The surface wave suppression using the second generation curvelet transform

In this paper,we develop a new and effective multiple scale and strongly directional method for identifying and suppressing ground roll based on the second generation curvelet transform.Making the best use of the curvelet transform＇s strong local directional characteristics,seismic frequency bands are transformed into scale data with and without noise.Since surface waves and primary reflected waves have less overlap in the curvelet domain,we can effectively identify and separate noise.Applying this method to prestack seismic data can successfully remove surface waves and,at the same time,protect the reflected events well,particularly in the low-frequency band.This indicates that the method described in this paper is an effective and amplitude-preserving method.

Estimating primaries by sparse inversion of the 3D Curvelet transform and the L1-norm constraint

In this paper, we built upon the estimating primaries by sparse inversion （EPSI） method. We use the 3D curvelet transform and modify the EPSI method to the sparse inversion of the biconvex optimization and Ll-norm regularization, and use alternating optimization to directly estimate the primary reflection coefficients and source wavelet. The 3D curvelet transform is used as a sparseness constraint when inverting the primary reflection coefficients, which results in avoiding the prediction subtraction process in the surface-related multiples elimination （SRME） method. The proposed method not only reduces the damage to the effective waves but also improves the elimination of multiples. It is also a wave equation- based method for elimination of surface multiple reflections, which effectively removes surface multiples under complex submarine conditions.

3D simultaneous seismic data reconstruction and noise suppression based on the curvelet transform

Seismic data contain random noise interference and are affected by irregular subsampling. Presently, most of the data reconstruction methods are carried out separately from noise suppression. Moreover, most data reconstruction methods are not ideal for noisy data. In this paper, we choose the multiscale and multidirectional 2D curvelet transform to perform simultaneous data reconstruction and noise suppression of 3D seismic data. We introduce the POCS algorithm, the exponentially decreasing square root threshold, and soft threshold operator to interpolate the data at each time slice. A weighing strategy was introduced to reduce the reconstructed data noise. A 3D simultaneous data reconstruction and noise suppression method based on the curvelet transform was proposed. When compared with data reconstruction followed by denoizing and the Fourier transform, the proposed method is more robust and effective. The proposed method has important implications for data acquisition in complex areas and reconstructing missing traces.

GPR data noise attenuation on the curvelet transform

Signal extraction is critical in GRP data processing and noise attenuation. When the target depth is shallow, its refl ection echo signal will overlap with the background noise, affecting the detection of arrival time and localization of the target. Thus, we propose a noise attenuation method based on the curvelet transform. First, the original signal is transformed into the curvelet domain, and then the curvelet coefficients of the background noise are extracted according to the distribution features that differ from the effective signal. In the curvelet domain, the coarse-scale curvelet atom is isotropic. Hence, a two-dimensional directional filter is designed to estimate the high-energy background noise in the coarsescale domain, and then, attenuate the background noise and highlight the effective signal. In this process, we also use a subscale threshold value of the curvelet domain to fi lter out random noise. Finally, we compare the proposed method with the average elimination and 2D continuous wavelet transform methods. The results show that the proposed method not only removes the background noise but also eliminates the coherent interference and random noise. The numerical simulation and the real data application suggest and verify the feasibility and effectiveness of the proposed method.

基于广义Curvelet变换和相空间特征聚类的VSP波场分离方法

垂直地震剖面(Vertical Seismic Profiling,VSP)蕴含大量的地层地质信息,是连接地震反射数据与测井资料之间的桥梁.VSP数据分辨率高,资料丰富,包括上行波、下行波、转换波等多种类型的波场,常被用于地层反射界面标定、介质衰减参数反演等.其中,如何有效地分离波场是将VSP资料应用于油气勘探的关键之一.广义Curvelet变换是一种具有多尺度、多角度的相空间变换,能够进行相空间域波场特性的提取.本文聚焦于VSP波场的上下行波分离问题,提出一种基于广义Curvelet变换和相空间特征聚类方法.首先,采用广义Curvelet变换对VSP波场进行特征提取,构造融入相空间角度信息的特征数据集;然后,利用K-means聚类算法在相空间对波场特征进行分类;最后,对分类结果进行反变换,完成VSP上下行波波场的自适应分离.为了验证方法的有效性,本文将所提出的方法用于合成数据和实际VSP数据的波场分离,并与常用的基于F-K变换的波场分离方法进行对比.处理结果表明,本文方法角度分辨率高、抗噪能力强,波场分离结果的保真保幅性好,这为后续的成像与地层的特征分析提供了重要基础资料.

