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

Abstract

Medical imaging, the process of visual representation of different organs and tissues of the human body, is employed for monitoring the normal as well as abnormal anatomy and physiology of the body. Imaging which can provide healthcare solutions ensuring a regular measurement of various complex diseases plays a critical role in the diagnosis and management of many complex diseases and medical conditions, and the quality of a medical image, which is not a single factor but a composite of contrast, artifacts, distortion, noise, blur, and so forth, depends on several factors such as the characteristics of the equipment, the imaging method in question as well as the imaging variables chosen by the operator. The medical images (ultrasound image, X-rays, CT scans, MRIs, etc.) may lose significant features and become degraded due to the emergence of noise as a result of which the process of improvement pertaining to medical images has become a thought-provoking area of inquiry with challenges related to detecting the speckle noise in the images and finding the applicable solution in a timely manner. The 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. In this research paper, we present a conformable fractional derivative-based anisotropic diffusion model for removing speckle noise in ultrasound images. 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. Furthermore, we aim at proving the viscosity solution of the fractional diffusion model. 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 comparative experimental results corroborate that the proposed, developed and extended mathematical model is capable of denoising and preserving the significant features in ultrasound towards better accuracy, precision and examination within the framework of biomedical imaging and other related medical, clinical, and image-signal related applied as well as computational processes.

Keywords

• anisotropic diffusion model
• nonlinear mathematical diffusion model
• fractional diffusion model
• fractional order derivatives
• biomedical imaging
• denoising
• chaotic signals and noise
• image smoothing
• viscosity solution
• explicit scheme
• multiplicative noise
• conformable fractional derivative
• partial differential equations (pdes)