Uniqueness theorem for inverse scattering problem with non-overdetermined data

Let $q(x)$ be real-valued compactly supported sufficiently smooth function, $q\in H_0^{\mathrm{\ell }}(B_a)$, $B_a:=\{x:\mathrm{\mid }x\mathrm{\mid }\le a,x\in R^3$ . It is proved that the scattering data $A(-\beta ,\beta ,k)$ $\mathrm{\forall }\beta \in S^2$, $\mathrm{\forall }k>0$ determine $q$ uniquely. here $A(\beta ,\alpha ,k)$ is the scattering amplitude, corresponding to the potential $q$.