Time domain sparsity promoting LSRTM with source estimation
|
|
- Spencer Haynes
- 5 years ago
- Views:
Transcription
1 Time domain sparsity promoting LSRTM with source estimation Mengmeng Yang, Philipp Witte, Zhilong Fang & Felix J. Herrmann SLIM University of British Columbia
2 Motivation Features of RTM: pros - no dip limitation - strong lateral velocity variations cons - inaccurate amplitudes & low resolution Problems of LS- RTM: iterations that touch all shots are too expensive data can be overfitted 2
3 RTM w/ correct wavelet Depth (km) Distance (km)
4 Sparsity promoting LS-RTM w/ correct wavelet Depth (km) Distance (km) -.3
5 Sparsity promoting LS-RTM w/ wrong wavelet Depth (km) Distance (km) -.3
6 LS-RTM min m P ns i=1 kj i[m, q i ] m b i k 2 m J i m : background model : Born modelling operator for shot : model perturbation i th q i b i : source wavelet for shot i th : vectorized reflections for shot i th 6
7 Herrmann F J, Li X. Efficient least-squares imaging with sparsity promotion and compressive sensing[j]. Geophysical prospecting, 212, 6(4): Sparsity promoting inversion min x kxk 1 s.t. ns X i=1 k J i [m, q i ]C {z } Ĵ x b i {z} b k 2 apple C : the transpose of Curvelet transform x : Curvelet coefficients : tolerance for noise or modelling error 7
8 Felix J. Herrmann,Ning Tu and Ernie Esser, Fast online migration with Compressive Sensing, EAGE Annual Conference Proceeding, 215, vol. 6, p , 212 Lorenz, Dirk A.; Wenger, Stephan; A sparse Kaczmarz solver and a linearized Bregman method for online compressed sensing. arxiv: Randomized subsampling Ĵ x = b Ĵ r(k) x = b r(k) n s n s n s 8
9 W, Yin. Analysis and generalizations of the linearized Bregman method. SIAM J. Imaging Sci., 3(4): , 21. Herrmann F J, Tu N, Esser E. Fast online migration with Compressive Sensing[J]. Solvers for sparsity promoting inversion Many solvers for sparse. inversion: Iterative soft thresholding (simple, but slow convergence, cooling of threshold...) Spectral projected gradients w/ L1 constraint SPGL1 (expensive, difficult to implement, slow convergence) Linearized Bregman (LB) (easy to implement, proven convergence w/ subsampling) 9
10 Sparsity promoting LS-RTM w/ correct wavelet & SPGL Depth (km) Distance (km) -.3
11 Sparsity promoting LS-RTM w/ correct wavelet & LB Depth (km) Distance (km) -.3
12 W, Yin. Analysis and generalizations of the linearized Bregman method. SIAM J. Imaging Sci., 3(4): , 21. Herrmann F J, Tu N, Esser E. Fast online migration with Compressive Sensing[J]. Modification minimize x kxk kxk2 s.t. kĵx bk 2 apple strongly convex objective function because of additional 2- norm term for big enough solves BP problem 12
13 Workflow for LB minimize x kxk kxk2 s.t. kĵx bk 2 apple 1. Initialize x =, z =, q,, batchsize n s n s 2. for k =, 1, Randomly choose shot subsets I 2 [1 n s ], I = n s Ĵ k = {J i (m,q i )C } i2i 5. b k = {b i } i2i 6. z k+1 = z k t k Ĵ T k P (Ĵ k x k 7. x k+1 = S (z k+1 ) b k ) 8. end note: S (z k+1 )=sign(z k+1 ) max{, z k+1 } P (Ĵ k x k b k ) = max{, 1 kĵ k x k b k k k x k b k ) 13
14 Toy example Sparsity recovery with tall ill- conditioned matrix A: 2 X 1, with Rank 5 x: 1 X 1, with 2 non- zeros 14
15 15 SPGL1 vs LB no subsampling
16 16 SPGL1 vs LB 5% subsampling
17 17 SPGL1 vs LB 8% subsampling
18 18 SPGL1 vs LB 9% subsampling
19 An analysis of seismic wavelet estimation. Ayon Kumar Dey, 1999, University of Calgary, PhD thesis What if source signature is unknown? Estimate source by solving least- square problem: min w P Ntr j kw b j b j k 2 s.t.kwk 2 =1 where Suppose that, and q is the same for all shots q = w q q = w q is the initial guess of q 19
20 Initial wavelet setting.3.2 signal in time domain initial q true q Amp approximate duration time (s) frequency spectrum Energy initial q true q frequency bandwidth wider due to factorization frequency (HZ) 2
21 Combine the image inversion & source estimation start w/ sufficiently small threshold to allow main reflectors to enter into solution update m start with initial wavelet update wavelet 21
22 Workflow for sparsity-promoting LS-RTM w/ source estimation 1. Initialize x =, z =, q,, 2, batchsize n s n s, weights r 2. for k =, 1, 3. Randomly choose shot subsets I 2 [1 n s ], I = n s 4. Ĵ k = {J i (m,q )C } i2i 5. b k = {b i } i2i 6. bk = Ĵ k x k 7. w k = arg min w PI kw b k b k k 2 + kr(w q )k kw q k 2 8. z k+1 = z k t k Ĵ w k k?p (w k b k b k ) 9. x k+1 = S (z k+1 ) 1. end 22
23 Experiments Data: 295 shots with shot interval 15m 295 receivers with receiver interval 15m 4s record, 15Hz peak frequency designed wavelet synthetic linearized data Experiments: one pass through the data with batch sizes 2.5% data randomized subset of shots normalized true source wavelet & initial guessed wavelet 23
24 background model and model perturbation.5 s 2 /km 2.4 Depth (km) Distance (km) 24
