基于重加权相关全变分模型的医学图像去噪方法
Medical Image Denoising Method Based on Reweighted Correlation Total Variation Model
摘要: 图像去噪一直是一个受到大量研究者关注的问题，并成功应用到医学等领域。典型的图像去噪方法是利用图像中存在的先验信息，例如低秩先验，局部光滑先验等。但是，目前的图像去噪方法并没有充分利用到图像的这些先验信息，导致去噪效果不是很理想。针对上述问题，本文提出了基于重加权相关全变分正则项的图像去噪模型。该模型利用重加权核范数的方式对相关全变分正则项进行约束，来保证更加充分地利用图像中的低秩先验和局部光滑先验，以此来提升图像恢复效果。我们应用该方法到医学图像中，并和常见的几种图像去噪方法进行比较，实验结果显示，该方法所得到的图像质量得到了明显的提升。
Abstract: Image denoising has always been a problem that attracts the attention of a large number of researchers, and has been successfully applied to medical fields. Typical image denoising methods use the prior information existing in the image, such as low-rank prior, local smooth prior, etc. However, the current image denoising methods do not make full use of the prior information of the image, resulting that the denoising effect is not very ideal. To solve the above problems, this paper proposed an image denoising model based on reweighted correlation total variation regularization term. In this model, the reweighted nuclear norm method is used to constrain the correlated total variation regularization term to ensure that the low-rank prior and local smooth prior in the image are fully utilized, so as to improve the image restoration effect. We applied this method to medical images and compared it with several common image denoising methods. The experimental results show that the image quality obtained by this method has been significantly improved.
文章引用：张芝浩, 李涛. 基于重加权相关全变分模型的医学图像去噪方法[J]. 人工智能与机器人研究, 2024, 13(2): 203-212. https://doi.org/10.12677/airr.2024.132022

参考文献

[1] Padilla, R., Netto, S.L. and Da Silva, E.A. (2020) A Survey on Performance Metrics for Object-Detection Algorithms. 2020 IEEE International Conference on Systems, Signals and Image Processing (IWSSIP), Niterói, 1-3 July 2020, 237-242. [Google Scholar] [CrossRef] 
[2] Zheng, S., Zhang, Y., Liu, W. and Zou, Y. (2020) Improved Image Representation and Sparse Representation for Image Classification. Applied Intelligence, 50, 1687-1698. [Google Scholar] [CrossRef] 
[3] Zhou, E., Xu, X., Xu, B. and Wu, H. (2023) An Enhancement Model Based on Dense Atrous and Inception Convolution for Image Semantic Segmentation. Applied Intelligence, 53, 5519-5531. [Google Scholar] [CrossRef] 
[4] Candès, E.J., Li, X., Ma, Y. and Wright, J. (2011) Robust Principal Component Analysis? Journal of the ACM (JACM), 58, 1-37. [Google Scholar] [CrossRef] 
[5] Wang, H., Cen, Y., He, Z., He, Z., Zhao, R. and Zhang, F. (2017) Reweighted Low-Rank Matrix Analysis with Structural Smoothness for Image Denoising. IEEE Transactions on Image Processing, 27, 1777-1792. [Google Scholar] [CrossRef] 
[6] Peng, J., Wang, Y., Zhang, H., Wang, J. and Meng, D. (2022) Exact Decomposition of Joint Low Rankness and Local Smoothness plus Sparse Matrices. IEEE Transactions on Pattern Analysis and Machine Intelligence, 45, 5766-5781. [Google Scholar] [CrossRef] 
[7] Gu, S., Zhang, L., Zuo, W. and Feng, X. (2014) Weighted Nuclear Norm Minimization with Application to Image Denoising. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Columbus, 23-28 June 2014, 2862-2869. [Google Scholar] [CrossRef] 
[8] Gu, S., Xie, Q., Meng, D., Zuo, W., Feng, X. and Zhang, L. (2017) Weighted Nuclear Norm Minimization and Its Applications to Low Level Vision. International Journal of Computer Vision, 121, 183-208. [Google Scholar] [CrossRef] 
[9] Xie, Y., Gu, S., Liu, Y., Zuo, W., Zhang, W. and Zhang, L. (2016) Weighted Schatten p-Norm Minimization for Image Denoising and Background Subtraction. IEEE Transactions on Image Processing, 25, 4842-4857. [Google Scholar] [CrossRef] 
[10] Huang, Y., Liao, G., Xiang, Y., Zhang, L., Li, J. and Nehorai, A. (2019) Low-Rank Approximation via Generalized Reweighted Iterative Nuclear and Frobenius Norms. IEEE Transactions on Image Processing, 29, 2244-2257. [Google Scholar] [CrossRef] 
[11] Chen, L., Jiang, X., Liu, X. and Haardt, M. (2022) Reweighted Low-Rank Factorization with Deep Prior for Image Restoration. IEEE Transactions on Signal Processing, 70, 3514-3529. [Google Scholar] [CrossRef] 
[12] Lin, Z., Chen, M. and Ma, Y. (2010) The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-Rank Matrices.
[13] Boyd, S., Parikh, N., Chu, E., Peleato, B. and Eckstein, J. (2011) Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers. Foundations and Trends® in Machine learning, 3, 1-122. [Google Scholar] [CrossRef] 
[14] Krishnan, D. and Fergus, R. (2009) Fast Image Deconvolution Using Hyper-Laplacian Priors, Supplementary Material. Neural Information Processing Systems Conference, Vancouver, 7-10 December 2009, 1033-1041.
[15] Donoho, D.L. (1995) De-Noising by Soft-Thresholding. IEEE Transactions on Information Theory, 41, 613-627. [Google Scholar] [CrossRef] 
[16] Cao, F., Chen, J., Ye, H., Zhao, J. and Zhou, Z. (2017) Recovering Low-Rank and Sparse Matrix Based on the Truncated Nuclear Norm. Neural Networks, 85, 10-20. [Google Scholar] [CrossRef] [PubMed]
[17] Dou, Y., Liu, X., Zhou, M. and Wang, J. (2023) Robust Principal Component Analysis via Weighted Nuclear Norm with Modified Second-Order Total Variation Regularization. The Visual Computer, 39, 3495-3505. [Google Scholar] [CrossRef] 
[18] Wang, Z., Bovik, A.C., Sheikh, H.R. and Simoncelli, E.P. (2004) Image Quality Assessment: From Error Visibility to Structural Similarity. IEEE Transactions on Image Processing, 13, 600-612. [Google Scholar] [CrossRef] 
[19] Sagheer, S.V. and George, S.N. (2020) A Review on Medical Image Denoising Algorithms. Biomedical Signal Processing and Control, 61, Article ID: 102036. [Google Scholar] [CrossRef] 

为你推荐