Majorize-minimize linesearch for inversion methods involving barrier function optimization (Q2898427)

The authors consider the frequent situation where the dependence of the observations \(y\in\mathbb{R}^M\) on the unknown discretized object \(x^0\in\mathbb{R}^N\) 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 \(F(x)= S(x)+\lambda R(x)\).NEWLINENEWLINE The efficiency of the proposed approach is illustrated through numerical examples in the field of signal and image processing.