  In this paper, we regularize the nonlinear inverse time heat problem in the
unbounded region by Fourier method. Some new convergence rates are obtained.
Meanwhile, some quite sharp error estimates between the approximate solution
and exact solution are provided. Especially, the optimal convergence of the
approximate solution at t = 0 is also proved. This work extends to many earlier
results in (f2,f3, hao1,Quan,tau1, tau2, Trong3,x1).
