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`IN THE UNITED STATES PATENT AND TRADEMARK OFFICE
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`______________________
`
`BEFORE THE PATENT TRIAL AND APPEAL BOARD
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`______________________
`
`IN-DEPTH GEOPHYSICAL, INC. AND IN-DEPTH COMPRESSIVE SEISMIC,
`INC.
`
`Petitioner,
`
`v.
`
`CONOCOPHILLIPS COMPANY,
`
`Patent Owner.
`______________________
`Case No. IPR2019-_________________
`U.S. Patent 9,632,193
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`
`DECLARATION OF OZGUR YILMAZ
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`Table of Contents
`Introduction ...................................................................................................... 4
`I.
`Education and Experience ............................................................................... 4
`II.
`III. Materials Considered ....................................................................................... 7
`IV. Overview of Compressive Sensing.................................................................. 9
`V.
`Person of Ordinary Skill in the Art ................................................................ 10
`VI. The ’193 Patent .............................................................................................. 12
`VII. Legal principles relevant to my analysis ....................................................... 14
`1. Claim Construction ...................................................................................... 14
`2. Anticipation ................................................................................................. 17
`3. Obviousness ................................................................................................. 18
`VIII. Claim construction and understanding. ......................................................... 20
`IX. Claims 1, 5 and 6 of the ‘193 Patent are obvious under 35 U.S.C. § 103 in
`view of Li, Donoho, Hennenfent I and Hennenfent II. ................................. 21
`1. Overview of Li ............................................................................................ 21
`2. Overview of Donoho ................................................................................... 22
`3. Overview of Hennenfent I ........................................................................... 23
`4. Overview of Hennenfent II .......................................................................... 23
`5. Motivation to combine and expectation of success. .................................... 24
`6. The combination of Li, Donoho, Hennenfent I and Hennenfent II discloses
`all the limitations of claims 1, 5 and 6. .............................................................. 27
`Claims 2 and 3 of the ‘193 Patent are obvious under 35 U.S.C. § 103 in view
`of Li, Donoho, Hennenfent I, Hennenfent II and Essays and Surveys in
`Metaheuristics ................................................................................................ 33
`1. Overview of Essays and Surveys ................................................................ 33
`2. Motivation to combine and expectation of success ..................................... 33
`3. The combination of Li, Donoho, Hennenfent I, Hennenfent II and Essays
`and Surveys discloses all the limitations of claims 2 and 3. ............................. 34
`
`X.
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`XI. Claim 4 of the ‘193 Patent is obvious under 35 U.S.C. § 103 in view of Li,
`Donoho, Hennenfent I, Hennenfent II and International Encyclopedia of
`Statistical Science .......................................................................................... 38
`1. Overview of International Encyclopedia ..................................................... 38
`2. Motivation to combine and expectation of success. .................................... 38
`3. The combination of Li, Donoho, Hennenfent I, Hennenfent II, and
`International Encyclopedia discloses all the limitations of claim 4. ................. 39
`XII. Conclusion ..................................................................................................... 41
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`I.
`Introduction
`I, Ozgur Yilmaz of Vancouver, British Columbia, Canada, do hereby declare that:
`
`1.
`
`2.
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`I am over the age of 18 and competent to make this declaration.
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`I have been retained by In-Depth Geophysical, Inc. and In-Depth
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`Compressive Seismic, Inc. (hereinafter “In-Depth”) to offer my professional
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`opinions in connection with the inter partes review (IPR) of U.S. Patent 9,632,193
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`(the ‘193 Patent). I am being compensated at my normal consulting rate (plus
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`expenses) of $500 per hour for my work related to the IPR. The compensation I
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`receive is in no way dependent on the outcome of this dispute or the testimony or
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`opinions that I give. I have no personal interest or financial stake in the outcome of
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`the litigation between the parties.
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`3.
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`It is my understanding that the ‘193 Patent (IDG-1001) was issued on
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`April 25, 2017, based on an application filed on October 31, 2014, which claims the
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`benefit of a provisional application filed November 1, 2013 (IDG-1009). It is my
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`understanding that the current owner of the ‘193 patent is ConocoPhillips.
