\emph{Koopman Regularization} is a constrained optimization-based method to learn the governing equations from sparse and corrupted samples of the vector field. \emph{Koopman Regularization} extracts a functionally independent set of Koopman Eigenfunctions from the samples. This set implements the principle of parsimony, since, even though its cardinality is finite, it restores the dynamics precisely. \emph{Koopman Regularization} formulates the Koopman Partial Differential Equation as the objective function and the condition of functional independence as the feasible region. Then, this work suggests a barrier method-based algorithm to solve this constrained optimization problem that yields promising results in denoising, generalization, and dimensionality reduction.