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UID:8190@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20150116T140000
DTEND;TZID=Europe/Paris:20150116T150000
DTSTAMP:20241120T210101Z
URL:https://www.i2m.univ-amu.fr/evenements/s-bourguignon-irccyn-exact-mini
 misation-of-l0-based-sparse-approximation-criteria-through-mixed-integer-p
 rogramming/
SUMMARY: (...): S. Bourguignon (IRCCYN): Exact minimisation of L0-based spa
 rse approximation criteria through mixed integer programming
DESCRIPTION:: Exact minimisation of L0-based sparse approximation criteria 
 through mixed integer programming\n\nby S. Bourguignon (IRRCYN)\n\nSparse 
 approximation addresses the problem of solving approximately a given syste
 m of linear equations y = Ax with a vector x having as few non-zero compon
 ents as possible. It formulates a bi-objective optimization problem\\\, wh
 ere both a discrepancy function and the L0-"norm" sparsity measure are min
 imized. Optimization is essentially combinatorial and is often tackled thr
 ough the convex relaxation of the L0 norm\\\, or by heuristic combinatoria
 l exploration techniques. Optimality conditions then rely on prior assumpt
 ions on near-orthogonality of A and on sufficient sparsity of the solution
  x.\nIn many inverse problems\\\, such conditions are not satisfied and th
 e aforementioned methods clearly fail in locating the global minimum. We s
 tudy global optimization methods of the L0-norm sparse approximation probl
 em based on Mixed Integer Programming\\\, which involves both continuous a
 nd integer variables. Different problem formulations are proposed. We show
  that exact optimization of such problems is possible on certain moderate 
 size inverse problems\\\, whereas usual methods fail in locating sparsest 
 solutions and exhaustive enumeration remains prohibitive. The resulting fo
 rmulations are studied in terms of computational efficiency\\\, and simula
 tions evaluate the support identification capacities of the different Lp-f
 itting-based formulations in the presence of noise\\\, depending on the no
 ise statistical distribution. Finally\\\, an application to spike train de
 convolution in ultrasonic non-destructive testing is presented.\n\n
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