A New Multiplicative Noise Elimination Method Based on Combining Homomorphic Filtering with Nonlinear Fourier Spectral Subtraction

When the spectrum of multiplicative noise is overlapped with the spectrum of the true signal, the effect of noise elimination is bad using homomorphic filtering method. The principle of Fourier spectral subtraction is analyzed, and a new method of multiplicative noise elimination based on homomorphic filtering and Fourier spectral subtraction is proposed. Firstly transform the Multiplicative noise into additive noise by means of homomorphic transform, then subtract the spectrum of noise in frequency domain using nonlinear Fourier spectral subtraction, finally get the original signal through inverse discrete Fourier transform, linear filtering and exponential transform. The results of simulation experiment show that, compared with homomorphic filtering, the output signal with this method is more likely to the real signal, and SNR (Signal to Noise Ratio) of output signal is improved remarkably, so it is a more effective method to eliminate the multiplicative noise.