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`4.
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`This declaration is provided in support of the Petition filed in
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`connection with the IPR.
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`II. Education and Experience
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`5.
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`I am qualified by education and experience to testify as an expert in the
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`field of seismic imaging and compressive sensing. My curriculum vitae is attached
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`as Exhibit A, which fully describes my experience, education and publications
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`within the last 10 years. I have not testified as an expert in a deposition or at trial in
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`the past 4 years.
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`6.
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`I am currently a Professor of Mathematics at the University of British
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`Columbia (“UBC”) and serve as the Associate Head for Research in the Mathematics
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`Department of UBC.
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`7.
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`I am also a Faculty Member in the Institute of Applied Mathematics at
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`UBC, a Faculty Member in the Institute for Computing, Information and Cognitive
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`Systems (“ICICS”) at UBC, and a Faculty Member of the UBC Data Science
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`Institute.
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`8.
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`I have extensive experience in the areas of applied and computational
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`harmonic analysis and signal processing, focusing on the areas of analog-to-digital
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`conversion, blind source separation, sparse approximations and compressive
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`sensing, and applications of these in seismic signal processing.
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`9.
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`I am on the Editorial Boards of two top-tier journals in the areas of my
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`expertise -- IEEE Transactions on Signal Processing and Applied and Computational
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`Harmonic Analysis.
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`10.
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`I have received several research grants from the Natural Sciences and
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`Engineering Research Council of Canada (“NSERC”) including a prestigious
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`NSERC Discovery Accelerator Award.
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`11. My research has also been funded by grants secured from the Pacific
`
`Institute of Mathematical Sciences (“PIMS”), the UBC Data Science Institute, in
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`addition to NSERC. Currently I am co-leading a PIMS “collaborative research
`
`group” in “High-dimensional data analysis” focusing on bridging the gap between
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`the theory of compressive sensing (and its offshoots) and the industrial uptake.
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`12.
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`I was one of the three co-principal investigators of two NSERC
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`Collaborative Research and Development grants that funded research on developing
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`ways to leverage results from compressive sensing and mathematical signal
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`processing to be used in cutting-edge problems in seismic data and image
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`processing. Our group made several fundamental contributions that paved the way
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`to the use of compressive sensing in exploration seismology.
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`13. The alumni of my group have an excellent track record. A former PhD
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`student of mine is now a tenured associate professor at University of California, San
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`Diego. A postdoctoral researcher I have supervised is now a tenure-track assistant
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`professor in Michigan State University. Another postdoctoral researcher I have
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`supervised is now an associate professor in DePaul University. I have also
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`supervised two PhD students working on industrial projects whose work was funded
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`by “Mitacs Accelerate” grants, which are industry partnership grants.
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`14.
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`I earned my Bachelor of Science Degrees in Mathematics and in
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`Electrical Engineering, both in June 1997, from Bogazici University (Istanbul). I
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`earned my PhD in Applied and Computational Mathematics from Princeton
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`University in 2001.
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`III. Materials Considered
`15. My opinions and conclusions are fully discussed later in this report. In
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`reaching these opinions and conclusions, I have relied upon my education,
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`experience and training, my review of the ‘193 Patent, its prosecution history and
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`other materials referred to herein. Throughout this report, I cite portions of the
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`documents I reviewed, which are intended only as examples. I reserve the right to
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`rely on other portions of the same documents in addition to those cited herein.
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`16.
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`In formulating my opinions, I have considered the following materials,
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`and any other materials referenced in this declaration by Exhibit Number:
`
`Exhibit Description
`---
`IPR Petition ‘193
`IDG-1001 U.S. Patent 9,632,193
`IDG-1002 Complaint, 4:18-CV-00803; ConocoPhillips Company v. In-Depth
`Compressive Seismic, Inc. and In-Depth Geophysical, Inc.; In the
`United States District Court for the Southern District of Texas,
`Houston Division (Lake)
`IDG-1004 U.S. Application 14/529,690 Image File Wrapper Index and File
`Wrapper
`IDG-1005 Li, et al.; Interpolated compressive sensing for seismic data
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`reconstruction; Society of Exploration Geophysicists; 2012 (“Li”)
`IDG-1006 Communication of October 19, 2016, European Patent Application
`No. 14857735.6, Compressive Sensing.
