Eigenvector Model Descriptors for the Seismic Inverse Problem

2020 ◽  
Author(s):  
Florian Faucher ◽  
Otmar Scherzer ◽  
Hélène Barucq
Keyword(s):  
Image Processing ◽  
Inverse Problem ◽  
Diffusion Equation ◽  
Surface Reconstruction ◽  
Wave Speed ◽  
Three Dimensional ◽  
Low Frequency ◽  
Minimization Algorithm ◽  
Iterative Minimization ◽  
Ill Posed

<p>We consider the quantitative inverse problem for the recovery of subsurface Earth's properties, which relies on an iterative minimization algorithm. Due to the scale of the domains and lack of apriori information, the problem is severely ill-posed. In this work, we reduce the ill-posedness by using the ``regularization by discretization'' approach: the wave speed is described by specific bases, which limits the number of coefficients in the representation. Those bases are associated with the eigenvectors of a diffusion equation, and we investigate several choices for the PDE, that are extracted from the field of image processing. We first compare the efficiency of these model descriptors to accurately capture the variation with a minimal number of coefficients. In the context of sub-surface reconstruction, we demonstrate that the method can be employed to overcome the lack of low-frequency contents in the data. We illustrate with two and three-dimensional acoustic experiments.</p>

scholarly journals Regularization of a sideways problem for a time-fractional diffusion equation with nonlinear source

2020 ◽  
Vol 28 (2) ◽  
pp. 211-235
Author(s):  
Tran Bao Ngoc ◽  
Nguyen Huy Tuan ◽  
Mokhtar Kirane
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Regularization Method ◽  
A Priori ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Nonlinear Source ◽  
Numerical Example ◽  
Ill Posed ◽  
Time Fractional Diffusion Equation

AbstractIn this paper, we consider an inverse problem for a time-fractional diffusion equation with a nonlinear source. We prove that the considered problem is ill-posed, i.e., the solution does not depend continuously on the data. The problem is ill-posed in the sense of Hadamard. Under some weak a priori assumptions on the sought solution, we propose a new regularization method for stabilizing the ill-posed problem. We also provide a numerical example to illustrate our results.

Identification of nonlinear B–H curves based on magnetic field computations and multigrid methods for ill-posed problems

2003 ◽  
Vol 14 (1) ◽  
pp. 15-38 ◽  
Author(s):  
BARBARA KALTENBACHER ◽  
MANFRED KALTENBACHER ◽  
STEFAN REITZINGER
Keyword(s):  
Magnetic Field ◽  
Inverse Problem ◽  
Numerical Solutions ◽  
Iterative Scheme ◽  
Three Dimensional ◽  
Multigrid Methods ◽  
Stopping Criterion ◽  
Nonlinear Inverse Problem ◽  
Field Problem ◽  
Ill Posed

Our task is the identification of the reluctivity $\nu\,{=}\,\nu(B)$ in $\vec{H}\,{=}\,\nu(B) \vec{B}$, ($B\,{=}\,|\vec{B}|$) from measurements of the magnetic flux for different excitation currents in a driving coil, in the context of a nonuniform magnetic field distribution. This is a nonlinear inverse problem and ill-posed in the sense of unstable data dependence, whose solution is done numerically by a Newton type iterative scheme, regularized by an appropriate stopping criterion. The computational complexity of this method is determined by the number of necessary forward evaluations, i.e. the number of numerical solutions to the three-dimensional magnetic field problem. We keep the effort minimal by applying a special discretization strategy to the inverse problem, based on multigrid methods for ill-posed problems. Numerical results demonstrate the efficiency of the proposed method.

scholarly journals Eigenvector models for solving the seismic inverse problem for the Helmholtz equation

2020 ◽  
Vol 221 (1) ◽  
pp. 394-414 ◽  
Author(s):  
Florian Faucher ◽  
Otmar Scherzer ◽  
Hélène Barucq
Keyword(s):  
Inverse Problem ◽  
Wave Speed ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Inversion Method ◽  
Reconstruction Procedure ◽  
Salt Domes ◽  
Full Waveform ◽  
Acoustic Media ◽  
Speed Parameter

SUMMARY We study the seismic inverse problem for the recovery of subsurface properties in acoustic media. In order to reduce the ill-posedness of the problem, the heterogeneous wave speed parameter is represented using a limited number of coefficients associated with a basis of eigenvectors of a diffusion equation, following the regularization by discretization approach. We compare several choices for the diffusion coefficient in the partial differential equations, which are extracted from the field of image processing. We first investigate their efficiency for image decomposition (accuracy of the representation with respect to the number of variables). Next, we implement the method in the quantitative reconstruction procedure for seismic imaging, following the full waveform inversion method, where the difficulty resides in that the basis is defined from an initial model where none of the actual structures is known. In particular, we demonstrate that the method may be relevant for the reconstruction of media with salt-domes. We use the method in 2-D and 3-D experiments, and show that the eigenvector representation compensates for the lack of low-frequency information, it eventually serves us to extract guidelines for the implementation of the method.

