A class of solutions for the inverse diffusion problem Original Research Article

The close relation between Hermitian wavelets transforms and the diffusion equation is used to derive a one-parameter family of distributed sources as solutions to the inverse diffusion problem in RN × R_. The class of solutions is interpreted in terms of energetically dominant events in the wavelet representation, where the scale of the event is proportional to its age. The construction procedure is a straightforward extension of the inverse wavelet transform formula. Simple examples illustrate the method.