`IDG-1007 Amendment by Applicant of April 27, 2017, European Patent
`Application No. 14857735.6, Compressive Sensing.
`IDG-1008 Hennenfent and Herrmann; Application of stable signal recovery to
`seismic data interpolation; Society of Exploration Geophysicists;
`2006 (“Hennenfent I”)
`IDG-1009 Provision Application 61/898,960, “Compressive Sensing,” filed
`November 1, 2013
`IDG-1010 Hennenfent and Herrmann; Simply denoise: Wavefield
`reconstruction via jittered undersampling; March 14, 2008
`(“Hennenfent II”)
`IDG-1011 Researchgate.net; Interpolated compressive sensing for seismic data
`reconstruction; 5 pages, retrieved January 31, 2019 (“Researchgate”)
`IDG-1012 Donoho, Elad, and Temlyakov; Stable Recovery of Sparse
`Overcomplete Representations in the Presence of Noise; IEEE
`Transactions on Information Theory, Vol. 52, No. 1, January 2006.
`(“Donoho”)
`IDG-1013 Festa and Resende; Chapter 15, GRASP: An Annotated
`Bibliography, Essays and Surveys in Metaheuristics; p. 325-367;
`2002 (“Essays and Surveys”)
`IDG-1015 Anatoly Zhigljavasky; International Encyclopedia of Statistical
`Science, “Stochastic Global Optimization” (“International
`Encyclopedia”)
`IDG-1016 P.R. 4-3 Joint Claim Construction and Prehearing Statement, 4:18-
`CV-00803; ConocoPhillips Company v. In-Depth Compressive
`Seismic, Inc. and In-Depth Geophysical, Inc.; In the United States
`District Court for the Southern District of Texas, Houston Division
`(Lake)
`
`17. For purposes of clarity and consistency, all references to an exhibit will
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`include the pdf page of the exhibit (e.g., IDG-1001, p. 3 is the third page in the IDG-
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`1001 pdf file) and not any internal page number.
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`18.
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`I wish to reserve any right that I may have to supplement this
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`declaration if further information becomes available or if I am asked to consider
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`additional information. Furthermore, I wish to reserve any right that I may have to
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`consider and comment on expert statements and testimony offered by any expert
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`designated by ConocoPhillips Company (“Conoco”) in the matter. I may also rely
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`on demonstrative exhibits to explain my testimony and opinions.
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`IV. Overview of Compressive Sensing
`19. Seismic surveys are used to acquire seismic data with the ultimate goal
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`of constructing seismic images from the seismic data acquired. Seismic images are
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`images of the underground. The acquisition involves (i) fixing a survey area – which
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`is on land or in a marine environment, (ii) placing a certain number of sensors (e.g.,
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`geophones when the survey area is on land), (iii) conducting seismic experiments by
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`placing sources (e.g., specialized air guns) at certain locations in the survey area and
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`sending mechanical perturbations down into the Earth, (iv) collecting recordings
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`(a.k.a., “measurements” or “samples”) via the sensors, and (v) processing the
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`acquired measurements using specialized software to bring the data into a form that
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`is amenable to producing a corresponding seismic image.
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`20. One of the attributes of step (ii) above is how the sensors are distributed
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`on the survey area. If they are spaced regularly (i.e., neighboring sensors are
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`uniformly spaced), the result is a “regular sampling grid” or “regular acquisition
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`grid.” Traditional processing and imaging methods prefer a regular sampling grid
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`because it is easier to interpret. However, in many applications, there are physical
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`obstacles (e.g., a river, a highway) or malfunctioning geophones that make it
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`impossible to collect the seismic data on a regular sampling grid. In this case, the
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`missing seismic data is recovered from the samples obtained on a sampling grid that,
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`due to obstacles, is irregular. This mathematical challenge, as shown by Hennenfent
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`II (IDG-1010), can be successfully resolved using “compressive sensing”
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`techniques.
