We propose a non-parametric approach to recovering the physical measure from market data without directly estimating the pricing kernel. Instead, we begin with the empirical risk-neutral measure, extracted from option prices, and refine it by projecting it onto a set of economically plausible densities, ensuring adherence to fundamental economic constraints. By leveraging optimal transport theory, precisely the Wasserstein metric, our method preserves the structural relationships between probability distributions, ensuring theoretical consistency with observed market data while offering a flexible reconstruction of the physical measure.