基于Curvelet域的注意力机制卷积网络地震数据去噪

【目的】地震资料中的噪声严重影响着对地下地层信息的准确解释。基于地震资料中横向相关性较强的有效信号在Curvelet域分布在特定系数上,而随机噪声在Curvelet域通常会均匀分布于所有系数,可对信号进行更有效的分离。【方法】基于注意力机制卷积神经网络能够聚焦图像的重要特征,自适应提取关键信息的特点,提出一种基于Curvelet变换和注意力机制卷积神经网络(Curvelet-AU-Net)的地震数据噪声衰减方法。首先,将含噪声的地震数据通过Curvelet变换得到Curvelet变换系数,分析有效信号和噪声在Curvelet域的分布情况。其次,使用加入CBAM(Convolutional block attention module)注意力机制的U-Net网络,以含噪地震数据的Curvelet变换系数制作训练集作为输入数据,用无噪地震数据的Curvelet变换系数作为标签,通过比较实际输出与标签的损失函数值,并逐层反向传播梯度来更新网络参数,当损失函数值达到最小时,网络训练完成。最后,将测试数据输入训练好的网络模型中,再对网络输出数据进行Curvelet反变换即可得到地震数据去噪结果。【结果和结论】模拟数据与实际数据处理结果表明,与传统方法和普通卷积网络相比,该方法在不同噪声水平和尺度条件下对常见噪声(如随机噪声等)的衰减效果更优,获得的地震信号信噪比和保真度更高。由于该方法融合了Curvelet变换的稀疏表示优势和深度学习模型的自适应性,将为地震数据噪声衰减提供一种新的解决途径。

Ground roll attenuation based on an empirical curvelet transform

In the field of seismic exploration, ground roll seriously affects the deep effective reflections from subsurface deep structures. Traditional curvelet transform cannot provide an adaptive basis function to achieve a suboptimal denoised result. In this paper, we propose a method based on empirical curvelet transform （ECT） for ground roll attenuation. Unlike the traditional curvelet transform, this method not only decomposes seismic data into multiscale and multi-directional components, but also provides an adaptive filter bank according to frequency content of seismic data itself. So, ground roll can be separated by using this method. However, as the frequency of reflection and ground roll components are close, we apply singular value decomposition （SVD） in the curvelet domain to differentiate the ground roll and reflection better. Examples of synthetic and field seismic data reveal that the proposed method based ECT performs better than the traditional curvelet method in terms of the suppression of ground roll.

Digital Image Watermarking Algorithm Based on Fast Curvelet Transform

A digital image watermarking algorithm based on fast curvelet transform is proposed. Firstly, the carrier image is decomposed by fast curvelet transform, and, the watermarking image is scrambled by Arnold transform. Secondly, the binary watermarking image is embedded into the medium frequency coefficients according to the human visual characteristics and curvelet coefficients. Experiment results show that the proposed algorithm has good performance in both invisibility and security and also has good robustness against the noise, cropping, filtering, JPEG compression and other attacks.

