  Anisotropic diffusion filtering for signal smoothing as a low-pass filter has
the advantage of the edge-preserving, i.e., it does not affect the edges that
contain more critical data than the other parts of the signal. In this paper,
we present a numerical algorithm based on least squares support vector
regression by using Legendre orthogonal kernel with the discretization of the
nonlinear diffusion problem in time by the Crank-Nicolson method. This method
transforms the signal smoothing process into solving an optimization problem
that can be solved by efficient numerical algorithms. In the final analysis, we
have reported some numerical experiments to show the effectiveness of the
proposed machine learning based approach for signal smoothing.
