and curvelet-based denoising methods on brain CT images

The purpose of this paper is to carry out the assessment of effect of cycle spinning on wavelet- and curvelet-based noise reduction methods on brain CT images. In particular, multiscale curvelet- and wavelet-based denoising methods are evaluated with and without cycle spinning. This assessment is focused not only on the noise suppression but also on fine details preservation. The experimental results show that the cycle spinning-based curvelet method outperforms not only other curvelet-based methods but also the wavelet-based methods. The quality assessment parameters taken in this paper are signal-to-noise ratio (SNR), peak-signal-to-noise ratio (PSNR), universal quality index (UQI), structural similarity index metrics (SSIM), and edge keeping index (EKI).

Curvelet-based method for orientation estimation of particles from optical images

A method based on the curvelet transform is introduced to estimate the orientation distribution from two-dimensional images of small anisotropic particles. Orientation of fibers in paper is considered as a particular application of the method. Theoretical aspects of the suitability of this method are discussed and its efficiency is demonstrated with simulated and real images of fibrous systems. Comparison is made with two traditionally used methods of orientation analysis, and the new curvelet-based method is shown to perform better than these tradi- tional methods. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this

Curvelet-based registration of multi-component seismic waves

Abstract Registration of the travel time of PP waves and PS waves on the same coordinate is critical for joint interpretation in multi-component seismic exploration. In this paper, we propose a new curvelet-based registration method to improve the precision of registration, especially for the data with heavy random noises. By making registration in curvelet multiscale spaces from coarser to finer scale, the proposed method is not sensitive to initial values of velocity ratio of PP waves and PS waves. Applications of the new method to real seismic dataset from Shengli Oilfield, China show good registered results in terms of both qualitative and quantitative analysis, in comparison with a traditional registration method and a wavelet-based method.

Image deblurring using empirical Wiener filter in the curvelet domain and joint non-local means filter in the spatial domain

In this paper, an efficient image deblurring algorithm is proposed. This algorithm restores the blurred image by incorporating a curvelet-based empirical Wiener filter with a spatial-based joint non-local means filter. Curvelets provide a multidirectional and multiscale decomposition that has been mathematically shown to represent distributed discontinuities such as edges better than traditional wavelets. Our method restores the image in the frequency domain to obtain a noisy result with minimal loss of image components, followed by an empirical Wiener filter in the curvelet domain to attenuate the leaked noise. Although the curvelet-based methods are efficient in edge-preserving image denoising, they are prone to producing edge ringing which relates to the structure of the underlying curvelet. In order to reduce the ringing, we develop an efficient joint non-local means filter by using the curvelet deblurring result. This filter could suppress the leaked noise while preserving image details. We compare our deblurring algorithm with a few competitive deblurring techniques in terms of improvement in signal-to-noise-ratio (ISNR) and visual quality.

Comparative evaluation of denoising methods on brain CT images

The purpose of the paper is to carry out a comparative assessment of different denoising methods, namely, Wiener filter, Median filter, Anisotropic Diffusion (AD), Waveletbased method, Total Variation (TV) and Curvelet-based method, on brain CT images. The focus of this work is to compare these methods not only for the suppression of noise but also for the preservation of edges on brain CT images. The experimental results show that the curveletbased denoising method shows the best performance, followed by the Wiener filter in terms of perceptual quality, noise suppression and edge preservation. However, the curvelet-based denoising method generates visual distortion in the homogenous regions. TV method induces staircase effect and loss the fine details. The wavelet-based method yields better denoising, particularly in homogenous regions, but does not gives better results in edgy regions, while AD shows the maximum blurring effects.

Efficient Denoising Technique for CT images to Enhance Brain Hemorrhage Segmentation

This paper presents an adaptive denoising approach aiming to improve the visibility and detectability of hemorrhage from brain computed tomography (CT) images. The suggested approach fuses the images denoised by total variation (TV) method, denoised by curvelet-based method, and edge information extracted from the noise residue of TV method. The edge information is extracted from the noise residue of TV method by processing it through curvelet transform. The visual interpretation shows that the proposed approach not only reduces the staircase effect caused by total variation method but also reduces visual distortion induced by curvelet transform in the homogeneous areas of the CT images. The denoising abilities of the proposed method are further evaluated by segmenting the hemorrhagic brain area using region-growing method. The sensitivity, specificity, Jaccard index, and Dice coefficients were calculated for different noise levels. The comparative results show that the significant improvement has yielded in the brain hemorrhage detection from CT images after denoising it with the proposed approach.

