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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Provably Robust Score-Based Diffusion Posterior Sa
mpling for Plug-and-Play Image Reconstruction - Yu
ejie Chi (Carnegie Mellon University)
DTSTART;TZID=Europe/London:20240719T100000
DTEND;TZID=Europe/London:20240719T110000
UID:TALK219067AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/219067
DESCRIPTION:In a great number of tasks in science and engineer
ing\, the goal is to infer an unknown image from a
small number of noisy measurements collected from
a known forward model describing certain sensing
or imaging modality. Due to resource constraints\,
this image reconstruction task is often extremely
ill-posed\, which necessitates the adoption of ex
pressive prior information to regularize the solut
ion space. Score-based diffusion models\, thanks t
o its impressive empirical success\, have emerged
as an appealing candidate of an expressive prior i
n image reconstruction. In order to accommodate di
verse tasks at once\, it is of great interest to d
evelop efficient\, consistent and robust algorithm
s that incorporate unconditional score functions o
f an image prior distribution in conjunction with
flexible choices of forward models. This work deve
lops an algorithmic framework for employing score-
based diffusion models as an expressive data prior
in nonlinear inverse problems with general forwar
d models. Motivated by the plug-and-play framework
in the imaging community\, we introduce a diffusi
on plug-and-play method (DPnP) that alternatively
calls two samplers\, a proximal consistency sample
r based solely on the likelihood function of the f
orward model\, and a denoising diffusion sampler b
ased solely on the score functions of the image pr
ior. The key insight is that denoising under white
Gaussian noise can be solved rigorously via both
stochastic (i.e.\, DDPM-type) and deterministic (i
.e.\, DDIM-type) samplers using the same set of sc
ore functions trained for generation. We establish
both asymptotic and non-asymptotic performance gu
arantees of DPnP\, and provide numerical experimen
ts to illustrate its promise in solving both linea
r and nonlinear image reconstruction tasks. To the
best of our knowledge\, DPnP is the first provabl
y-robust posterior sampling method for nonlinear i
nverse problems using unconditional diffusion prio
rs. \;
LOCATION:External
CONTACT:
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