8,378 research outputs found
A signomial programming approach for binary image restoration by penalized least squares
The authors present a novel optimization approach, using signomial programming (SP), to restore noise-corrupted binary and grayscale images. The approach requires the minimization of a penalized least squares functional over binary variables, which has led to the design of various approximation methods in the past. In this brief, we minimize the functional as a SP problem which is then converted into a reversed geometric programming (GP) problem and solved using standard GP solvers. Numerical experiments show that the proposed approach restores both degraded binary and grayscale images with good accuracy, and is over 20 times faster than the positive semidefinite programming approach. © 2007 IEEE.published_or_final_versio
From Steiner Formulas for Cones to Concentration of Intrinsic Volumes
The intrinsic volumes of a convex cone are geometric functionals that return
basic structural information about the cone. Recent research has demonstrated
that conic intrinsic volumes are valuable for understanding the behavior of
random convex optimization problems. This paper develops a systematic technique
for studying conic intrinsic volumes using methods from probability. At the
heart of this approach is a general Steiner formula for cones. This result
converts questions about the intrinsic volumes into questions about the
projection of a Gaussian random vector onto the cone, which can then be
resolved using tools from Gaussian analysis. The approach leads to new
identities and bounds for the intrinsic volumes of a cone, including a
near-optimal concentration inequality.Comment: This version corrects errors in Propositions 3.3 and 3.4 and in Lemma
8.3 that appear in the published versio
- …