Tokamaks offer an interesting direction in the research of controlled nuclear fusion. To maintain control over the plasma column during a discharge a reliable estimate of its boundary is needed. Using magnetic measurements taken in the vicinity of the tokamak, a linear problem can be constructed with potentially infinitely many regressors. Furthermore, the theoretical model may not hold during certain phases of a discharge. To address these issues, we propose a prior distribution model with the aim of sparsity and outlier detection. Using the Variational Bayes theorem, an iterative algorithm based on least squares problem is derived. Results of boundary estimation are compared to traditional methods and validated both on simulated and real data from the COMPASS tokamak.