Summary: A VARIATIONAL METHOD IN IMAGE RECOVERY #
GILLES AUBERT + AND LUMINITA VESE #
SIAM J. NUMER. ANAL. c
# 1997 Society for Industrial and Applied Mathematics
Vol. 34, No. 5, pp. 1948--1979, October 1997 016
Abstract. This paper is concerned with a classical denoising and deblurring problem in image
recovery. Our approach is based on a variational method. By using the Legendre--Fenchel transform,
we show how the nonquadratic criterion to be minimized can be split into a sequence of half­quadratic
problems easier to solve numerically. First we prove an existence and uniqueness result, and then we
describe the algorithm for computing the solution and we give a proof of convergence. Finally, we
present some experimental results for synthetic and real images.
Key words. image processing, Legendre--Fenchel transform, partial di#erential equations, cal­
culus of variations
AMS subject classifications. 35J, 49J, 65N
PII. S003614299529230X
1. Introduction. An important problem in image analysis is the reconstruc­
tion of an original image f describing a real scene from an observed image p. The
transformation (or degradation) connecting f to p is in general the result of two phe­
nomena. The first phenomenon is deterministic and is related to the mode of image
acquisition (for example, the computation of integral projections in tomography) or to

Source: Aubert, Gilles - Laboratoire Jean Alexandre Dieudonné, Université de Nice Sophia Antipolis

Collections: Mathematics