Complex seismic wavefi eld interpolation based on the Bregman iteration method in the sparse transform domain

In seismic prospecting, fi eld conditions and other factors hamper the recording of the complete seismic wavefi eld; thus, data interpolation is critical in seismic data processing. Especially, in complex conditions, prestack missing data affect the subsequent highprecision data processing workfl ow. Compressive sensing is an effective strategy for seismic data interpolation by optimally representing the complex seismic wavefi eld and using fast and accurate iterative algorithms. The seislet transform is a sparse multiscale transform well suited for representing the seismic wavefield, as it can effectively compress seismic events. Furthermore, the Bregman iterative algorithm is an efficient algorithm for sparse representation in compressive sensing. Seismic data interpolation methods can be developed by combining seismic dynamic prediction, image transform, and compressive sensing. In this study, we link seismic data interpolation and constrained optimization. We selected the OC-seislet sparse transform to represent complex wavefields and used the Bregman iteration method to solve the hybrid norm inverse problem under the compressed sensing framework. In addition, we used an H-curve method to choose the threshold parameter in the Bregman iteration method. Thus, we achieved fast and accurate reconstruction of the seismic wavefi eld. Model and fi eld data tests demonstrate that the Bregman iteration method based on the H-curve norm in the sparse transform domain can effectively reconstruct missing complex wavefi eld data.

Anti-aliasing nonstationary signals detecion algorithm based on interpolation in the frequency domain using the short time Fourier transform

To eliminate the aliasing that appeared during the measurement of multi-components nonstationary signals, a novel kind of anti-aliasing algorithm based on the short time Fourier transform （STFT） is brought forward. First the physical essence of aliasing that occurs is analyzed; second the interpolation algorithm model is setup based on the Hamming window; then the fast implementation of the algorithm using the Newton iteration method is given. Using the numerical simulation the feasibility of algorithm is validated. Finally, the electrical circuit experiment shows the practicality of the algorithm in the electrical engineering.

Interpolation of Images Using Discrete Wavelet Transform to Simulate Image Resizing as in Human Vision

This paper presents discrete wavelet transform （DWT） and its inverse （IDWT） with Haar wavelets as tools to compute the variable size interpolated versions of an image at optimum computational load. As a human observer moves closer to or farther from a scene, the retinal image of the scene zooms in or out, respectively. This zooming in or out can be modeled using variable scale interpolation. The paper proposes a novel way of applying DWT and IDWT in a piecewise manner by non-uniform down- or up-sampling of the images to achieve partially sampled versions of the images. The partially sampled versions are then aggregated to achieve the final variable scale interpolated images. The non-uniform down- or up-sampling here is a function of the required scale of interpolation. Appropriate zero padding is used to make the images suitable for the required non-uniform sampling and the subsequent interpolation to the required scale. The concept of zeroeth level DWT is introduced here, which works as the basis for interpolating the images to achieve bigger size than the original one. The main emphasis here is on the computation of variable size images at less computational load, without compromise of quality of images. The interpolated images to different sizes and the reconstructed images are benchmarked using the statistical parameters and visual comparison. It has been found that the proposed approach performs better as compared to bilinear and bicubic interpolation techniques.

改进视觉Transformer的视频插帧方法

针对现有的视频插帧方法无法有效处理大运动和复杂运动场景的问题,提出了一种改进视觉Transformer的视频插帧方法。该方法融合了基于跨尺度窗口的注意力和可分离的时空局部注意力,增大了注意力的感受野并聚合了多尺度信息;对时空依赖和远程像素依赖关系进行联合建模,进而增强了模型对大运动场景的处理能力。实验结果表明,该方法在Vimeo90K测试集和DAVIS数据集上的PSNR指标分别达到了37.13 dB和28.28 dB,SSIM指标分别达到了0.978和0.891。同时,可视化结果表明,该方法针对存在大运动、复杂运动和遮挡场景的视频能产生清晰合理的插帧结果。

Power System Harmonic Detection Using Frequency-Domain Interpolation Wavelet Transform

Aiming at harmonic detection, fast Fourier transform can only detect integer harmonics precisely, short time Fourier transform can detect non-integer harmonics with low resolution, and some former wavelet based methods have no aliasing-reduction scheme which result in low measurement precision and poor robustness. A frequency-domain interpolation algorithm to detect harmonics is proposed by choosing Shannon wavelet. Shannon wavelet is an orthogonal wavelet possessing best ideal frequency domain localization ability, it can restrict wavelet abasing but bring about Gibbs oscillation phenomenon simultaneously. An interpolation algorithm is developed to overcome this problem. Simulation reveals that the proposed method can effectively cancel aliasing, spectral leakage and Gibbs phenomenon, so it provides an effective means for power system harmonic analysis.

