A Spatially Selective Correlative Filtration Method Based on the Multiscale Edge Shift-Correlative Technique

In terms of signal denoising, filtering out high-frequency noise while effectively preserving the useful high-frequency information is a hot topic for research. In this paper, we propose a wavelet modulus maxima spatially selective correlative filtration (SSCF) algorithm to filter out the high-frequency noise mixed in the useful signals. The proposed algorithm is different from traditional noise filtration algorithms in that it need not estimate noise and is not easily affected by noise. The SSCF algorithm first searches the modulus maxima from the multiscale wavelet coefficients of the signal and analyzes the corresponding edge information. Then, it identifies the noise components and useful components from the edge information. For noise components, the algorithm smoothes them away. For useful edge information, the algorithm aligns the corresponding modulus maxima in the wavenumber domain using the shift-related technique. This process amends the “drift” phenomenon of modulus maxima across scales. Next, the proposed algorithm multiplies the aligned multiscale wavelet coefficients that can strengthen the useful signal and attenuate the noise information. We apply the proposed SSCF algorithm to denoise the infrared absorption spectrum of electric insulation gas SF6. Experiments show that the proposed scheme can effectively suppress noise and, at the same time, preserving the useful components.