Image denoising for magnetic resonance imaging medical images using improved generalized cross-validation based on the diffusivity function

Various image denoising algorithms have been developed for medical imaging. But some disadvantages have been found, including the block effect, which increases smoothing, and the loss of image detail. Using the statistical properties of observed noisy images, we propose a new diffusivity function-based partial differential equation method for image denoising. This model incorporates a Quaternion Wavelet Transform for the generation of the various noisy image coefficients, an improved generalized cross-validation function for generating the optimal threshold value via the soft threshold function, and a new diffusivity function for controlling the diffusion process. The fourth-order PDE diffusivity function, which is presented in this article, is a novel diffusion coefficient that is more effective at removing noise and preserving edges than previous approaches. Finally, the performance of the proposed method is evaluated using the peak signal-to-noise ratio, mean square error, structural similarity index, and comparisons to other traditional methods.