Paulo Goncalves

 

Justin Romberg
http://users.ece.gatech.edu/justin/Justin_Romberg.html
School of Electrical and Computer Engineering, Georgia Tech

VENUE

ENS Lyon, Site Jacques Monod.
Room: Amphitheater B – 3rd floor

(local correspondant: Paulo Gonçalves)

PROGRAM and MATERIAL

Basis decompositions and frames (3-4 hours)
[notation, basis, frames, dct-notes, wavelets, sparsity-overview]

  • fundamentals of basis and frame decompositions
  • the discrete cosine transform and applications to image/video compression
  • the lapped orthogonal transform
  • wavelets
  • thresholding for noise reduction

Sparsest decomposition from a dictionary (3-4 hours)
[lecture-2-1-sparseapprox, lecture-2-2-bp, lecture-2-3-upsparse]

  • omp and basis pursuit for selecting atoms
  • uncertainty principles and sparsest decomposition
  • the « spikes+sines » dictionary
  • general unions of orthobases

Introduction to compressive sampling and applications (2 hours)
[csoverview-part1,csoverview-part2,csoverview-part3,csoverview-part4] 

Recovering sparse vectors from linear measurements (6 hours/ 1 day)
[lecture-3-1-invprobs,lecture-3-2-ls,lecture-3-3-l1dual,lecture-3-4-l1cone,lecture-3-5-stable]

  • review of classical least-squares theory:
  • the svd, pseudo-inverse, stability analysis, regularization
  • sparse recovery conditions: l1 duality
  • sparsest decomposition revisited (with random support)
  • the restricted isometry property and sparse recovery
  • l1 for perfect recovery from noise-free measurements
  • l1 stability
  • l2 stability

Random matrices are restricted isometries (2 hours)
[lecture-4-1-gaussrip] 

Optimization (6 hours / 1 day)
[lecture-5-1-sdcg,lecture-5-2-newtonlog,lecture-5-3-streamingl2,lecture-5-4-streamingl1,lasso-dual-notes]
[siamOptimTalk] 

  • conjugate gradients
  • newton iterations
  • newton iterations
  • log-barrier methods
  • first-order l1 solvers
  • greedy algorithms and iterative thresholding
  • recursive least-squares
  • the Kalman filter
  • dynamic l1 updating

Low-rank recovery (2 hours)

TIMETABLE

Monday 9:  10:00am – 12:00am ; 2:00pm – 5:00pm  (5 hours)
Tuesday 10:  9:30am – 12:00am ;  2:00pm – 5:00pm  (5,5 hours)
Wednesday 11:  9:30am – 12:00am ; 2:00pm – 5:00pm  (5,5 hours)
Thursday 12:  9:30am – 12:30pm ; free afternoon  (3 hours)
Friday 13:  9:00am – 12:00am ; 2:00pm – 4:00pm  (5 hours)