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To improve the visual quality of noisy medical images acquired by low radiation dose imaging, medical image denoising is highly desirable for clinical disease diagnosis. In this paper, a geometric regularization method is proposed for medical image denoising. To the best of our knowledge, this is the first work aiming at reconstructing surface by minimizing the gradient error and approximation error of the surface to suppress the noise in medical images. The proposed denoising method consists of two stages: one is to output a basic estimate and the other is for the residual noise reduction. Specifically, the method first exploits a biquadratic polynomial surface to generate an initial estimate of the noise-free image. The surface is constructed by dividing its coefficients into two groups. With the reconstruction error constraint, one group is used to minimize the gradient of the surface, and the other is to minimize the approximation accuracy of the surface. Then the residual noise in the initial result is further reduced by using the singular value thresholding mechanism, which exploits the self-similarity of medical images and the intrinsic low-rank property. Unlike the traditional truncated singular value thresholding scheme, the proposed singular value thresholding is derived by optimizing an objective function with a constraint. Experimental results on a real clinical data set demonstrate the effectiveness of the proposed denoising method, especially in detail-preserving. Compared with several widely used denoising methods, our method can achieve a better performance in terms of both quantitative metrics and subjective visual quality.

Medical Image Denoising Based on Biquadratic Polynomial With Minimum Error Constraints and Low-Rank Approximation