25 Sparsity promoting LS-RTM w/ correct wavelet & LB Depth (km) Distance (km) -.3
26 Sparsity promoting LS-RTM w/ wrong wavelet & LB Depth (km) Distance (km) -.3
27 Sparsity promoting LS-RTM w/ source estimation w/ LB Depth (km) Distance (km) -.3
28 Sparsity promoting LS-RTM w/ source estimation, via LB Depth (km) Distance (km)
29 Sparsity promoting LS-RTM w/ source estimation.3.2 signal in time domain estimated initial q true q Amp time (s) frequency spectrum 4 estimated initial q true q Energy frequency (HZ) 29
30 Residual & model error Residuals Relative model error 3
31 31 Robustness of source estimation starting w/ zero-phase wavelet
32 32 Sparsity promoting LS-RTM w/ correct wavelet & LB
33 33 Sparsity promoting LS-RTM w/ source estimation & LB
34 Conclusions LB with correct source signature gives image with sharp interfaces w/ correct amplitudes Computational complexity is controlled to ~1 RTM w/ randomized source subsampling LB improves inversion results compared to other one- norm solvers LB can be combined w/ on- the- fly source estimation w/o a large computational overhead 34
35 Acknowledgements This research was carried out as part of the SINBAD project with the support of the member organizagons of the SINBAD Consorgum. 35
Sparsity-promoting migration with multiples
Sparsity-promoting migration with multiples Tim Lin, Ning Tu and Felix Herrmann SLIM Seismic Laboratory for Imaging and Modeling the University of British Columbia Courtesy of Verschuur, 29 SLIM Motivation..
More informationFWI with Compressive Updates Aleksandr Aravkin, Felix Herrmann, Tristan van Leeuwen, Xiang Li, James Burke
Consortium 2010 FWI with Compressive Updates Aleksandr Aravkin, Felix Herrmann, Tristan van Leeuwen, Xiang Li, James Burke SLIM University of British Columbia Full Waveform Inversion The Full Waveform
More informationWavefield Reconstruction Inversion (WRI) a new take on wave-equation based inversion Felix J. Herrmann
Wavefield Reconstruction Inversion (WRI) a new take on wave-equation based inversion Felix J. Herrmann SLIM University of British Columbia van Leeuwen, T and Herrmann, F J (2013). Mitigating local minima
More informationSeismic data interpolation and denoising using SVD-free low-rank matrix factorization
Seismic data interpolation and denoising using SVD-free low-rank matrix factorization R. Kumar, A.Y. Aravkin,, H. Mansour,, B. Recht and F.J. Herrmann Dept. of Earth and Ocean sciences, University of British
More informationMatrix Probing and Simultaneous Sources: A New Approach for Preconditioning the Hessian
Matrix Probing and Simultaneous Sources: A New Approach for Preconditioning the Hessian Curt Da Silva 1 and Felix J. Herrmann 2 1 Dept. of Mathematics 2 Dept. of Earth and Ocean SciencesUniversity of British
More informationAccelerated large-scale inversion with message passing Felix J. Herrmann, the University of British Columbia, Canada
Accelerated large-scale inversion with message passing Felix J. Herrmann, the University of British Columbia, Canada SUMMARY To meet current-day challenges, exploration seismology increasingly relies on
More informationCompressive Sensing Applied to Full-wave Form Inversion
Compressive Sensing Applied to Full-wave Form Inversion Felix J. Herrmann* fherrmann@eos.ubc.ca Joint work with Yogi Erlangga, and Tim Lin *Seismic Laboratory for Imaging & Modeling Department of Earth
More informationSource estimation for frequency-domain FWI with robust penalties
Source estimation for frequency-domain FWI with robust penalties Aleksandr Y. Aravkin, Tristan van Leeuwen, Henri Calandra, and Felix J. Herrmann Dept. of Earth and Ocean sciences University of British
More informationSeismic wavefield inversion with curvelet-domain sparsity promotion
Seismic wavefield inversion with curvelet-domain sparsity promotion Felix J. Herrmann* fherrmann@eos.ubc.ca Deli Wang** wangdeli@email.jlu.edu.cn *Seismic Laboratory for Imaging & Modeling Department of
More informationRecent results in curvelet-based primary-multiple separation: application to real data
Recent results in curvelet-based primary-multiple separation: application to real data Deli Wang 1,2, Rayan Saab 3, Ozgur Yilmaz 4, Felix J. Herrmann 2 1.College of Geoexploration Science and Technology,
More informationSparse and TV Kaczmarz solvers and the linearized Bregman method
Sparse and TV Kaczmarz solvers and the linearized Bregman method Dirk Lorenz, Frank Schöpfer, Stephan Wenger, Marcus Magnor, March, 2014 Sparse Tomo Days, DTU Motivation Split feasibility problems Sparse
More informationSimultaneous estimation of wavefields & medium parameters
Simultaneous estimation of wavefields & medium parameters reduced-space versus full-space waveform inversion Bas Peters, Felix J. Herrmann Workshop W- 2, The limit of FWI in subsurface parameter recovery.
