  In this work we consider the operator
  \[
  (\mathbf{T} G) (x)= \int_{\mathbb{S}^2} G(x\cdot \omega, \omega) d\omega,
\quad x\in \mathbb{R}^3, \; G\in L^2(\mathbb{R}\times \mathbb{S}^2).
  \]
  This is the adjoint operator of the Radon transform. We manage to give an
optimal $L^6$ decay estimate of $\mathbf{T} G$ near the infinity by a geometric
method, if the function $G$ is compactly supported. As an application we give
decay estimate of non-radiative solutions to the 3D linear wave equation in the
exterior region $\{(x,t)\in \mathbb{R}^3 \times \mathbb{R}: |x|>R+|t|\}$. This
kind of decay estimate is useful in the channel of energy method for wave
equations
