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SUMMARY:Luca Calatroni (Laboratoire d'Informatique\, Signaux et Systèmes 
 de Sophia-Antipolis (I3S)\, France)
DTSTART:20210601T140000Z
DTEND:20210601T150000Z
DTSTAMP:20260423T021041Z
UID:SNAP/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SNAP/3/">Sca
 led\, inexact and adaptive generalised FISTA for (strongly) convex imaging
  problems</a>\nby Luca Calatroni (Laboratoire d'Informatique\, Signaux et 
 Systèmes de Sophia-Antipolis (I3S)\, France) as part of Seminars on Numer
 ics and Applications\n\n\nAbstract\nWe consider an inexact\, scaled genera
 lised Fast Iterative Soft-Thresholding Algorithm (FISTA) for minimising th
 e sum of two (possibly strongly) convex functions\, which we name SAGE-FIS
 TA. Here\, the inexactness is explicitly taken into account so as to descr
 ibe standard situations where proximal operators cannot be evaluated in cl
 osed form. The idea of considering data-dependent scaling in forward-backw
 ard splitting methods has furthermore been shown to be effective in incorp
 orating Newton-type information along the optimisation via suitable variab
 le-metric updates. Finally\, in order to account for the adjustment of the
  algorithmic step-size along the iterations\, we propose a non-monotone ba
 cktracking strategy which improves the convergence speed compared to stand
 ard Armijoo-type analogs. Analytically\, linear convergence result for the
  function values is proved. The result depends on the strong convexity mod
 uli of the two functions\, the upper and lower bounds on the spectrum of t
 he variable metric operators and the inexactness/backtracking parameters. 
 The performance of SAGE-FISTA is validated on convex and strongly-convex e
 xemplar image denoising\, deblurring and super-resolution problems where s
 parsity-promoting regularisation is combined with data-dependent Kullback-
 Leibler-type fidelity terms.<br />\n<i>This is joint work with S. Rebegold
 i (University of Florence).</i>\n
LOCATION:https://researchseminars.org/talk/SNAP/3/
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