More informationCompressive sampling meets seismic imaging
Compressive sampling meets seismic imaging Felix J. Herrmann fherrmann@eos.ubc.ca http://slim.eos.ubc.ca joint work with Tim Lin and Yogi Erlangga Seismic Laboratory for Imaging & Modeling Department of
More informationLow-rank Promoting Transformations and Tensor Interpolation - Applications to Seismic Data Denoising
Low-rank Promoting Transformations and Tensor Interpolation - Applications to Seismic Data Denoising Curt Da Silva and Felix J. Herrmann 2 Dept. of Mathematics 2 Dept. of Earth and Ocean Sciences, University
More informationSUMMARY. H (ω)u(ω,x s ;x) :=
Interpolating solutions of the Helmholtz equation with compressed sensing Tim TY Lin*, Evgeniy Lebed, Yogi A Erlangga, and Felix J Herrmann, University of British Columbia, EOS SUMMARY We present an algorithm
More informationMigration with Implicit Solvers for the Time-harmonic Helmholtz
Migration with Implicit Solvers for the Time-harmonic Helmholtz Yogi A. Erlangga, Felix J. Herrmann Seismic Laboratory for Imaging and Modeling, The University of British Columbia {yerlangga,fherrmann}@eos.ubc.ca
More informationStructured tensor missing-trace interpolation in the Hierarchical Tucker format Curt Da Silva and Felix J. Herrmann Sept. 26, 2013
Structured tensor missing-trace interpolation in the Hierarchical Tucker format Curt Da Silva and Felix J. Herrmann Sept. 6, 13 SLIM University of British Columbia Motivation 3D seismic experiments - 5D
More informationFighting the Curse of Dimensionality: Compressive Sensing in Exploration Seismology
Fighting the Curse of Dimensionality: Compressive Sensing in Exploration Seismology Herrmann, F.J.; Friedlander, M.P.; Yilmat, O. Signal Processing Magazine, IEEE, vol.29, no.3, pp.88-100 Andreas Gaich,
More informationMitigating data gaps in the estimation of primaries by sparse inversion without data reconstruction
Mitigating data gaps in the estimation of primaries by sparse inversion without data reconstruction Tim T.Y. Lin SLIM University of British Columbia Talk outline Brief review of REPSI Data reconstruction
More informationFull-Waveform Inversion with Gauss- Newton-Krylov Method
Full-Waveform Inversion with Gauss- Newton-Krylov Method Yogi A. Erlangga and Felix J. Herrmann {yerlangga,fherrmann}@eos.ubc.ca Seismic Laboratory for Imaging and Modeling The University of British Columbia
More information3D INTERPOLATION USING HANKEL TENSOR COMPLETION BY ORTHOGONAL MATCHING PURSUIT A. Adamo, P. Mazzucchelli Aresys, Milano, Italy
3D INTERPOLATION USING HANKEL TENSOR COMPLETION BY ORTHOGONAL MATCHING PURSUIT A. Adamo, P. Mazzucchelli Aresys, Milano, Italy Introduction. Seismic data are often sparsely or irregularly sampled along
More informationComparison between least-squares reverse time migration and full-waveform inversion
Comparison between least-squares reverse time migration and full-waveform inversion Lei Yang, Daniel O. Trad and Wenyong Pan Summary The inverse problem in exploration geophysics usually consists of two
More informationApplication of matrix square root and its inverse to downward wavefield extrapolation
Application of matrix square root and its inverse to downward wavefield extrapolation Polina Zheglova and Felix J. Herrmann Department of Earth and Ocean sciences, University of British Columbia, Vancouver,
More informationSource function estimation in extended full waveform inversion
Source function estimation in extended full waveform inversion Lei Fu The Rice Inversion Project (TRIP) May 6, 2014 Lei Fu (TRIP) Source estimation in EFWI May 6, 2014 1 Overview Objective Recover Earth
More informationCompressed Sensing: Extending CLEAN and NNLS
Compressed Sensing: Extending CLEAN and NNLS Ludwig Schwardt SKA South Africa (KAT Project) Calibration & Imaging Workshop Socorro, NM, USA 31 March 2009 Outline 1 Compressed Sensing (CS) Introduction
More informationUncertainty quantification for inverse problems with a weak wave-equation constraint