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`21. Compressive sensing is a data acquisition paradigm proposed by David
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`Donoho in “Compressed Sensing,” IEEE Transactions on Information Theory, Vol.
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`52, No. 4, April of 2006 and has evolved since then. By 2013, the application of
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`compressive sensing to particular fields such as medical imaging and seismic
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`imaging was also well-known.
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`22. Compressive sensing has improved techniques for designing seismic
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`data surveys and reconstructing seismic data based on the acquired seismic data, in
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`a more cost-efficient way compared to conventional techniques. These techniques
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`were observed and derived in 2008, as evidenced by Hennenfent II (IDG-1010).
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`V. Person of Ordinary Skill in the Art
`23.
`I understand that a person of ordinary skill in the art (a “POSITA”) is a
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`hypothetical person considered to have normal skills and knowledge in the field to
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`which the patent relates as of the effective filing date of the patent application, which
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`I understand to be November 1, 2013 for the ‘193 Patent. I also understand that the
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`following factors may be considered in determining the level of ordinary skill in the
`
`art: type of problems encountered in the art; prior art solutions to those problems;
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`speed with which innovations are made; sophistication of the technology; and
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`educational level of active workers in the field.
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`24. After reviewing the ‘193 Patent and other materials referred to herein,
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`it is my opinion that a POSITA in the field of the ‘193 patent as of November 1,
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`2013 would have possessed a graduate degree (Masters) in Earth Sciences,
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`Geophysics, Applied Mathematics, or a similar discipline, and had at least two years
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`of experience working on seismic data and/or seismic image processing, and the
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`design and/or use of software tailored to seismic signal processing. Such a person
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`would be familiar with basic principles of compressive sensing including those that
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`can be leveraged to improve the design of seismic surveys. It is possible that a person
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`of ordinary skill in the art may have possessed a more advanced degree in a
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`particularly relevant field but less work experience or may lack the graduate degree
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`but have more work experience. This level of knowledge and skill as of November
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`1, 2013 is applied throughout my opinion.
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`25.
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`In arriving at my opinions, I have relied on my experience in seismic
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`imaging and compressive sensing and have considered the point of view of POSITA,
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`that is, a POSITA in the field of seismic imaging and compressive sensing in
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`November 2013.
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`26. Based on my educational background and work experience, I met the
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`standard for a POSITA well before November 1, 2013. My opinions therefore are
`
`based on my qualifications as a POSITA.
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`VI. The ’193 Patent
`27. The ‘193 Patent discloses computer-implemented methods for
`
`determining an optimal sampling grid during seismic data reconstruction. IDG-1001
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`at Abstract, 3:16-39. The ‘193 Patent observes that processing seismic data for
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`imaging may require recovering missing pieces of information from irregularly
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`acquired seismic data. Id. at 1:22-24. Such irregularities may be caused by, for
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`example, dead or severely corrupted seismic traces, surface obstacles, acquisition
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`apertures, economic limits, and the like. Id. at 1:25-27. Seismic processing
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`techniques may be employed to spatially transform irregularly acquired seismic data
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`to regularly sampled data that is easier to interpret. Id. at 1:27-30. This regularization
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`can involve processing techniques such as interpolation and reconstruction of
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`seismic data. Id. at 1:30-32.
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`28. Compressive sensing techniques are well-known and have been used
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`for seismic data reconstruction since at least 2008. Id. at 1:33-36. Compressive
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`sensing techniques have also been used for survey design using an irregular sampling
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`grid since at least 2008. Id. at 2:8-12. Designing such a survey based on
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`compressive sensing can be summarized by the following steps: 1) determine a
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`nominal regular grid for the survey area, 2) choose a subset of locations from the
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`nominal grid in a random or randomly jittered fashion, 3) acquire seismic data based
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`on the chosen locations, and 4) reconstruct the data back to the original nominal grid.
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`Id. at 2:12-19.
