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Majorize-minimize linesearch for inversion methods involving barrier function optimization. (English) Zbl 1256.65051
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 $$F(x)= S(x)+\lambda R(x)$$.
The efficiency of the proposed approach is illustrated through numerical examples in the field of signal and image processing.

##### MSC:
 65K05 Numerical mathematical programming methods 90C05 Linear programming 90C59 Approximation methods and heuristics in mathematical programming 94A08 Image processing (compression, reconstruction, etc.) in information and communication theory 94A12 Signal theory (characterization, reconstruction, filtering, etc.)
LSMM; tn
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