scholarly journals On an initial inverse problem for a diffusion equation with a conformable derivative

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Tran Thanh Binh ◽  
Nguyen Hoang Luc ◽  
Donal O’Regan ◽  
Nguyen H. Can
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Regularization Method ◽  
Conformable Derivative ◽  
Parameter Choice ◽  
Backward Problem ◽  
Ill Posed ◽  
Two Parameter ◽  
Parameter Choice Rules ◽  
Regularized Solution

AbstractIn this paper, we consider the initial inverse problem for a diffusion equation with a conformable derivative in a general bounded domain. We show that the backward problem is ill-posed, and we propose a regularizing scheme using a fractional Landweber regularization method. We also present error estimates between the regularized solution and the exact solution using two parameter choice rules.

scholarly journals Enhancing SNR and generating contrast for cryo-EM images with convolutional neural networks

2020 ◽  
Author(s):  
Eugene Palovcak ◽  
Daniel Asarnow ◽  
Melody G. Campbell ◽  
Zanlin Yu ◽  
Yifan Cheng
Keyword(s):  
Image Processing ◽  
High Frequency ◽  
Signal To Noise Ratio ◽  
Three Dimensional ◽  
Low Frequency ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Processing Pipeline ◽  
Visual Contrast ◽  
Low Pass

AbstractIn cryogenic electron microscopy (cryo-EM) of radiation-sensitive biological samples, both the signal-to-noise ratio (SNR) and the contrast of images are critically important in the image processing pipeline. Classic methods improve low-frequency image contrast experimentally, by imaging with high defocus, or computationally, by applying various types of low-pass filter. These contrast improvements typically come at the expense of high-frequency SNR, which is suppressed by high-defocus imaging and removed by low pass filtration. Here, we demonstrate that a convolutional neural network (CNN) denoising algorithm can be used to significantly enhance SNR and generate contrast in cryo-EM images. We provide a quantitative evaluation of bias introduced by the denoising procedure and its influences on image processing and three-dimensional reconstructions. Our study suggests that besides enhancing the visual contrast of cryo-EM images, the enhanced SNR of denoised images may facilitate better outcomes in the other parts of the image processing pipeline, such as classification and 3D alignment. Overall, our results provide a ground of using denoising CNNs in the cryo-EM image processing pipeline.

Image Processing and Splicing Method for 3D Optical Scanning Surface Reconstruction of Wood Grain

2019 ◽  
Vol 34 (08) ◽  
pp. 2054021
Author(s):  
Shufeng Jiang ◽  
Keqi Wang
Keyword(s):  
Image Processing ◽  
Surface Reconstruction ◽  
Cross Section ◽  
Optimal Path ◽  
Three Dimensional ◽  
Recognition Algorithm ◽  
Cloud Data ◽  
Section Model ◽  
Wood Grain ◽  
Scanning Imaging

Based on environment compensation, scanning image processing technology was employed to investigate point cloud data and space matching method for wood grain. Collision avoidance recognition algorithm was used to collocate mark points, when remarkably reduced the error matching of distance coincidence mark points. The proposed method used marking of flag sample points based on weight to compensate for the marking points ambiguity of distinguishing information in scanning environment, and select the optimal path for the weighted results. The same splicing points in different images was identified, solving the problem of fuzzy splicing by distance matching. Experimental results and three-dimensional (3D) printing wood cross-section model reconstructed by surface fitting were compared. Results showed that the 3D scanning image mosaic of wood growth texture at the cross-section had no obvious stereo characteristics. The proposed method has improved the accuracy of surface mosaic in reverse scanning imaging for wood grain. This method can be applied to support the application needs of reverse surface reconstruction.

Information and estimation in image processing

1987 ◽  
Vol 45 ◽  
pp. 14-17
Author(s):  
B. Roy Frieden
Keyword(s):  
Image Processing ◽  
Optical System ◽  
Large Amplitude ◽  
Communication Theory ◽  
Image Data ◽  
Direct Approach ◽  
Ill Posed

Despite the skill and determination of electro-optical system designers, the images acquired using their best designs often suffer from blur and noise. The aim of an “image enhancer” such as myself is to improve these poor images, usually by digital means, such that they better resemble the true, “optical object,” input to the system. This problem is notoriously “ill-posed,” i.e. any direct approach at inversion of the image data suffers strongly from the presence of even a small amount of noise in the data. In fact, the fluctuations engendered in neighboring output values tend to be strongly negative-correlated, so that the output spatially oscillates up and down, with large amplitude, about the true object. What can be done about this situation? As we shall see, various concepts taken from statistical communication theory have proven to be of real use in attacking this problem. We offer below a brief summary of these concepts.