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`29. The irregular sampling grid (step 2) is based, in part, on an optimization
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`model. One optimization model is given by:
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`
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`wherein S is a discrete transform matrix, b is seismic data on an observed grid, u is
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`seismic data on a reconstruction grid, and matrix R is a sampling operator Id. at 3:40-
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`46, 6:1-16 and 13:40-44 (referencing “Candes et al. 2008”). The irregular sampling
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`grid is also based on defining mutual coherence and deriving a mutual coherence
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`proxy.
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`30. Mutual coherence can be used to quantify the irregularity in seismic
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`data. Id. at 4:61-62. Mutual coherence is further described as “an important metric
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`in compressive sensing theory” and “can also be expensive to compute.” Id. at 1:50-
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`51. Mutual coherence is defined by equation 32 (EQ32), which is a function of S and
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`R and prohibitively expensive to compute: µ(R,S)=maxi≠j |d*idj|, i,j=1…n. Id. at 14:2-
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`20. Due to the computational expense in computing mutual coherence, the ‘193
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`Patent proposes deriving a mutual coherence proxy that is more efficient to compute
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`than the mutual coherence in EQ 32. Id. at 14:16-24.
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`31. The process for deriving the mutual coherence proxy is described in the
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`specification using a discrete Fourier transform (DFT) matrix. Id. at 14:25-67. “If
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`S is a discrete Fourier transform matrix, then [S]i,j=ꞷij where ꞷ=exp(-2π√−1/𝑛).”
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`Id. at 14:45-46. Equation 37 (EQ 37) can be computed efficiently using the fast
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`Fourier transform, and is expressly defined as “our mutual coherence proxy.” Id. at
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`14:63-65. “It is exactly the mutual coherence when S is the Fourier transform, and
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`a proxy for mutual coherence when S is some overcomplete dictionary.” Id. at
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`14:65-67.
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`32. The sampling grid is given by equation 38:
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`r⁎=arg minr μ(r)
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`which is determined by minimizing the mutual coherence proxy. Id. at 15:4-13. The
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`sample grid is therefore, optimized by minimizing the MC proxy.
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`VII. Legal principles relevant to my analysis
`33. For the purposes of this Declaration, I have been informed about certain
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`aspects of the law that are relevant to my opinions. My understanding of the law is
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`set forth below.
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`1. Claim Construction
`34.
`I understand that ultimately the Board will determine the matter of how
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`specific terms shall be construed. The intent of this Declaration is to help inform the
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`Board how a person of ordinary skill in the art would understand the meaning of
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`certain disputed claim terms in a manner that will assist the Board in the process of
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`finding a proper set of constructions.
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`35.
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`I understand that the proper construction of a claim term is the ordinary
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`meaning that a POSITA would have given to that term at the time of the invention
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`(i.e., as of the effective filing date of the patent application) in the context of the
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`claim as a whole, the specification and prosecution history. I understand these
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`sources are referred to collectively as “intrinsic evidence,” which may also include
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`publications incorporated by reference in the specification and the prosecution
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`history.
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`36. Additionally, I understand
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`that “extrinsic” evidence, such as
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`dictionaries, articles, or learned treatises concerning relevant scientific principles,
`
`and the state of the art at the time of the invention may be considered in claim
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`construction. I understand, however, that extrinsic evidence should not be used to
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`override the meaning a claim term would have had to a POSITA based on the
`
`intrinsic evidence if the meaning is clear from the intrinsic evidence, and that in any
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`event, extrinsic evidence must be considered in the context of the intrinsic evidence.
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`37.
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`I also understand that in claim construction, features from examples in
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`the patent should not be imported into the definitions of the claim language if the
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`claim language is broader than the examples.
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`38.
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`It is also my understanding, however, that a term may be interpreted
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`more narrowly than it otherwise would if the patentee distinguished the term from
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`prior art on the basis of a particular embodiment, expressly disclaimed subject
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`matter, or described a particular embodiment as important to the invention.
`
`39.
`
`I understand that if the patent or prosecution history includes a clear
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`definition of a term, then the term should be construed consistent with that definition.
`
`40.
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`It is also my understanding that different terms used in a claim should
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`generally be construed to have different meanings.
`
`41.
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`I further understand that if, during prosecution, there are statements that
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`the invention is limited in any way, then a claim should not be construed to cover
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`the disclaimed subject matter.
