We consider the problem of finding, from the final data $u(x, T)$, the function $u$ satisfying $$u_t - u_{xx} = f(x, t, u(x, t), u_x(x, t)),\quad (x, t) \in \mathbb R \times (0, T).$$ The problem is ill-posed and we shall use the Fourier transform to get a nonlinear integral equation in the frequency space. By truncating high frequencies, we give a regularized solution. Error estimates are given.