A quantum derived image transformation and threshold denoising algorithm based on the Schr?dinger equation is proposed to make full use of image information and effectively remove Gaussian noise and Poisson noise from the image. In the discrete Schr?dinger equation, the image is regarded as the potential field, and the characteristic function obtained by solving the stationary Schr?dinger equation constitutes the adaptive basis. The image is then projected onto the adaptive basis. Since the noise is mainly represented by the high-order characteristic function corresponding to the high energy, the soft threshold function is used to deal with the projection coefficient in terms of energy to achieve denoising. To reduce the influence of Anderson localization in the quantum system on denoising, the image is preprocessed with a Gaussian filter. The proposed algorithm has a good denoising effect in Gaussian noise and Poisson noise scenes, according to experimental results.