Combining Cubic Spline Interpolation and Fast Fourier Transform to Extend Measuring Range of Reflectometry

The reflectometry is a common method used to measure the thickness of thin films. Using a conventional method,its measurable range is limited due to the low resolution of the current spectrometer embedded in the reflectometer.We present a simple method, using cubic spline interpolation to resample the spectrum with a high resolution,to extend the measurable transparent film thickness. A large measuring range up to 385 m in optical thickness is achieved with the commonly used system. The numerical calculation and experimental results demonstrate that using the FFT method combined with cubic spline interpolation resampling in reflectrometry, a simple,easy-to-operate, economic measuring system can be achieved with high measuring accuracy and replicability.

Image interpolation based on Wavelet Transform

Image interpolation is widely studied and used in digital image processing. In this paper, a method of image magnification according to the properties of fi＇actal interpolation and wavelet transformation are presented. We focus the development of edge forming methods to be applied as a post process of standard image zooming methods for grayscale images, with the hope of retaining edges. Experiments make sure it valid.

A new interpolation method based on satellite physical character in using IGS precise ephemeris

Due to the deficiency of sliding Lagrange polynomial interpolation, the author proposes a new interpolation method, which considers the physical character of satellite movement in coordinate transformation and reasonable selection of interpolation function. Precision of the two methods is compared by a numerical example. The result shows that the new method is superior to the sliding Lagrange polynomial interpolation in interpolation and extrapolation, especially in extrapolation that is over short time spans.

An Explicit Fractal Interpolation Algorithm for Reconstruction of Seismic Data

Based on our previous investigation and the pioneering work of other researchers, a novel explicit fractal interpolation method based on affine transform is proposed, in which we approximate the vertical scaling factors by the locally explicit expression. Numerical experiments indicate that the explicit fractal interpolation method shows great accuracy of reconstruction of the seismic profile and yields significant improvement over wave-equation based trace interpolation methods （unified approach）.

基于卷积和Transformer联合网络的地震数据插值

地震数据插值是地震数据处理的关键步骤,旨在高精度地恢复出缺失地震数据,提升地震数据信噪比。近年来,基于卷积神经网络的插值方法发展迅速,该方法基于数据驱动,通过搭建卷积神经网络恢复缺失数据。卷积神经网络依赖卷积提取地震数据特征,然而由于受到卷积核局部感受野的限制,卷积运算只能捕捉地震数据局部信息,限制了网络的插值性能。因此本文提出了基于卷积和Transformer联合网络的地震数据插值方法,该方法通过引入Transformer,构建卷积和Transformer融合模块提取地震数据特征,旨在捕捉地震数据更多的细节信息,提升地震数据插值性能。通过仿真数据实验和真实数据实验显示,和基于Unet网络的插值方法相比,本文方法具有更好的插值性能,能够恢复地震数据更多纹理细节,插值结果的信噪比提升了2~3 dB。

New Edge-Directed Interpolation Based-Lifting DWT and MSPIHT Algorithm for Image Compression

The amount of image data generated in multimedia applications is ever increasing. The image compression plays vital role in multimedia applications. The ultimate aim of image compression is to reduce storage space without degrading image quality. Compression is required whenever the data handled is huge they may be required to sent or transmitted and also stored. The New Edge Directed Interpolation (NEDI)-based lifting Discrete Wavelet Transfrom (DWT) scheme with modified Set Partitioning In Hierarchical Trees (MSPIHT) algorithm is proposed in this paper. The NEDI algorithm gives good visual quality image particularly at edges. The main objective of this paper is to be preserving the edges while performing image compression which is a challenging task. The NEDI with lifting DWT has achieved 99.18% energy level in the low frequency ranges which has 1.07% higher than 5/3 Wavelet decomposition and 0.94% higher than traditional DWT. To implement this NEDI with Lifting DWT along with MSPIHT algorithm which gives higher Peak Signal to Noise Ratio (PSNR) value and minimum Mean Square Error (MSE) and hence better image quality. The experimental results proved that the proposed method gives better PSNR value (39.40 dB for rate 0.9 bpp without arithmetic coding) and minimum MSE value is 7.4.

