Ultrasonography is one of the most important modalities of medical imaging system

and medical ultrasound images play a significant role in medical imaging techniques. However

medical ultrasound images are always contaminated by a noise called "speck noise"

which has a visual effect similar to speck

instead of the point-like Gaussian white noise. Speck noise seriously degrades the quality of medical ultrasound images. Thus

in a contaminated medical ultrasound image

the observer has difficulty discriminatingthe fine details and structural features

hindering the application of ultrasound images in clinical diagnosis and treatment. In this paper

the quantum-inspired diffusion coefficient is introduced to discuss the challenge of despeckling while preserving the edge detail and structural features of ultrasound images. The proposed method improves the diffusion coefficient in traditional P-M equations based on the denoising method by some foundational knowledge in quantum theory.Anisotropic diffusion model is built on the basis of the traditional P-M equations. The proposed quantum-inspired diffusion coefficient changes over the gradient direction to take advantage of the better directional selectivity of wavelet coefficients. The optimization of this coefficient can be strengthened by the improved anisotropic diffusion model. Thus

a novel quantum-inspired partial differential equation based on medical ultrasound image despeckling method is proposed. Experiments are conducted on both images with simulation speck noise and real medical ultrasound images to show the performance of the proposed method in comparison with other classic despeckling methods. Among all compared methods

the proposed method obtains the best objective evaluation

such as signal-to-noise ratio

edge preserve measurement

structural similarity index measurement

and equivalent number of looks. Experimental results of both images with simulation speck noise and real medical ultrasound images can demonstrate that the proposed method efficiently reduces the speck noise and maintains the edge

detail

and structure of the images. An effective despeckling method inspired by quantum theory and based on partial differential equations is proposed for medical ultrasound image despeckling; experiments are conducted to demonstrate the effectiveness of this method. The proposed method effectively addresses the problem of reducing speck noise in a medical ultrasound image while maintaining the details

edge

and structure of the image.Good despeckling results are obtained. The introduction of quantum theory can not only provide a solution to the present medical ultrasound image despeckling problems but also inspire researchers to make use of the theory in various medical image processing methods. A new path of interdisciplinary exploration can be achieved in the medical image processing research and even in other complicated problems in various disciplines by combining the quantum-inspired theory or other advanced theories in multiple fields to gain better processing performance.