Uncertainty quantification for inverse problems with a weak wave-equation constraint Zhilong Fang*, Curt Da Silva*, Rachel Kuske** and Felix J. Herrmann* *Seismic Laboratory for Imaging and Modeling (SLIM),
More informationYouzuo Lin and Lianjie Huang
PROCEEDINGS, Thirty-Ninth Workshop on Geothermal Reservoir Engineering Stanford University, Stanford, California, February 24-26, 2014 SGP-TR-202 Building Subsurface Velocity Models with Sharp Interfaces
More informationSPARSE SIGNAL RESTORATION. 1. Introduction
SPARSE SIGNAL RESTORATION IVAN W. SELESNICK 1. Introduction These notes describe an approach for the restoration of degraded signals using sparsity. This approach, which has become quite popular, is useful
More informationSUMMARY. The main contribution of this paper is threefold. First, we show that FWI based on the Helmholtz equation has the advantage
Randomized full-waveform inversion: a dimenstionality-reduction approach Peyman P. Moghaddam and Felix J. Herrmann, University of British Columbia, Canada SUMMARY Full-waveform inversion relies on the
More informationc 2011 International Press Vol. 18, No. 1, pp , March DENNIS TREDE
METHODS AND APPLICATIONS OF ANALYSIS. c 2011 International Press Vol. 18, No. 1, pp. 105 110, March 2011 007 EXACT SUPPORT RECOVERY FOR LINEAR INVERSE PROBLEMS WITH SPARSITY CONSTRAINTS DENNIS TREDE Abstract.
More informationStochastic Gradient Descent. CS 584: Big Data Analytics
Stochastic Gradient Descent CS 584: Big Data Analytics Gradient Descent Recap Simplest and extremely popular Main Idea: take a step proportional to the negative of the gradient Easy to implement Each iteration
More informationAdaptive Primal Dual Optimization for Image Processing and Learning
Adaptive Primal Dual Optimization for Image Processing and Learning Tom Goldstein Rice University tag7@rice.edu Ernie Esser University of British Columbia eesser@eos.ubc.ca Richard Baraniuk Rice University
More informationUncertainty quantification for Wavefield Reconstruction Inversion
Uncertainty quantification for Wavefield Reconstruction Inversion Zhilong Fang *, Chia Ying Lee, Curt Da Silva *, Felix J. Herrmann *, and Rachel Kuske * Seismic Laboratory for Imaging and Modeling (SLIM),
More informationSparsity- and continuity-promoting seismic image recovery. with curvelet frames
Sparsity- and continuity-promoting seismic image recovery with curvelet frames Felix J. Herrmann, Peyman Moghaddam and Chris Stolk Seismic Laboratory for Imaging and Modeling, Department of Earth and Ocean
More information2012 SEG SEG Las Vegas 2012 Annual Meeting Page 1
Wei Huang *, Kun Jiao, Denes Vigh, Jerry Kapoor, David Watts, Hongyan Li, David Derharoutian, Xin Cheng WesternGeco Summary Since the 1990s, subsalt imaging in the Gulf of Mexico (GOM) has been a major
More informationUncertainty quantification for Wavefield Reconstruction Inversion
using a PDE free semidefinite Hessian and randomize-then-optimize method Zhilong Fang *, Chia Ying Lee, Curt Da Silva, Tristan van Leeuwen and Felix J. Herrmann Seismic Laboratory for Imaging and Modeling
More information23855 Rock Physics Constraints on Seismic Inversion
23855 Rock Physics Constraints on Seismic Inversion M. Sams* (Ikon Science Ltd) & D. Saussus (Ikon Science) SUMMARY Seismic data are bandlimited, offset limited and noisy. Consequently interpretation of
More informationMaking Flippy Floppy
Making Flippy Floppy James V. Burke UW Mathematics jvburke@uw.edu Aleksandr Y. Aravkin IBM, T.J.Watson Research sasha.aravkin@gmail.com Michael P. Friedlander UBC Computer Science mpf@cs.ubc.ca Current
More informationCurvelet imaging & processing: sparseness constrained least-squares migration
Curvelet imaging & processing: sparseness constrained least-squares migration Felix J. Herrmann and Peyman P. Moghaddam (EOS-UBC) felix@eos.ubc.ca & www.eos.ubc.ca/~felix thanks to: Gilles, Peyman and
More informationMaking Flippy Floppy
