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The Coronal Multichannel Polarimeter (CoMP) routinely performs coronalpolarimetric measurements using the Fe XIII 10747 $\AA$ and 10798 $\AA$ lines,which are sensitive to the coronal magnetic field. However, inverting suchpolarimetric measurements into magnetic field data is a difficult task becausethe corona is optically thin at these wavelengths and the observed signal istherefore the integrated emission of all the plasma along the line of sight. Toovercome this difficulty, we take on a new approach that combines aparameterized 3D magnetic field model with forward modeling of the polarizationsignal. For that purpose, we develop a new, fast and efficient, optimizationmethod for model-data fitting: the Radial-basis-functions OptimizationApproximation Method (ROAM). Model-data fitting is achieved by optimizing auser-specified log-likelihood function that quantifies the differences betweenthe observed polarization signal and its synthetic/predicted analogue. Speedand efficiency are obtained by combining sparse evaluation of the magneticmodel with radial-basis-function (RBF) decomposition of the log-likelihoodfunction. The RBF decomposition provides an analytical expression for thelog-likelihood function that is used to inexpensively estimate the set ofparameter values optimizing it. We test and validate ROAM on a synthetic testbed of a coronal magnetic flux rope and show that it performs well with asignificantly sparse sample of the parameter space. We conclude that ouroptimization method is well-suited for fast and efficient model-data fittingand can be exploited for converting coronal polarimetric measurements, such asthe ones provided by CoMP, into coronal magnetic field data.

ROAM: a Radial-basis-function Optimization Approximation Method for diagnosing the three-dimensional coronal magnetic field