Majorize-minimize linesearch for inversion methods involving barrier function optimization The authors consider the frequent situation where the dependence of the observations $yinbfR^M$ on the unknown discretized object $x^0inbfR^N$ is represented by a linear model $y= Kx^0+varepsilon$ with $K$ being a known ill-conditioned matrix and $varepsilon$ an additive noise term representing measurement errors and model uncertainties. To handle the ill-posedness of such problems, several efficient inversion methods are based on the minimization of a composite criterion $F(x)= S(x)+lambda R(x)$.par The efficiency of the proposed approach is illustrated through numerical examples in the field of signal and image processing.