Making Flippy Floppy James V. Burke UW Mathematics jvburke@uw.edu Aleksandr Y. Aravkin IBM, T.J.Watson Research sasha.aravkin@gmail.com Michael P. Friedlander UBC Computer Science mpf@cs.ubc.ca Vietnam
More informationFrequency-Domain Rank Reduction in Seismic Processing An Overview
Frequency-Domain Rank Reduction in Seismic Processing An Overview Stewart Trickett Absolute Imaging Inc. Summary Over the last fifteen years, a new family of matrix rank reduction methods has been developed
More informationCompressed sensing. Or: the equation Ax = b, revisited. Terence Tao. Mahler Lecture Series. University of California, Los Angeles
Or: the equation Ax = b, revisited University of California, Los Angeles Mahler Lecture Series Acquiring signals Many types of real-world signals (e.g. sound, images, video) can be viewed as an n-dimensional
More informationSparsity- and continuity-promoting seismic image recovery with curvelet frames
Appl. Comput. Harmon. Anal. 24 (2008) 150 173 www.elsevier.com/locate/acha Sparsity- and continuity-promoting seismic image recovery with curvelet frames Felix J. Herrmann a,, Peyman Moghaddam a, Christiaan
More informationCoherent imaging without phases
Coherent imaging without phases Miguel Moscoso Joint work with Alexei Novikov Chrysoula Tsogka and George Papanicolaou Waves and Imaging in Random Media, September 2017 Outline 1 The phase retrieval problem
More informationCompressive simultaneous full-waveform simulation
Compressive simultaneous full-waveform simulation Felix J. Herrmann 1, Yogi Erlangga 1 and Tim T. Y. Lin 1 (August 14, 2008) Running head: compressive simulations ABSTRACT The fact that the numerical complexity
More informationSparse Solutions of Systems of Equations and Sparse Modelling of Signals and Images
Sparse Solutions of Systems of Equations and Sparse Modelling of Signals and Images Alfredo Nava-Tudela ant@umd.edu John J. Benedetto Department of Mathematics jjb@umd.edu Abstract In this project we are
More informationEdge preserved denoising and singularity extraction from angles gathers
Edge preserved denoising and singularity extraction from angles gathers Felix Herrmann, EOS-UBC Martijn de Hoop, CSM Joint work Geophysical inversion theory using fractional spline wavelets: ffl Jonathan
More informationIntroduction to Compressed Sensing
Introduction to Compressed Sensing Alejandro Parada, Gonzalo Arce University of Delaware August 25, 2016 Motivation: Classical Sampling 1 Motivation: Classical Sampling Issues Some applications Radar Spectral
More informationSparsity and Compressed Sensing
Sparsity and Compressed Sensing Jalal Fadili Normandie Université-ENSICAEN, GREYC Mathematical coffees 2017 Recap: linear inverse problems Dictionary Sensing Sensing Sensing = y m 1 H m n y y 2 R m H A
More informationFull Waveform Inversion (FWI) with wave-equation migration. Gary Margrave Rob Ferguson Chad Hogan Banff, 3 Dec. 2010
Full Waveform Inversion (FWI) with wave-equation migration (WEM) and well control Gary Margrave Rob Ferguson Chad Hogan Banff, 3 Dec. 2010 Outline The FWI cycle The fundamental theorem of FWI Understanding
More informationSparsity Regularization
Sparsity Regularization Bangti Jin Course Inverse Problems & Imaging 1 / 41 Outline 1 Motivation: sparsity? 2 Mathematical preliminaries 3 l 1 solvers 2 / 41 problem setup finite-dimensional formulation
More informationCombining Sparsity with Physically-Meaningful Constraints in Sparse Parameter Estimation
UIUC CSL Mar. 24 Combining Sparsity with Physically-Meaningful Constraints in Sparse Parameter Estimation Yuejie Chi Department of ECE and BMI Ohio State University Joint work with Yuxin Chen (Stanford).
More informationCompressive-wavefield simulations
Compressive-wavefield simulations Felix Herrmann Yogi Erlangga, Tim. Lin To cite this version: Felix Herrmann Yogi Erlangga, Tim. Lin. Compressive-wavefield simulations. Laurent Fesquet and Bruno Torrésani.
