An image denoising method based on the nonlinear Schrödinger equation and spectral subband decomposition

Abstract

Most denoising methods inevitably smooth the image while denoising, which makes it difficult to effectively maintain the structural information and detail information of the original noise-free image. Stochastic resonance can directly convert the noise energy into signal energy, and denoising by stochastic resonance retains the signal energy. Therefore, this paper presents an image denoising method based on the nonlinear Schrödinger equation. First, by analyzing the dynamic stochastic resonance effect in a nonlinear optical system, the nonlinear Schrödinger equation is derived to describe the signal propagation in the system, and the equation is extended to construct a two-dimensional image denoising model. Then, we propose an image denoising algorithm based on image spectral subband decomposition. The algorithm decomposes the image spectrum into different frequency domain subbands and uses the Schrödinger denoising model to denoise the high-frequency subbands containing the rich structure and detailed information of the image. A series of comparative experiments show that the proposed method can significantly improve the image signal-to-noise ratio while effectively restoring image details and has better performance than other typical methods in the case of high-intensity noise.