A New Fractional-order Derivative-based Nonlinear Anisotropic Diffusion Model for Biomedical Imaging

Abstract

Nonlinear anisotropic diffusion equations are employed to ensure the improvement of the image quality by removing noise while retaining the subtle details and edges. Image denoising is observed to be of utmost importance in image processing and computer vision to prepare the images with better resolutions. Partial differential equations (PDEs), in this sense, can be used extensively in different aspects with regard to image processing ranging from filtering to restoration, segmentation to edge enhancement and detection, denoising in particular, among the other ones. The medical images (ultrasound images, X-rays, CT scans, MRIs, etc.) may lose significant features and become degraded due to the emergence of noise. As a result, the process of improvement pertaining to medical images has become a thought-provoking area of inquiry with challenges related to detecting the additive noise in the images and finding the applicable solution in a timely manner. To this end, numerous denoising techniques have been established. In this research paper, we present a conformable fractional derivative-based anisotropic diffusion model for removing speckle noise in ultrasound images. Chaos, as a ubiquitous phenomenon in nature, manifests the fact that the observed chaotic and noisy signals are often disrupted by external interferences. Edge, as one of the most remarkable features for images, requires denoising via nonlinear means to attain optimal outcomes. The finite difference method is used to discretize the fractional diffusion model and classical diffusion models. The peak signal-to-noise ratio (PSNR) is used for the quality of the smooth images. The aim of this study is to prove the viscosity solution of the diffusion model with the proposed model providing to be efficient in reducing noise by preserving the essential image features like edges, corners and other sharp structures for ultrasound images in comparison to the classical anisotropic diffusion model. Comparative experimental results corroborate that the proposed and extended mathematical model is capable of denoising and preserving the significant features in ultrasound within the framework of biomedical imaging and other related medical, clinical and image-signal related applied as well as computational processes.