More informationGraph Partitioning Using Random Walks
Graph Partitioning Using Random Walks A Convex Optimization Perspective Lorenzo Orecchia Computer Science Why Spectral Algorithms for Graph Problems in practice? Simple to implement Can exploit very efficient
More informationElastic least-squares reverse time migration
CWP-865 Elastic least-squares reverse time migration Yuting Duan, Paul Sava, and Antoine Guitton Center for Wave Phenomena, Colorado School of Mines ABSTRACT Least-squares migration (LSM) can produce images
More informationTRACKING SOLUTIONS OF TIME VARYING LINEAR INVERSE PROBLEMS
TRACKING SOLUTIONS OF TIME VARYING LINEAR INVERSE PROBLEMS Martin Kleinsteuber and Simon Hawe Department of Electrical Engineering and Information Technology, Technische Universität München, München, Arcistraße
More informationAttenuation compensation in least-squares reverse time migration using the visco-acoustic wave equation
Attenuation compensation in least-squares reverse time migration using the visco-acoustic wave equation Gaurav Dutta, Kai Lu, Xin Wang and Gerard T. Schuster, King Abdullah University of Science and Technology
More informationPluto 1.5 2D ELASTIC MODEL FOR WAVEFIELD INVESTIGATIONS OF SUBSALT OBJECTIVES, DEEP WATER GULF OF MEXICO*
Pluto 1.5 2D ELASTIC MODEL FOR WAVEFIELD INVESTIGATIONS OF SUBSALT OBJECTIVES, DEEP WATER GULF OF MEXICO* *This paper has been submitted to the EAGE for presentation at the June 2001 EAGE meeting. SUMMARY
More informationSparsity-Preserving Difference of Positive Semidefinite Matrix Representation of Indefinite Matrices
Sparsity-Preserving Difference of Positive Semidefinite Matrix Representation of Indefinite Matrices Jaehyun Park June 1 2016 Abstract We consider the problem of writing an arbitrary symmetric matrix as
More informationNew Coherence and RIP Analysis for Weak. Orthogonal Matching Pursuit
New Coherence and RIP Analysis for Wea 1 Orthogonal Matching Pursuit Mingrui Yang, Member, IEEE, and Fran de Hoog arxiv:1405.3354v1 [cs.it] 14 May 2014 Abstract In this paper we define a new coherence
More informationMLCC 2018 Variable Selection and Sparsity. Lorenzo Rosasco UNIGE-MIT-IIT
MLCC 2018 Variable Selection and Sparsity Lorenzo Rosasco UNIGE-MIT-IIT Outline Variable Selection Subset Selection Greedy Methods: (Orthogonal) Matching Pursuit Convex Relaxation: LASSO & Elastic Net
More informationIs the test error unbiased for these programs? 2017 Kevin Jamieson
Is the test error unbiased for these programs? 2017 Kevin Jamieson 1 Is the test error unbiased for this program? 2017 Kevin Jamieson 2 Simple Variable Selection LASSO: Sparse Regression Machine Learning
More informationSummary. Introduction
Detailed velocity model building in a carbonate karst zone and improving sub-karst images in the Gulf of Mexico Jun Cai*, Hao Xun, Li Li, Yang He, Zhiming Li, Shuqian Dong, Manhong Guo and Bin Wang, TGS
More informationWE SRS2 11 ADAPTIVE LEAST-SQUARES RTM FOR SUBSALT IMAGING
Technical paper WE SRS2 11 ADAPTIVE LEAST-SQUARES RTM FOR SUBSALT IMAGING Authors C. Zeng (TGS), S. Dong (TGS), B. Wang (TGS) & Z. Zhang* (TGS) 2016 TGS-NOPEC Geophysical Company ASA. All rights reserved.
More informationECS171: Machine Learning
ECS171: Machine Learning Lecture 4: Optimization (LFD 3.3, SGD) Cho-Jui Hsieh UC Davis Jan 22, 2018 Gradient descent Optimization Goal: find the minimizer of a function min f (w) w For now we assume f
More informationTu N Fault Shadow Removal over Timor Trough Using Broadband Seismic, FWI and Fault Constrained Tomography
Tu N118 05 Fault Shadow Removal over Timor Trough Using Broadband Seismic, FWI and Fault Constrained Tomography Y. Guo* (CGG), M. Fujimoto (INPEX), S. Wu (CGG) & Y. Sasaki (INPEX) SUMMARY Thrust-complex
More informationGeneralized Orthogonal Matching Pursuit- A Review and Some
Generalized Orthogonal Matching Pursuit- A Review and Some New Results Department of Electronics and Electrical Communication Engineering Indian Institute of Technology, Kharagpur, INDIA Table of Contents
More informationCS598 Machine Learning in Computational Biology (Lecture 5: Matrix - part 2) Professor Jian Peng Teaching Assistant: Rongda Zhu
CS598 Machine Learning in Computational Biology (Lecture 5: Matrix - part 2) Professor Jian Peng Teaching Assistant: Rongda Zhu Feature engineering is hard 1. Extract informative features from domain knowledge
More informationIncomplete Cholesky preconditioners that exploit the low-rank property
anapov@ulb.ac.be ; http://homepages.ulb.ac.be/ anapov/ 1 / 35 Incomplete Cholesky preconditioners that exploit the low-rank property (theory and practice) Artem Napov Service de Métrologie Nucléaire, Université
