Math 290J (section 2) current literature in applied mathematics
Mathematical models in image processing and analysis

Organizers: Luminita Vese and Hayden Schaeffer.
E-mail: lvese@math.ucla.edu
Presentations, Time and Location:
Most meetings will be on Fridays, time 12:00-1:00pm, in MS 5233. Please note that some meetings will be at a different time and location. All meetings will be announced by email and posted on the class webpage.
Format: Graduate students give presentations from current literature in applied mathematics, image processing, computer vision. Sometimes, we may also have a guest lecturer.


SCHEDULE
  • Friday, September 30; Time 12:00pm-1:00pm; Location MS 5233
    Melissa Tong: "Rician denoising"
  • Friday, October 7: Time 12:00pm-1:00pm; Location MS 5233
    Joshua Hernandez: "Constant-Variance Resampling of Noisy Images"
  • Friday, October 14: Time 12:00pm-1:00pm; Location MS 5233
  • Friday, October 21: Time 12:00pm-1:00pm; Location MS 5233
    Yi Yang: "Algorithms for Solving Basis Pursuit Problems."
  • Friday, October 28: Time 12:00pm-1:00pm; Location MS 5233
    Igor Yanovsky (JPL / UCLA): Multilayer Separation using Split Bregman Methods and Applications to Separating Layers of Clouds
  • Friday, November 4: Time 12:00pm-1:00pm; Location MS 5233
    Alejandro Cantarero (UCLA): "Inverse Problems in Elliptic PDEs"
    Abstract. In this talk, we will present two methods for the estimation of the parameters and interface location from solution data to embedded interface elliptic PDEs with piecewise constant coefficients. The first approach is a variational method where we are able to obtain an explicit update for the coefficients, eliminating the need to solve a non-linear system at each iteration. In the second approach we use the piecewise constant nature of the coefficients to derive approximate coefficient functions. The interface location and coefficient values can then be recovered by applying any standard piecewise constant segmentation method. We demonstrate the methods on Poisson's equation and linear elasticity.
  • Friday, November 11: no meeting
  • Friday, November 18: Time 12:00pm-1:00pm; Location MS 5233
    Ming Yan: "TBA"
  • Friday, November 25: no meeting
  • Friday, December 2: Time 12:00pm-1:00pm; Location MS 5233
    Yonggang Shi (LONI, UCLA): Intrinsic Methods for Brain Image Analysis Speaker: Yonggang Shi, Assistant Professor, Lab of Neuro Imaging (LONI), UCLA School of Medicine
    Abstract: In this talk, I will present a suite of novel algorithms and tools for brain mapping using intrinsic geometry. The key idea in our method is the use of Laplace-Beltrami eigenfunctions for modeling brain shapes, such as hippocampus and cortex. These tools have the advantage of being invariant to pose and scale variances, and robust to deformations from development and pathology. Using the LB eigenfunctions and topology-preserving evolution, we have developed a robust approach for surface reconstruction that can remove outliers while accurately retaining volume information. We also developed metric optimization methods for highly accurate surface mapping. Combing these two algorithms, we have a fully automated workflow for the mapping of hippocampus and other brain structures. Applications these new methods in the studying of neurological diseases will be demonstrated.