1. 研究目的与意义（文献综述包含参考文献）
毕业设计(论文)任务书课题名称 Low-Rank Matrix Recovery and Applications in Image Restoration院（系） 电气工程与控制科学学院 专业 自动化（留学生） 姓名 MD MEHEDI HASSAN学号 201824404006起讫日期 2022年1月-2022年6月指导教师 董静 2021 年 12 月 24 日毕 业 设 计（论 文）开 题 报 告1．结合毕业设计（论文）课题情况，根据所查阅的文献资料，每人撰写2000字左右的文献综述：文 献 综 述Low-rank matrices play a fundamental role in modeling and computational methods for signal processing and machine learning. In many applications where low-rank matrices arise, these matrices cannot be fully sampled or directly observed, and one encounters the problem of recovering the matrix given only incomplete and indirect observations. This project will focus on models and algorithms for low-rank matrix recovery, including their applications in image restoration.1. Research BackgroundThe rapid growth of computer technology in today's information age allows for the digital recording of rich visual information in photographs, movies, and other formats. Data loss and missing image information owing to damage and poor transmission, on the other hand, have a severe influence on visual media communication and study [13]. Digital image restoration and enhancement are primarily concerned with restoring missing and damaged parts of digital images using residual information, imaging context, and past image knowledge in order to bring the restored image as similar to its original as feasible [49]. Digital restoration of deteriorated photos allows people from various professions to communicate, appreciate, and investigate more quickly [3, 4, 10].Low-rank matrix recovery, and its applications in image restoration, is a fundamental ill-posed inverse issue in image processing and low-level vision that tries to recreate a latent high-quality image from its degraded observation [7,11]. Image restoration technology has progressed significantly, and several advanced methods based on a range of optimization models, including variational calculus and partial differential equations [4, 5, 8, 12], have been introduced exemplar matching and synthesis [1315], sparse representation and low rank matrix completion [1618], and so on. On the basis of a smoothness prior, image restoration algorithms based on variational calculus and partial differential equations propagate/diffuse local structural information from the external to the internal of missing areas [4]. Several variants utilize various models (linear, nonlinear, isotropic, or anisotropic) to extend the information in a certain propagation direction or to account for geometric information such as the curvature of local neighborhood pixels [4, 5, 12]. However, a vast number of studies reveal that these methods have certain limitations: while they are effective for images with piecewise smooth structures or small gaps, they are ineffective for textured images, particularly when the missing area is big. After a few revisions, in order to keep the edges. It can easily cause excessive smoothness and blur in the areas that have been corrected [7].2. Literature ReviewTo reestablish harmed areas of finished structures, based on spearheading works of surface amalgamation [28], one more picture reclamation strategy is placed ahead in light of model coordinating and amalgamation. For a model required to be fixed, a surface fix technique attempts to track down the best matching example to it in a specific area and reestablishes missing data by testing or duplicating relating pixels for model combination [13-15]. A better picture restoration can be obtained if enough similar candidate blocks are located in the image or in an external image database. Recent studies in this area have focused on multiscale refinement of exemplar matching and synthesis, improvement in the distance measure used to find matching blocks, a faster-searching method for matching blocks, optimized block processing ordering, and filling unknown pixels with matching blocks [7].Sparse representation theory of signal and image has been a popular study subject in signal processing for the past two decades. Sparse prior knowledge has been integrated Low-rank matrix recovery into image restoration algorithms as a result of the rapid growth of sparse sampling and compressed sensing [16, 17, 18]. The image is supposed to be a sparse signal subjected to a set of specified transformation bases (the signal's sparsity is mostly determined by the supplied bases). These bases are made up of atoms stored in a dictionary matrix, which can be produced using various dictionary learning methods [19].Over