Quasi-greedy systems of integer translates

We consider quasi-greedy systems of integer translates in a finitely generated shift-invariant subspace of L2(Rd)L2(Rd), that is systems for which the thresholding approximation procedure is well behaved. We prove that every quasi-greedy system of integer translates is also a Riesz basis for its closed linear span. The result shows that there are no conditional quasi-greedy bases of integer translates in a finitely generated shift-invariant space.