In view of the trend term of nonlinear signal

propose a sparse optimization method based on wavelet transform. The method calculates the l1 norm sparse optimal solution to reconstruct the trend of signal by setting two boundary constraints. Simulation signal and measured signal processing result show that the method define trend item according to its self characteristic

don’t need to make any assumptions and it is fully data-driven

and has a good robustness in different noise intensity environment

the method has higher precision and reliability than the traditional method.