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`42.
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`I understand that 35 U.S.C. § 112(a) recites: “The specification shall
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`conclude with one or more claims particularly pointing out and distinctly claiming
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`the subject matter which the applicant regard as his invention.” In order to meet this
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`standard, it is my understanding that a patent’s claims, read in light of the intrinsic
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`evidence, must apprise a POSITA of the scope of the invention with reasonable
`
`certainty. Put another way, the scope of the claims must be sufficiently definite to
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`inform the public of the subject matter that is covered by the exclusive rights of the
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`patent.
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`43.
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`I further understand that any special definition for a claim term must be
`
`set forth with reasonable clarity, deliberateness, and precision in the patent.
`
`44.
`
`I have considered the claim terms of the ‘362 patent using the
`
`aforementioned standard and rules of construction.
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`2. Anticipation
`45.
`I understand that the validity of patent claims is assessed on a claim-
`
`by-claim basis. In other words, each claim in a patent must be evaluated individually
`
`to determine if it is invalid in view of the relevant prior art. Therefore, it is possible
`
`that some claims in a patent may be valid and other claims may not be valid in view
`
`of the prior art.
`
`46.
`
`I understand that a patent claim is invalid if it is anticipated, which
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`requires that each and every element of the patent claim is disclosed expressly or
`
`inherently in a single prior art reference.
`
`47.
`
`I understand that an element of patent claim may be inherent in the prior
`
`art, even if it is not expressly disclosed in a prior art reference, when the device
`
`described in the prior art reference necessarily includes that element of the patent
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`claim.
`
`48.
`
`I also understand that a prior art reference must enable a POSITA to
`
`make and use the invention in the patent claim in order to anticipate the patent claim.
`
`49.
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`I understand that it is appropriate to consider references, in addition to
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`the particular prior art reference, in the context of analyzing anticipation where the
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`prior art reference is silent about an inherent characteristic and/or to determine
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`whether the prior art reference enables a POSITA to make and use a claimed
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`invention.
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`3. Obviousness
`50.
`I understand that a patent claim is invalid as obvious if the differences
`
`between the patent claim and the prior art are such that the subject matter of the
`
`claim as a whole would have been obvious to a POSITA at the relevant time.
`
`51.
`
`I further understand that a patent can be obvious in light of a single prior
`
`art reference if it would have been obvious to modify that reference to arrive at the
`
`patented invention.
`
`52.
`
`I also understand that the motivation to modify a prior art reference to
`
`arrive at the claimed invention need not be the same motivation that the patentee
`
`had.
`
`53.
`
`I understand that a patent claim is invalid as obvious if the differences
`
`between the patent claim and the prior art are such that the subject matter of the
`
`claim as a whole would have been obvious to a POSITA at the relevant time.
`
`54.
`
`I understand that the following factors are used in determining whether
`
`a patent claim is obvious: a) the scope and content of the prior art; b) the differences
`
`between the prior art and the patent claim; c) the level of ordinary skill in the art;
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`and d) any secondary considerations that tend to show the patent claim is not
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`obvious, such as commercial success of the patented invention, long-felt but unmet
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`need for the patented invention, failure of others to solve the problem the patented
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`invention solves, prior skepticism of the patented invention, praise for the patented
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`invention, and copying of the patented invention by competitors.
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`55.
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`I have been informed that a patent claim requiring several elements is
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`not obvious only if each of the elements was individually known or in the prior art,
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`but that there must have been an apparent reason (or “motivation to combine”) for a
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`POSITA to combine the teachings of the prior art references.
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`56.
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`I have also been informed that a POSITA must have had a “reasonable
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`expectation of success” that he or she would have arrived at the invention in a
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`particular patent claim by combining the teachings in the prior art references
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`57.
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`I understand that the motivation to combine and expectation of success
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`do not need to be explicit in the prior art references, but instead, a POSITA would
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`have used his or her own judgment, logic, and common sense.
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`58.
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`I have been informed that knowledge of a problem and a motivation to
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`solve that problem are not enough to make a patent claim obvious, and are different
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`from motivation to combine particular prior art references and an expectation of
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`success in doing so.