More informationSparse Optimization Lecture: Basic Sparse Optimization Models
Sparse Optimization Lecture: Basic Sparse Optimization Models Instructor: Wotao Yin July 2013 online discussions on piazza.com Those who complete this lecture will know basic l 1, l 2,1, and nuclear-norm
More informationOptimal Value Function Methods in Numerical Optimization Level Set Methods
Optimal Value Function Methods in Numerical Optimization Level Set Methods James V Burke Mathematics, University of Washington, (jvburke@uw.edu) Joint work with Aravkin (UW), Drusvyatskiy (UW), Friedlander
More informationSparse Approximation of Signals with Highly Coherent Dictionaries
Sparse Approximation of Signals with Highly Coherent Dictionaries Bishnu P. Lamichhane and Laura Rebollo-Neira b.p.lamichhane@aston.ac.uk, rebollol@aston.ac.uk Support from EPSRC (EP/D062632/1) is acknowledged
More informationSPARSE signal representations have gained popularity in recent
6958 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 57, NO. 10, OCTOBER 2011 Blind Compressed Sensing Sivan Gleichman and Yonina C. Eldar, Senior Member, IEEE Abstract The fundamental principle underlying
More informationInverse problems and sparse models (1/2) Rémi Gribonval INRIA Rennes - Bretagne Atlantique, France
Inverse problems and sparse models (1/2) Rémi Gribonval INRIA Rennes - Bretagne Atlantique, France remi.gribonval@inria.fr Structure of the tutorial Session 1: Introduction to inverse problems & sparse
More informationSparse regression. Optimization-Based Data Analysis. Carlos Fernandez-Granda
Sparse regression Optimization-Based Data Analysis http://www.cims.nyu.edu/~cfgranda/pages/obda_spring16 Carlos Fernandez-Granda 3/28/2016 Regression Least-squares regression Example: Global warming Logistic
More informationOne-step extrapolation method for reverse time migration
GEOPHYSICS VOL. 74 NO. 4 JULY-AUGUST 2009; P. A29 A33 5 FIGS. 10.1190/1.3123476 One-step extrapolation method for reverse time migration Yu Zhang 1 and Guanquan Zhang 2 ABSTRACT We have proposed a new
More information1 / 21 Perturbation of system dynamics and the covariance completion problem Armin Zare Joint work with: Mihailo R. Jovanović Tryphon T. Georgiou 55th
1 / 21 Perturbation of system dynamics and the covariance completion problem Armin Zare Joint work with: Mihailo R. Jovanović Tryphon T. Georgiou 55th IEEE Conference on Decision and Control, Las Vegas,
More informationReconstruction of Block-Sparse Signals by Using an l 2/p -Regularized Least-Squares Algorithm
Reconstruction of Block-Sparse Signals by Using an l 2/p -Regularized Least-Squares Algorithm Jeevan K. Pant, Wu-Sheng Lu, and Andreas Antoniou University of Victoria May 21, 2012 Compressive Sensing 1/23
More informationFighting the curse of dimensionality: compressive sensing in exploration seismology
Fighting the curse of dimensionality: compressive sensing in exploration seismology Felix J. Herrmann, Michael P. Friedlander, Özgür Yılmaz January 2, 202 Abstract Many seismic exploration techniques rely
More informationTOM 1.7. Sparse Norm Reflection Tomography for Handling Velocity Ambiguities
SEG/Houston 2005 Annual Meeting 2554 Yonadav Sudman, Paradigm and Dan Kosloff, Tel-Aviv University and Paradigm Summary Reflection seismology with the normal range of offsets encountered in seismic surveys
More informationIntroduction How it works Theory behind Compressed Sensing. Compressed Sensing. Huichao Xue. CS3750 Fall 2011
Compressed Sensing Huichao Xue CS3750 Fall 2011 Table of Contents Introduction From News Reports Abstract Definition How it works A review of L 1 norm The Algorithm Backgrounds for underdetermined linear
More informationImproving L-BFGS Initialization for Trust-Region Methods in Deep Learning
Improving L-BFGS Initialization for Trust-Region Methods in Deep Learning Jacob Rafati http://rafati.net jrafatiheravi@ucmerced.edu Ph.D. Candidate, Electrical Engineering and Computer Science University
More informationParticle Filtered Modified-CS (PaFiMoCS) for tracking signal sequences
Particle Filtered Modified-CS (PaFiMoCS) for tracking signal sequences Samarjit Das and Namrata Vaswani Department of Electrical and Computer Engineering Iowa State University http://www.ece.iastate.edu/
More informationSparse Approximation and Variable Selection
Sparse Approximation and Variable Selection Lorenzo Rosasco 9.520 Class 07 February 26, 2007 About this class Goal To introduce the problem of variable selection, discuss its connection to sparse approximation
