Next-generation fusion reactors such as DEMO pose significant challenges in the design of diagnostic systems due to stringent spatial limitations and cost constraints. In response to these challenges, we apply Bayesian experimental design methodologies to optimize the magnetic diagnostics of the WEST tokamak, with a focus on its pick-up coil system. Mutual information is used as a quantitative metric to evaluate the information gain and select coil configurations that preserve diagnostic accuracy while reducing the total number of sensors. Our findings show that up to 35% of the coils can be removed while preserving reconstruction behavior consistent with the corrected reference tomogram: the total plasma current deviates by less than 0.3%, the current centroid remains within 0.2 cm, and the X point position deviation remains below 1.2 cm. The Bayesian framework and information-theoretic criteria employed here offer a versatile and principled basis for optimizing diagnostic configurations across a range of operational constraints in fusion environments.