A novel curvelet thresholding denoising method based on chi-squared distribution

In this paper, we first explored the advantages and disadvantages of the classical curvelet thresholding functions. To circumvent the inherent drawbacks of them, we introduced the chi-squared cumulative distribution to develop a novel thresholding function. The theoretical analysis and mathematical proofs show that the proposed thresholding function represents a compromise between soft and hard thresholding function and offers potential advantages of generally less sensitivity to small perturbations in the data over hard thresholding function and smaller bias and overall reconstruction error over soft thresholding function. Additionally, the proposed function is comparable to the semisoft thresholding function, while the latter requires two thresholds. Moreover, our proposed function can adjust flexibly between the hard and soft thresholding function through the parameter n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document}, providing a better balance between noise removal and detail preservation. Numerical experiments also demonstrate that the proposed thresholding function outperforms the three classical ones in terms of PSNR and visual quality.