Signal denoising by piecewise continuous polynomial fitting

Piecewise smooth signal denoising is cast as a non-linear optimization problem in terms of transition boundaries and a parametric smooth signal family. Optimal transition boundaries for a given number of transitions are obtained by using particle swarm optimization. The piece-wise smooth section parameters are obtained as the maximum likelihood estimates conditioned on the optimal transition boundaries. The proposed algorithm is extended to the case where the number of transition boundaries are unknown by sequentially increasing number of sections until the residual error is at the level of noise standard deviation. Performance comparison with the state of the art techniques reveals the important advantages of the proposed technique.