Integer Wavelet-Based Image Interpolation in Lifting Structure for Image Resolution Enhancement

A floating-point wavelet-based and an integer wavelet-based image interpolations in lifting structures and polynomial curve fitting for image resolution enhancement are proposed in this paper. The proposed prediction methods estimate high-frequency wavelet coefficients of the original image based on the available low-frequency wavelet coefficients, so that the original image can be reconstructed by using the proposed prediction method. To further improve the reconstruction performance, we use polynomial curve fitting to build relationships between actual high-frequency wavelet coefficients and estimated high-frequency wavelet coefficients. Results of the proposed prediction algorithm for different wavelet transforms are compared to show the proposed prediction algorithm outperforms other methods.

Improvement of Orbit Prediction Algorithm for Spacecraft Through Simplified Precession-Nutation Model Using Cubic Spline Interpolation Method

For the on-orbit flight missions,the model of orbit prediction is critical for the tasks with high accuracy requirement and limited computing resources of spacecraft.The precession-nutation model,as the main part of extended orbit prediction,affects the efficiency and accuracy of on-board operation.In this paper,the previous research about the conversion between the Geocentric Celestial Reference System and International Terrestrial Reference System is briefly summarized,and a practical concise precession-nutation model is proposed for coordinate transformation computation based on Celestial Intermediate Pole(CIP).The idea that simplifying the CIP-based model with interpolation method is driven by characteristics of precession-nutation parameters changing with time.A cubic spline interpolation algorithm is applied to obtain the required CIP coordinates and Celestial Intermediate Origin locator.The complete precession nutation model containing more than 4000 parameters is simplified to the calculation of a cubic polynomial,which greatly reduces the computational load.In addition,for evaluating the actual performance,an orbit propagator is built with the proposed simplified precession-nutationmodel.Compared with the orbit prediction results obtained by the truncated series of IAU2000/2006 precession-nutation model,the simplified precession-nutation model with cubic spline interpolation can significantly improve the accuracy of orbit prediction,which implicates great practical application value in further on-orbit missions of spacecraft.

Two-Dimensional Interpolation Criterion Using DFT Coefficients

In this paper,we address the frequency estimator for 2-dimensional(2-D)complex sinusoids in the presence of white Gaussian noise.With the use of the sinc function model of the discrete Fourier transform(DFT)coefficients on the input data,a fast and accurate frequency estimator is devised,where only the DFT coefficient with the highest magnitude and its four neighbors are required.Variance analysis is also included to investigate the accuracy of the proposed algorithm.Simulation results are conducted to demonstrate the superiority of the developed scheme,in terms of the estimation performance and computational complexity.

Distance Transform Based Enhancement for Linear Interpolated Images

An approach of distane map based imageenhancement (DMIE) is proposed. It is applied toconventional interpolations to get sharp images. Edgedetection is performed after images are interpolatedby linear interpolations. To meet the two conditionsset for DMIE, i. e., no abrupt changes and no over-boosting, different boosting rate should be used inadjusting pixel intensities. When the boosting rate isdetermined by using the distance from enhancedpixels to nearest edges, edge-oriented imageenhancement is obtained. By using Erosion technique,the range for pixel intensity adiustment is set.Over-enhancement is avoided by limiting the pixel iutensities in enhancement within the range. A unifled linear-time algoritiml for disance transform is adopted to deal with the calculation of Euelidean distance of the images.Its computation complexity is 0(N).After the preparation,i.e.,distance transforming and erosion,the images get more and more sharpened while no over.boosting.Occurs by repeating the enhancement procedure ,The simplicity of the enhancement operation makes DMIE suitable for enhancement rate adjusting