Weak Seismic Signal Extraction Based on the Curvelet Transform

Seismic signal denoising is a key step in seismic data processing.Airgun signals are easy to be interfered with by noise when it travels a long distance due to the weak energy of active source signal of the airgun.Aiming to solve this problem,and considering that the conventional Curvelet transform threshold processing method does not use the seismic spectrum information,we independently process the Curvelet scale layer corresponding to valid data based on the characteristics of the Curvelet transform of multi-scale,multi-direction and capable of expressing the sparse seismic signals in order to fully excavate the information features.Combined with the Curvelet adaptive threshold denoising the algorithm,we apply the Curvelet transform to denoising seismic signals while retaining the weak information in the signal as much as possible.The simulation experiments show that the improved threshold denoising method based on Curvelet transform is superior to the frequency domain filtering,wavelet denoising and traditional Curvelet denoising method in detailed information extraction and signal denoising of low SNR signals.The calculation accuracy of the relative wave velocity variation of underground medium is improved.

Speckle suppression in synthetic aperture radar ocean internal solitary wave images with curvelet transform

This paper proposes a speckle-suppression method for ocean internal solitary wave（ISW） synthetic aperture radar（SAR） images by using the curvelet transform.The band-shaped signatures of ocean ISWs in SAR images show obvious scale and directional characteristics.The curvelet transform possesses a very high scale and directional sensitivity.Therefore,the curvelet transform is very efficient in analyzing wave signals in SAR images.A noisy ocean ISW SAR image can be decomposed at different scales,directions,and positions using the curvelet transform.The information of the ISWs is centralized in the curvelet coefficients of certain directions under certain scales,whereas the speckle noise is distributed in every scale and direction.By manipulating the curvelet coefficients,the signals of the ISWs can be extracted from the noisy SAR image.Finally,the speckle noise is suppressed and the ISW feature is enhanced by adding the signals of the ISWs back to the original SAR image.Experiments demonstrate the effectiveness of this method.

Curvelet Transform-Based Denoising Method for Doppler Frequency Extraction

A novel image denoising method based on curvelet transform is proposed in order to improve the performance of Doppler frequency extraction in low signal-noise-ratio (SNR) environment. The echo can be represented as a gray image with spectral intensity as its gray values by time-frequency transform. And the curvelet coefficients of the image are computed. Then an adaptive soft-threshold scheme based on dual-median operation is implemented in curvelet domain. After that, the image is reconstructed by inverse curvelet transform and the Doppler curve is extracted by a curve detection scheme. Experimental results show the proposed method can improve the detection of Doppler frequency in low SNR environment.

Junk band recovery for hyperspectral image based on curvelet transform

Under consideration that the profiles of bands at close wavelengths are quite similar and the curvelets are good at capturing profiles, a junk band recovery algorithm for hyperspectral data based on curvelet transform is proposed. Both the noisy bands and the noise-free bands are transformed via curvelet band by band. The high frequency coefficients in junk bands are replaced with linear interpolation of the high frequency coefficients in noise-flee bands, and the low frequency coefficients remain the same to keep the main spectral characteristics from being distorted. Jutak bands then are recovered after the inverse curvelet transform. The performance of this method is tested on the hyperspectral data cube obtained by airborne visible/infrared imaging spectrometer （AVIRIS）. The experimental results show that the proposed method is superior to the traditional denoising method BayesShrink and the art-of-state Curvelet Shrinkage in both roots of mean square error （RMSE） and peak-signal-to-noise ratio （PSNR） of recovered bands.

Curvelet Transform Based on Edge Preserving Filter for Retinal Blood Vessel Segmentation

Segmentation of vessel in retinal fundus images is a primary step for the clinical identification for specific eye diseases.Effective diagnosis of vascular pathologies from angiographic images is thus a vital aspect and generally depends on segmentation of vascular structure.Although various approaches for retinal vessel segmentation are extensively utilized,however,the responses are lower at vessel’s edges.The curvelet transform signifies edges better than wavelets,and hence convenient for multiscale edge enhancement.The bilateral filter is a nonlinear filter that is capable of providing effective smoothing while preserving strong edges.Fast bilateral filter is an advanced version of bilateral filter that regulates the contrast while preserving the edges.Therefore,in this paper a fusion algorithm is recommended by fusing fast bilateral filter that can effectively preserve the edge details and curvelet transform that has better capability to detect the edge direction feature and better investigation and tracking of significant characteristics of the image.Afterwards C mean thresholding is used for the extraction of vessel.The recommended fusion approach is assessed on DRIVE dataset.Experimental results illustrate that the fusion algorithm preserved the advantages of the both and provides better result.The results demonstrate that the recommended method outperforms the traditional approaches.

