Nonlinear diffusion filtering for peak-preserving smoothing of a spectrum signal

• Nonlinear diffusion filtering for peak-preserving smoothing.
• Diffusion strength controlled by the diffusion function.
• Smooth enough signal can be obtained as iteration times increase.
• Nonlinear diffusion filtering is very suitable for spectrum smoothing.

How to reduce the noise while preserving the peak is a challenging task in analytical techniques. In this paper, the nonlinear diffusion was proposed as a general method to accomplish peak-preserving smoothing. The implement of the nonlinear diffusion is simple. Taking the noisy signal as the initial condition of a nonlinear diffusion equation, the solution is a smoothed signal, and signal becomes increasingly smooth as iteration number increases. Details of the nonlinear diffusion filtering and its implementation were given clearly. Some simulated signals and an NMR spectrum has been used to verify the proposed method and compare the performance of other methods such as regularization method, Savitzky-Golay method and wavelet method. Results indicated that the nonlinear diffusion is an excellent smoothing method, it can reduce the noise while preserve the peak shape.