  In this work, an accurate regularization technique based on the Meyer wavelet
method is developed to solve the ill-posed backward heat conduction problem
with time-dependent thermal diffusivity factor in an infinite "strip". In
principle, the extremely ill-posedness of the considered problem is caused by
the amplified infinitely growth in the frequency components which lead to a
blow-up in the representation of the solution. Using the Meyer wavelet
technique, some new stable estimates are proposed in the H\"older and
Logarithmic types which are optimal in the sense of given by Tautenhahn. The
stability and convergence rate of the proposed regularization technique are
proved. The good performance and the high-accuracy of this technique is
demonstrated through various one and two dimensional examples. Numerical
simulations and some comparative results are presented.
