Inversion of the Heat Equation by a Block Based Algorithm Using Spline Wavelet Packets
We present a robust algorithm starting from 1D or 2D discrete noised data to approximately invert the heat equation, which is an ill-conditioned problem. Relative contributions of the coherent structure and the noise in different frequency bands of the available data are different. We propose to solve the inversion problem separately in different frequency bands by methods similar to the Tikhonov regularization. This separation is achieved by using spline wavelet packets. The solutions are derived as linear combinations of those wavelet packets.