Super-Resolution Based on Curvelet Transform and Sparse Representation

Super-resolution techniques are used to reconstruct an image with a high resolution from one or more low-resolution image(s).In this paper,we proposed a single image super-resolution algorithm.It uses the nonlocal mean filter as a prior step to produce a denoised image.The proposed algorithm is based on curvelet transform.It converts the denoised image into low and high frequencies(sub-bands).Then we applied a multi-dimensional interpolation called Lancozos interpolation over both sub-bands.In parallel,we applied sparse representation with over complete dictionary for the denoised image.The proposed algorithm then combines the dictionary learning in the sparse representation and the interpolated sub-bands using inverse curvelet transform to have an image with a higher resolution.The experimental results of the proposed super-resolution algorithm show superior performance and obviously better-recovering images with enhanced edges.The comparison study shows that the proposed super-resolution algorithm outperforms the state-of-the-art.The mean absolute error is 0.021±0.008 and the structural similarity index measure is 0.89±0.08.

An Optimised Defensive Technique to Recognize Adversarial Iris Images Using Curvelet Transform

Deep Learning is one of the most popular computer science techniques,with applications in natural language processing,image processing,pattern iden-tification,and various otherfields.Despite the success of these deep learning algorithms in multiple scenarios,such as spam detection,malware detection,object detection and tracking,face recognition,and automatic driving,these algo-rithms and their associated training data are rather vulnerable to numerous security threats.These threats ultimately result in significant performance degradation.Moreover,the supervised based learning models are affected by manipulated data known as adversarial examples,which are images with a particular level of noise that is invisible to humans.Adversarial inputs are introduced to purposefully confuse a neural network,restricting its use in sensitive application areas such as bio-metrics applications.In this paper,an optimized defending approach is proposed to recognize the adversarial iris examples efficiently.The Curvelet Transform Denoising method is used in this defense strategy,which examines every sub-band of the adversarial images and reproduces the image that has been changed by the attacker.The salient iris features are retrieved from the reconstructed iris image by using a pretrained Convolutional Neural Network model(VGG 16)followed by Multiclass classification.The classification is performed by using Support Vector Machine(SVM)which uses Particle Swarm Optimization method(PSO-SVM).The proposed system is tested when classifying the adversarial iris images affected by various adversarial attacks such as FGSM,iGSM,and Deep-fool methods.An experimental result on benchmark iris dataset,namely IITD,produces excellent outcomes with the highest accuracy of 95.8%on average.

Medical Image Compression Using Wrapping Based Fast Discrete Curvelet Transform and Arithmetic Coding

Due to the development of CT (Computed Tomography), MRI (Magnetic Resonance Imaging), PET (Positron Emission Tomography), EBCT (Electron Beam Computed Tomography), SMRI (Stereotactic Magnetic Resonance Imaging), etc. has enhanced the distinguishing rate and scanning rate of the imaging equipments. The diagnosis and the process of getting useful information from the image are got by processing the medical images using the wavelet technique. Wavelet transform has increased the compression rate. Increasing the compression performance by minimizing the amount of image data in the medical images is a critical task. Crucial medical information like diagnosing diseases and their treatments is obtained by modern radiology techniques. Medical Imaging (MI) process is used to acquire that information. For lossy and lossless image compression, several techniques were developed. Image edges have limitations in capturing them if we make use of the extension of 1-D wavelet transform. This is because wavelet transform cannot effectively transform straight line discontinuities, as well geographic lines in natural images cannot be reconstructed in a proper manner if 1-D transform is used. Differently oriented image textures are coded well using Curvelet Transform. The Curvelet Transform is suitable for compressing medical images, which has more curvy portions. This paper describes a method for compression of various medical images using Fast Discrete Curvelet Transform based on wrapping technique. After transformation, the coefficients are quantized using vector quantization and coded using arithmetic encoding technique. The proposed method is tested on various medical images and the result demonstrates significant improvement in performance parameters like Peak Signal to Noise Ratio (PSNR) and Compression Ratio (CR).