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`59.
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`I understand that using a patent’s claims as a blueprint to piece together
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`various elements in the prior art amounts to what is known as “hindsight reasoning,”
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`which is impermissible in an obviousness analysis.
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`60.
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`I understand that where there was market pressure to address a
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`particular problem, and a patent claim addresses one or more solutions to that
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`problem that had been identified previously, and were predictable solutions to solve
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`the problem, that tends to show that the patent claim is obvious.
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`61.
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`I also understand that if a POSITA could have arrived at the invention
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`in a patent claim through routine experimentation that tends to show that the patent
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`claim is obvious.
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`62.
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`I understand that in accordance with the above, obviousness may be
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`determined by asking whether a POSITA, facing the range of needs created by
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`developments in the field of endeavor, would have seen a benefit to modifying the
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`closest prior art by adding or removing the elements that differ between the prior art
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`and the patent claim at issue.
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`VIII. Claim construction and understanding.
`63. My opinions are based on the agreed and proposed claim constructions
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`in Section VII of the IPR Petition, which would be consistent with the understanding
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`of a POSITA. In my opinion, there is no industry standard or ordinary meaning
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`associated with deriving a Mutual Coherence proxy. In view of the prior art cited
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`herein, my opinions would not change under any reasonable construction of those
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`terms which are not agreed.
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`IX. Claims 1, 5 and 6 of the ‘193 Patent are obvious under 35 U.S.C. § 103
`in view of Li, Donoho, Hennenfent I and Hennenfent II.
`1. Overview of Li
`64. Li discloses the use of compressive sensing for seismic data
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`reconstruction. IDG-1005 at p. 1, Col. 1. Li notes that the optimal nominal grid for
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`reconstruction depends on factors including bandwidth of the data, geology and
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`noise level in the acquired data. Id. at p. 1. Col. 1. Li describes constructing an
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`optimization model based on the principles of compressed sensing for use in seismic
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`data reconstruction that is identical to the optimization model given in step (a) of
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`claim 1 for reconstruction of the seismic data. Id. at p. 1, Col. 2. Li discloses how
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`to use this optimization model after choosing a restriction operator that maps the
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`data acquired on a given sampling grid to data reconstructed on a nominal grid of
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`choice (which can be different from the sampling grid). Id. at p. 2, Col. 2, Eq (11).
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`Li focuses on improving the reconstruction by manipulating the choice of the
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`nominal grid while assuming the sampling grid given is fixed.
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`65. Li also references the potential application of mutual coherence to
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`acquisition design for compressive sensing data reconstruction. Id. at p. 5 (citing
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`Kaplan et al. “Application of mutual coherence to acquisition design for compressive
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`sensing data reconstruction,” 2012, personal communication)). Finally, Patent
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`Owner admits that Li is prior art that describes constructing the optimization model
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`given in step (a) and determining the same sample grid required in step (d). IDG-
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`1007 at replacement specification ¶7.
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`2. Overview of Donoho
`66. Donoho addresses overcomplete representations of sparse signals.
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`IDG-1012. Finding such representations corresponds to a linear algebra problem.
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`Consider “a matrix Φ so that Φ is n by m and m > n. A representation of y ∈ Rn can
`be thought of as a vector α ∈ Rm satisfying y = Φα. However, linear algebra tells us
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`that because m > n, the problem of representation is underdetermined. Hence, as is
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`widely taught in elementary courses, there is no unique solution to the representation
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`problem, and far more disturbingly, if the data are even slightly inaccurate, some
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`familiar algorithms will be staggeringly unstable.” IDG-1012 at p. 1, Col. 2. Donoho
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`considers this problem when there is a sparse solution in the ideal, noiseless problem
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`and further discloses that when Φ has a small mutual coherence, one can recover the
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`original sparse signal exactly in the noise-free case by solving the optimization
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`problem (1.3). Id. at p. 2, Col. 2. Donoho also discloses that when y above is
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`corrupted by some noise, it can be recovered with an error within the noise level by
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`solving the optimization problem (1.7). Id. at p. 5, Col. 1, Theorem 3.1. Th