EMCAT: An automatic image-processing system for electron-microscopic tomography

1994 ◽  
Vol 52 ◽  
pp. 418-419
Author(s):  
Weiping Liu ◽  
John W. Sedat ◽  
David A. Agard
Keyword(s):  
Image Processing ◽  
Structural Information ◽  
Imaging Technique ◽  
Three Dimensional ◽  
Processing System ◽  
Electron Microscopic ◽  
Data Set ◽  
Ordered Structures ◽  
Automatic Image Processing ◽  
Em Tomography

Any real world object is three-dimensional. The principle of tomography, which reconstructs the 3-D structure of an object from its 2-D projections of different view angles has found application in many disciplines. Electron Microscopic (EM) tomography on non-ordered structures (e.g., subcellular structures in biology and non-crystalline structures in material science) has been exercised sporadically in the last twenty years or so. As vital as is the 3-D structural information and with no existing alternative 3-D imaging technique to compete in its high resolution range, the technique to date remains the kingdom of a brave few. Its tedious tasks have been preventing it from being a routine tool. One keyword in promoting its popularity is automation: The data collection has been automated in our lab, which can routinely yield a data set of over 100 projections in the matter of a few hours. Now the image processing part is also automated. Such automations finish the job easier, faster and better.

Three-Dimensional Structure of Rotavirus-Fab Complex

1990 ◽  
Vol 48 (1) ◽  
pp. 238-239
Author(s):  
B.V.V. Prasad ◽  
E. Marietta ◽  
J.W. Burns ◽  
M.K. Estes ◽  
W. Chiu
Keyword(s):  
Image Processing ◽  
Smooth Surface ◽  
Three Dimensional ◽  
Outer Shell ◽  
Dimensional Structure ◽  
Structural Studies ◽  
Cell Penetration ◽  
Electron Cryomicroscopy ◽  
Image Processing Techniques ◽  
Processing Techniques

Rotaviruses are spherical, double-shelled particles. They have been identified as a major cause of infantile gastroenteritis worldwide. In our earlier studies we determined the three-dimensional structures of double-and single-shelled simian rotavirus embedded in vitreous ice using electron cryomicroscopy and image processing techniques to a resolution of 40Å. A distinctive feature of the rotavirus structure is the presence of 132 large channels spanning across both the shells at all 5- and 6-coordinated positions of a T=13ℓ icosahedral lattice. The outer shell has 60 spikes emanating from its relatively smooth surface. The inner shell, in contrast, exhibits a bristly surface made of 260 morphological units at all local and strict 3-fold axes (Fig.l).The outer shell of rotavirus is made up of two proteins, VP4 and VP7. VP7, a glycoprotein and a neutralization antigen, is the major component. VP4 has been implicated in several important functions such as cell penetration, hemagglutination, neutralization and virulence. From our earlier studies we had proposed that the spikes correspond to VP4 and the rest of the surface is composed of VP7. Our recent structural studies, using the same techniques, with monoclonal antibodies specific to VP4 have established that surface spikes are made up of VP4.

Shifting perspectives: method, media and the complex image

1998 ◽  
Vol 10 (1-3) ◽  
pp. 100-108 ◽  
Author(s):  
Alicia Colson ◽  
Ross Parry
Keyword(s):  
Image Processing ◽  
Three Dimensional ◽  
Geographical Location ◽  
Spatial Relationship ◽  
Two Dimensional ◽  
Dimensional Approach ◽  
Complex Image ◽  
Cultural Resonance

This article argues that the analysis of a threedimensional image demanded a three-dimensional approach. The authors realise that discussions of images and image processing inveterately conceptualise representation as being flat, static, and finite. The authors recognise the need for a fresh acuteness to three-dimensionality as a meaningful – although problematic – element of visual sources. Two dramatically different examples are used to expose the shortcomings of an ingrained two-dimensional approach and to facilitate a demonstration of how modern (digital) techniques could sanction new historical/anthropological perspectives on subjects that have become all too familiar. Each example could not be more different in their temporal and geographical location, their cultural resonance, and their historiography. However, in both these visual spectacles meaning is polysemic. It is dependent upon the viewer's spatial relationship to the artifice as well as the spirito-intellectual viewer within the community. The authors postulate that the multi- faceted and multi-layered arrangement of meaning in a complex image could be assessed by working beyond the limitations of the two-dimensional methodological paradigm and by using methods and media that accommodated this type of interconnectivity and representation.

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