Skip to main content    

An official website of the United States government

Here’s how you know

**Official websites use .gov**              A **.gov** website belongs to an official government organization in the United States.            

**Secure .gov websites use HTTPS**              A **lock** (  LockA locked padlock) or **https://** means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.            

https://www.nist.gov/itl/math/acmd-seminar-efficient-variational-methods-parallel-mri-reconstruction-using-sensitivity

            -  Topics  -  All Topics 
-  Advanced communications 
-  Artificial intelligence 
-  Bioscience 
-  Buildings and construction 
-  Chemistry 
-  Climate 
-  Cybersecurity 
-  Electronics 
-  Energy 
-  Environment 
-  Fire 
-  Forensic science 
-  Health 
-  Information technology 
-  Infrastructure 
-  Manufacturing 
-  Materials 
-  Mathematics and statistics 
-  Metrology 
-  Nanotechnology 
-  Neutron research 
-  Performance excellence 
-  Physics 
-  Public safety 
-  Resilience 
-  Standards 
-  Transportation 
 
            -  Publications 
            -  Labs & Major Programs  -  Laboratories    -  Communications Technology Laboratory 
  -  Engineering Laboratory 
  -  Information Technology Laboratory 
  -  Material Measurement Laboratory 
  -  Physical Measurement Laboratory 
-  User Facilities    -  NIST Center for Neutron Research 
  -  CNST NanoFab 
-  Research Test Beds 
-  Research Projects 
-  Tools & Instruments 
-  Major Programs    -  Baldrige Performance Excellence Program 
  -  CHIPS for America Initiative 
  -  Manufacturing Extension Partnership (MEP) 
  -  Office of Advanced Manufacturing 
  -  Special Programs Office 
  -  Technology Partnerships Office 
 
            -  Services & Resources  -  Standards and Measurements    -  Calibration Services 
  -  Laboratory Accreditation (NVLAP) 
  -  Quality System 
  -  Standard Reference Materials (SRMs) 
  -  Standards.gov 
  -  Time Services 
  -  Office of Weights and Measures 
-  Software 
-  Data    -  Chemistry WebBook 
  -  National Vulnerability Database 
  -  Physical Reference Data 
  -  Standard Reference Data (SRD) 
-  Storefront 
-  License & Patents 
-  Computer Security Resource Center (CSRC) 
-  NIST Research Library 
 
            -  News & Events  -  News 
-  Events 
-  Blogs 
-  Feature Stories 
-  Awards 
-  Video Gallery 
-  Image Gallery 
-  Media Contacts 
 
            -  About NIST  -  About Us    -  Leadership 
  -  Organization Structure 
  -  Budget & Planning 
-  Contact Us 
-  Visit 
-  Careers    -  Student programs 
-  Work with NIST 
-  History    -  NIST Digital Archives 
  -  NIST Museum 
  -  NIST and the Nobel 
-  Educational Resources 
 

Information Technology Laboratory

## Applied and Computational Mathematics Division

-  Projects/Programs 
-  How to Work With Us 
-  NIST Publications Searchable Database 
-  Staff Directory 
-  News & Updates 
-  Resources/Services 

# ACMD Seminar: Efficient Variational Methods for Parallel MRI Reconstruction using Sensitivity Encoding

## Share

Facebook

Linkedin

Twitter

Email

Maryam Yashtini*Department of Mathematics and Statistics, Georgetown University*

Tuesday, March 10, 2020, 3:00–4:00PMBuilding 101, Lecture Room AGaithersburg

Tuesday, March 10, 2020, 1:00–2:00PMBuilding 1, Room 3304Boulder

**Host:** Gunay Dogan

**Abstract:** SENSitivity Encoding (SENSE) is an effective mathematical formulation for reconstructing under-sampled MRI data obtained in Parallel Magnetic Resonance Imaging (Parallel MRI). The functional model includes a regularization term and a data fidelity term which needs to be minimized to obtain a high quality MRI result. The proper choice of regularization is essential for image quality.  In the first part of the talk, I consider the Total Variation (TV) based model, and I introduce Bregman operator splitting algorithm with variable step size (BOSVS) to solve TV-regularized SENSE. This algorithm is based on operator splitting and alternating direction method of multipliers to tackle the non-smoothness of TV. Moreover, the algorithm employs a novel back-tracking line search and step size strategies to handle the dense structure and ill-conditioning of the operator in the fidelity term. The step size rule starts with a Barzilai-Borwein (BB) stepsize and increases the nominal step until a termination condition is satisfied. Global convergence as well as rate of convergence of BOSVS will be discussed.  In the second part, I consider the Euler's elastica regularization, and I solve the Euler's Elastica regularized SENSE problem. Euler's Elastica has an advantage over TV in better connecting the separated parts and enforcing better geometrical features of the image. The Euler’s elastica functional is however complex to minimize as it is nonconvex, nonsmooth, and highly nonlinear. I will propose a new numerical method based on variable splitting approaches, and proper relaxation of the functional to solve it efficiently. Numerical examples will be presented to show the effectiveness and efficiency of the proposed method. In particular, I show that Euler's Elastica based model improves the signal to noise ratio (SNR) and image relative error in comparison to the TV-based model. Since Euler's elastica enforces a better connectivity of separated parts, it also allows the use of much sparser under-sampling pattern hence it improves the imaging speed in addition to image quality. 

**Bio:** Maryam Yashtini is a Tenure-Track Assistant Professor in the Department of Mathematics and Statistics at Georgetown University. Prior to joining the faculty at Georgetown, she was an NSF Postdoctoral Fellow at the Georgia Institute of Technology. She received a PhD Degree in Computational Mathematics and two Master's Degrees one in Applied Mathematics and one in Industrial Systems and Engineering from the University of Florida in 2009. Maryam's areas of expertise are computational optimization and scientific computing. Her research contributes efficient and practical algorithms to solve large-scale problems with applications to imaging. The optimization models of these problems are often non-differentiable, non-convex, ill-conditioned, and/or highly nonlinear. Maryam validates her algorithms by numerical implementation and rigorous theoretical analysis.

**Note:** Visitors from outside NIST must contact Cathy Graham; (301) 975-3800; at least 24 hours in advance.

This talk will be broadcast on-line using BlueJeans.  Contact acmdseminar [at] nist.gov (acmdseminar[at]nist[dot]gov) for details.

Mathematics and statistics

## Contacts

                -  Gunay Dogan  gunay.dogan@nist.gov      (301) 975-8883   
                -  Stephen Langer  stephen.langer@nist.gov      (301) 975-5423   

### HEADQUARTERS

301-975-2000

Webmaster | Contact Us | Our Other Offices

TwitterFacebookLinkedInInstagramYouTubeGiphyRSS FeedMailing List

Feedback

            -  Site Privacy 
            -  Accessibility 
            -  Privacy Program 
            -  Copyrights 
            -  Vulnerability Disclosure 
            -  No Fear Act Policy 
            -  FOIA 
            -  Environmental Policy 
            -  Scientific Integrity 
            -  Information Quality Standards 
            -  Commerce.gov 
            -  Science.gov 
            -  USA.gov 
            -  Vote.gov