Image denoising based on adaptive fusion of curvelet transform and Total Variation

This paper proposed an adaptive denoising approach, which fuses the images denoised by Total Variation (TV), curvelet-based method and edge information. Edge information is extracted from the noise residue of TV method by processing it through curvelet transform. The denoising abilities of the proposed method are evaluated on standard Lena image as well as on brain Computed Tomography (CT) images. Experimental results show that the proposed approach reduces the staircase effect caused by TV method and also reduces fuzzy edges induced by curvelet transform in the homogeneous areas of the image. This proposed adaptive fusion-based approach gives superior results not only for noise suppression but also for edge preservation.

Nonequispaced curvelet transform for seismic data reconstruction: A sparsity-promoting approach

We extend our earlier work on the nonequispaced fast discrete curvelet transform (NFDCT) and introduce a second generation of the transform. This new generation differs from the previous one by the approach taken to compute accurate curvelet coefficients from irregularly sampled data. The first generation relies on accurate Fourier coefficients obtained by an [Formula: see text]-regularized inversion of the nonequispaced fast Fourier transform (FFT) whereas the second is based on a direct [Formula: see text]-regularized inversion of the operator that links curvelet coefficients to irregular data. Also, by construction the second generation NFDCT is lossless unlike the first generation NFDCT. This property is particularly attractive for processing irregularly sampled seismic data in the curvelet domain and bringing them back to their irregular record-ing locations with high fidelity. Secondly, we combine the second generation NFDCT with the standard fast discrete curvelet transform (FDCT) to form a new curvelet-based method, coined nonequispaced curvelet reconstruction with sparsity-promoting inversion (NCRSI) for the regularization and interpolation of irregularly sampled data. We demonstrate that for a pure regularization problem the reconstruction is very accurate. The signal-to-reconstruction error ratio in our example is above [Formula: see text]. We also conduct combined interpolation and regularization experiments. The reconstructions for synthetic data are accurate, particularly when the recording locations are optimally jittered. The reconstruction in our real data example shows amplitudes along the main wavefronts smoothly varying with limited acquisition imprint.

Curvelet-based fingerprint anti-spoofing

Existing perspiration-based liveness detection algorithms need two successive images (captured in certain time interval), hence they are slow and not useful for real-time applications. Liveness detection methods using extra hardware increase the cost of the system. To alleviate these problems, we propose new curvelet-based method which needs only one fingerprint to detect liveness. Wavelets are very effective in representing objects with isolated point singularities, but fail to represent line and curve singularities. Curvelet transform allows representing singularities along curves in a more efficient way than the wavelets. Ridges oriented in different directions in a fingerprint image are curved; hence curvelets are very significant to characterize fingerprint texture. Textural measures based on curvelet energy and co-occurrence signatures are used to characterize fingerprint image. Dimensionalities of feature sets are reduced by running Pudil’s sequential forward floating selection (SFFS) algorithm. Curvelet energy and co-occurrence signatures are independently tested on three different classifiers: AdaBoost.M1, support vector machine and alternating decision tree. Finally, all the aforementioned classifiers are fused using the “Majority Voting Rule” to form an ensemble classifier. A fingerprint database consisting of 185 real, 90 Fun-Doh and 150 Gummy fingerprints is created by using varieties of artificial materials for casts and moulds of spoof fingerprints. Performance of the new liveness detection approach is found very promising, as it needs only one fingerprint and no extra hardware to detect vitality.

Remote sensing image fusion using the curvelet transform

This paper presents an image fusion method suitable for pan-sharpening of multispectral (MS) bands, based on nonseparable multiresolution analysis (MRA). The low-resolution MS bands are resampled to the fine scale of the panchromatic (Pan) image and sharpened by injecting highpass directional details extracted from the high-resolution Pan image by means of the curvelet transform (CT). CT is a nonseparable MRA, whose basis functions are directional edges with progressively increasing resolution. The advantage of CT with respect to conventional separable MRA, either decimated or not, is twofold. Firstly, directional detail coefficients matching image edges may be preliminarily soft-thresholded to achieve a noise reduction that is better than that obtained in the separable wavelet domain. Secondly, modeling of the relationships between high-resolution detail coefficients of the MS bands and of the Pan image is more fitting, being accomplished in the directional multiresolution domain. Experiments are carried out on very-high-resolution MS + Pan images acquired by the QuickBird and Ikonos satellite systems. Fusion simulations on spatially degraded data, whose original MS bands are available for reference, show that the proposed curvelet-based fusion method performs slightly better than the state-of-the art. Fusion tests at the full scale reveal that an accurate and reliable Pan-sharpening, little affected by local inaccuracies even in the presence of complex and detailed urban landscapes, is achieved by the proposed method.