  In this work we consider the problem of recovering non-uniform splines from
their projection onto spaces of algebraic polynomials. We show that under a
certain Chebyshev-type separation condition on its knots, a spline whose
inner-products with a polynomial basis and boundary conditions are known, can
be recovered using Total Variation norm minimization. The proof of the
uniqueness of the solution uses the method of `dual' interpolating polynomials
and is based on \cite{SR}, where the theory was developed for trigonometric
polynomials. We also show results for the multivariate case.