Downhole microseismic data reconstruction and imaging based on combination of spline interpolation and curveletsparse constrained interpolation

When cause of the aliasing lack probl using borehole sensors and microseimic events to image, spatial aliasing often occurred be- of sensors underground and the distance between the sensors which were too large. To solve em, data reconstruction is often needed. Curvelet transform sparsity constrained inversion was widely used in the seismic data reconstruction field for its anisotropic, muhiscale and local basis. However, for the downhole ease, because the number of sampling point is mueh larger than the number of the sensors, the advantage of the cnrvelet basis can＇t perform very well. To mitigate the problem, the method that joints spline and curvlet-based compressive sensing was proposed. First, we applied the spline interpolation to the first arri- vals that to be interpolated. And the events are moved to a certain direction, such as horizontal, which can be represented by the curvelet basis sparsely. Under the spasity condition, curvelet-based compressive sensing was applied for the data, and directional filter was also used to mute the near vertical noises. After that, the events were shifted to the spline line to finish the interpolation workflow. The method was applied to a synthetic mod- el, and better result was presented than using curvelet transform interpolation directly. We applied the method to a real dataset, a mieroseismic downhole observation field data in Nanyang, using Kirchhoff migration method to image the microseimic event. Compared with the origin data, artifacts were suppressed on a certain degree.

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.

利用瑞利面波提高近地表横波速度精度的方法

二维油气地震勘探中,由于受野外施工条件、成本效益等诸多因素限制,地震记录的野外采集道间距往往较大,这种地震记录往往容易产生空间假频,降低其频率—速度谱信噪比。为此,提出利用小波变换良好的时频分析特性,对大时空采样记录进行基于小波基的道内插值,以提高P-SV转换波地震资料中的瑞利面波频散高频信息的精度,从而提高反演表层横波速度结构精度,提高P-SV转换波的横波静校正精度。对理论模型和实际数据进行的验证计算表明,基于小波基的道内插值方法具有抗假频性,瑞利面波基阶频散曲线拐点更清晰,高频段能量更加集中,反演的横波速度精度更高,取得了较好效果。

任意大小图像的量子描述及双线性插值方法

为解决任意大小图像的量子描述及缩放问题,提出一种改进的量子图像描述方法。采用量子基态描述像素值,采用量子叠加态描述像素位置,该叠加态可包含任意数量的基态,描述任意大小的图像。提出一种基于量子傅里叶变换的图像双线性插值方法。基于量子傅里叶变换基本原理,设计实现加法和乘法的量子线路,利于这两个模块及其它辅助模块,研究实现图像双线性插值的量子线路设计方法,设计双线性插值放大和缩小两种具体的量子线路。基于线路中采用的量子基本门的数量,分析线路的复杂度,其结果表明,该方法可以实现对经典方法的指数加速。经典计算机上的仿真结果验证了提出方法的有效性。

四向加权香农熵最大化导向的自动阈值分割方法

灰度图像的灰度直方图可以呈现出无峰、单峰、双峰或多峰的形态特征,但传统熵阈值分割方法大多仅适合处理具有单峰或双峰形态特征的灰度图像。为了提高熵阈值分割方法的分割精度和分割适应性,提出一种四向加权香农熵最大化导向的自动阈值分割方法 FWSE(Four-directional Weighted Shannon Entropy)。首先用新设计的方向性Prewitt卷积核在4个方向进行多尺度乘积变换(MPT),以获得一系列方向性MPT图像;再基于三次样条插值函数和曲率最大化准则自动计算出每个方向的最优MPT图像;其次在每个方向上通过内外轮廓图像对最优MPT图像的像素进行重新取样,以获取重构的灰度直方图,并在此基础上计算相应的香农熵;最后以4个方向的加权香农熵最大化为准则选取最佳分割阈值。与新近的3种阈值分割方法以及2种非阈值分割方法在4幅合成图像和100幅真实世界图像上进行实验,结果显示:在合成图像上,FWSE方法的平均马修斯相关系数(MCC)达到了0.999;在真实世界图像上,FWSE方法与其他5个分割方法的平均MCC分别是0.974、0.927、0.668、0.595、0.550和0.525。这表明FWSE方法具有更高的分割精度和更灵活的分割适应性。