More informationRobust one-step (deconvolution + integration) seismic inversion in the frequency domain Ivan Priezzhev* and Aaron Scollard, Schlumberger
Robust one-step (deconvolution + integration) seismic inversion in the frequency domain Ivan Priezzhev and Aaron Scollard, Schlumberger Summary Seismic inversion requires two main operations relative to
More informationBlock stochastic gradient update method
Block stochastic gradient update method Yangyang Xu and Wotao Yin IMA, University of Minnesota Department of Mathematics, UCLA November 1, 2015 This work was done while in Rice University 1 / 26 Stochastic
More informationSolving DC Programs that Promote Group 1-Sparsity
Solving DC Programs that Promote Group 1-Sparsity Ernie Esser Contains joint work with Xiaoqun Zhang, Yifei Lou and Jack Xin SIAM Conference on Imaging Science Hong Kong Baptist University May 14 2014
More informationLine Search Methods for Unconstrained Optimisation
Line Search Methods for Unconstrained Optimisation Lecture 8, Numerical Linear Algebra and Optimisation Oxford University Computing Laboratory, MT 2007 Dr Raphael Hauser (hauser@comlab.ox.ac.uk) The Generic
More informationResearch Project Report
Research Project Report Title: Prediction of pre-critical seismograms from post-critical traces Principal Investigator: Co-principal Investigators: Mrinal Sen Arthur Weglein and Paul Stoffa Final report
More informationEarth models for early exploration stages
ANNUAL MEETING MASTER OF PETROLEUM ENGINEERING Earth models for early exploration stages Ângela Pereira PhD student angela.pereira@tecnico.ulisboa.pt 3/May/2016 Instituto Superior Técnico 1 Outline Motivation
More informationApproximate Message Passing for Bilinear Models
Approximate Message Passing for Bilinear Models Volkan Cevher Laboratory for Informa4on and Inference Systems LIONS / EPFL h,p://lions.epfl.ch & Idiap Research Ins=tute joint work with Mitra Fatemi @Idiap
More informationMultiplicative and Additive Perturbation Effects on the Recovery of Sparse Signals on the Sphere using Compressed Sensing
Multiplicative and Additive Perturbation Effects on the Recovery of Sparse Signals on the Sphere using Compressed Sensing ibeltal F. Alem, Daniel H. Chae, and Rodney A. Kennedy The Australian National
More informationA robust multilevel approximate inverse preconditioner for symmetric positive definite matrices
DICEA DEPARTMENT OF CIVIL, ENVIRONMENTAL AND ARCHITECTURAL ENGINEERING PhD SCHOOL CIVIL AND ENVIRONMENTAL ENGINEERING SCIENCES XXX CYCLE A robust multilevel approximate inverse preconditioner for symmetric
More informationAnisotropic tomography for TTI and VTI media Yang He* and Jun Cai, TGS
media Yang He* and Jun Cai, TGS Summary A simultaneous anisotropic tomographic inversion algorithm is developed. Check shot constraints and appropriate algorithm preconditioning play an important role
More informationLecture 22: More On Compressed Sensing
Lecture 22: More On Compressed Sensing Scribed by Eric Lee, Chengrun Yang, and Sebastian Ament Nov. 2, 207 Recap and Introduction Basis pursuit was the method of recovering the sparsest solution to an
More informationDenosing Using Wavelets and Projections onto the l 1 -Ball
1 Denosing Using Wavelets and Projections onto the l 1 -Ball October 6, 2014 A. Enis Cetin, M. Tofighi Dept. of Electrical and Electronic Engineering, Bilkent University, Ankara, Turkey cetin@bilkent.edu.tr,
More informationwhere κ is a gauge function. The majority of the solvers available for the problems under consideration work with the penalized version,
SPARSE OPTIMIZATION WITH LEAST-SQUARES CONSTRAINTS ON-LINE APPENDIX EWOUT VAN DEN BERG AND MICHAEL P. FRIEDLANDER Appendix A. Numerical experiments. This on-line appendix accompanies the paper Sparse optimization
More informationWhy should you care about the solution strategies?
Optimization Why should you care about the solution strategies? Understanding the optimization approaches behind the algorithms makes you more effectively choose which algorithm to run Understanding the
More informationof Orthogonal Matching Pursuit
A Sharp Restricted Isometry Constant Bound of Orthogonal Matching Pursuit Qun Mo arxiv:50.0708v [cs.it] 8 Jan 205 Abstract We shall show that if the restricted isometry constant (RIC) δ s+ (A) of the measurement
More informationTh P7 02 A Method to Suppress Salt-related Converted Wave Using 3D Acoustic Modelling
Th P7 0 A Method to Suppress Salt-related Converted Wave Using 3D Acoustic Modelling J. Kumar* (Petroleum Geo-Services), M. Salem (ENI E&P), D.E. Cegani (ENI E&P) Summary Converted waves can be recorded
More information