一种基于Curvelet变换的地震数据去噪方法和应用

如何去除噪声且不损失有效信号是地震数据处理中的一个重难点。实验将一种Curvelet自适应阈值去噪法应用到地震数据处理中,Curvelet变换系数由自适应阈值约束,经阈值函数映射得到估计系数,最后对所得的估计系数进行逆变换,实现地震数据去噪,有效提高地震数据信噪比。模型和实际数据处理结果表明,Curvelet自适应阈值去噪法较好地压制了噪声的同时保护有效信号,克服了F-X域滤波产生新噪声的缺陷,取得了较好去噪效果。

Enhanced Steganalysis for Color Images Using Curvelet Features and Support Vector Machine

Algorithms for steganography are methods of hiding data transfers in media files.Several machine learning architectures have been presented recently to improve stego image identification performance by using spatial information,and these methods have made it feasible to handle a wide range of problems associated with image analysis.Images with little information or low payload are used by information embedding methods,but the goal of all contemporary research is to employ high-payload images for classification.To address the need for both low-and high-payload images,this work provides a machine-learning approach to steganography image classification that uses Curvelet transformation to efficiently extract characteristics from both type of images.Support Vector Machine(SVM),a commonplace classification technique,has been employed to determine whether the image is a stego or cover.The Wavelet Obtained Weights(WOW),Spatial Universal Wavelet Relative Distortion(S-UNIWARD),Highly Undetectable Steganography(HUGO),and Minimizing the Power of Optimal Detector(MiPOD)steganography techniques are used in a variety of experimental scenarios to evaluate the performance of the proposedmethod.Using WOW at several payloads,the proposed approach proves its classification accuracy of 98.60%.It exhibits its superiority over SOTA methods.

基于先验信息约束的Curvelet域地震数据POCS插值方法

由于野外采集环境的限制,常常无法采集得到完整规则的野外地震数据,为后续地震处理、解释工作的顺利进行,需要进行地震数据重构。凸集投影(POCS)方法利用地震波形在Curvelet域的稀疏特性,可以重构出高信噪比地震数据,该迭代算法稳定,其收敛速度较快。但在地震数据恢复的时候,由于直达波和炮集上部空白区域的影响,随着迭代的进行,重构数据中噪声干扰越来越严重,导致最终恢复的地震数据信噪比较低。本文在实现POCS迭代阈值算法基础上,引入先验信息约束的思想对算法进行优化。通过先进行坐标映射的方法进行炮集插值,然后将其作为先验信息约束进行插值,可以有效地压制迭代噪音对重构地震波形数据的影响。通过合成地震炮记录与实际炮集进行测试,结果表明本文提出的改进方法可以明显改善重构地震数据的信噪比,并提高地震波场同相轴的连续性。

An iterative curvelet thresholding algorithm for seismic random noise attenuation

In this paper,we explore the use of iterative curvelet thresholding for seismic random noise attenuation.A new method for combining the curvelet transform with iterative thresholding to suppress random noise is demonstrated and the issue is described as a linear inverse optimal problem using the L1 norm.Random noise suppression in seismic data is transformed into an L1 norm optimization problem based on the curvelet sparsity transform. Compared to the conventional methods such as median filter algorithm,FX deconvolution, and wavelet thresholding,the results of synthetic and field data processing show that the iterative curvelet thresholding proposed in this paper can sufficiently improve signal to noise radio（SNR） and give higher signal fidelity at the same time.Furthermore,to make better use of the curvelet transform such as multiple scales and multiple directions,we control the curvelet direction of the result after iterative curvelet thresholding to further improve the SNR.