the last decade, progress in the image classification problem has been achieved by using more powerful classifiers and building or learning better image representations. On one hand, standard discriminative approaches such as Support Vector Machines or Boosting have been extended to the multi-label case [20] and incorporated under frameworks such as Multiple Instance Learning [ 21] and Multi-task Learning [22][23] The nuclear norm regularizer has been used to solve categorization problems. In discriminative circumstances, most of these techniques use the nuclear norm to impose correlations between classifiers [24] or to allow for dimensionality reduction. The nuclear norm was reduced into a proxy infinite-dimensional optimization by Harchaoui et al. [25], allowing coordinate descent in large scale situations with smooth losses.Zhong and Wang presented a multiplespectral-band conditional random field model in [26] to model and apply spatial and spectral dependences simultaneously in a unified probabilistic framework.Chen et al. [27] proposed a spatialspectral domain mixing prior model based on a maximum a posteriori framework that takes advantage of the differing features of HSIs in the spatial and spectral domains.References[1] F. Stanco, S. Battiato, and G. Gallo, Digital Imaging for Cultural Heritage Preservation: Analysis, Restoration, and Reconstruction of Ancient Artworks, CRC Press, Boca Raton, FL, USA, 2011.[2] F. Wang, Comparative study on digital image enhancement for virtual restoration of mural painting, International Journal of Engineering and Technical Research, vol. 7, no. 12, pp. 137140, 2017.[3] M. Jmal, W. Souidene, and R. Attia, Efficient cultural heritage image restoration with nonuniform illumination enhancement, Journal of Electronic Imaging, vol. 26, no. 1, Article ID 011020, 2017.[4] M. Bertalmio, G. Sapiro, V. Caselles, and C. Ballester, Image inpainting, in Proceedings of ACM SIGGRAPH, pp. 417424, New Orleans, LA, USA, July 2000.[5] T. F. Chan and J. Shen, Mathematical models for local nontexture inpaintings, SIAM Journal on Applied Mathematics, vol. 62, no. 3, pp. 10191043, 2002.[6] M. Bertalmio, L. Vese, G. Sapiro, and S. Osher, Simultaneous structure and texture image inpainting, IEEE Transactions on Image Processing, vol. 12, no. 8, pp. 882889, 2003.[7] C. Guillemot and O. Le Meur, Image inpainting: overview and recent advances, IEEE Signal Processing Magazine, vol. 31, no. 1, pp. 127144, 2014.[8] S.-J. Fu and Q.-Q. Ruan, A local nontexture image inpainting and denoising based on nonlinear PDEs, in Proceedings of the 7th International Conference on Signal Processing, 2004. Proceedings. ICSP 04. 2004, vol. 2, pp. 10291032, Beijing, China, September 2004.[9] K. Zhang, W. Zuo, S. Gu, and L. Zhang, Learning deep CNN denoiser prior for image restoration, in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, pp. 39293938, Honolulu, HI, USA, July 2017.[10] F. Wang, A study of digital image enhancement for cultural relic restoration, International Journal of Engineering and Technical Research, vol. 7, no. 11, pp. 4144, 2017.[11] R. C. Gonzalez and R. E. Woods, Digital Image Processing, Prentice-Hall, New York, NY, USA, 2nd edition, 2004.[12] T. F. Chan and J. Shen, Nontexture inpainting by curvature driven diffusions, Journal ofVisual Communication and Image Representation, vol. 12, no. 4, pp. 436449, 2001[13] J.-P. Lewis, Texture synthesis for digital painting, ACM SIGGRAPH Computer Graphics, vol. 18, no. 3, pp. 245252, 1984[14] A. Efros and T. K. Leung, Texture synthesis by nonparametric sampling, in Proceedings of IEEE International Conference on Computer Vision, pp. 10331038, Kerkyra, Greece, September 1999.[15] Vahid and F. Yaghmaee, Introducing a new fast exemplar-based inpainting algorithm, in Proceedings of the 2014 22nd Iranian Conference on Electrical Engineering (ICEE), pp. 874878, Tehran, Iran, May 2014.[16] Dong, Jing, et al. "Low rank matrix completion using truncated nuclear norm and sparse regularizer." Signal Processing: Image Communication 68 (2018): 76-87.[17] H. Ji, C. Liu, Z. Shen, Y. Xu, Robust video denoising using low rank matrix completion, in: 2010 IEEE Conference on Computer Vision and Pattern Recognition, CVPR, 2010, pp. 17911798[18] N. Merhav, R. Kresch, Approximate convolution using DCT coefficient multipliers, IEEE Trans. Circuits Syst. Video Technol. 8 (4) (1998) 378385.[19] Ma, Long, et al. "Sparse representation for face recognition based on discriminative low-rank dictionary learning." 2012 IEEE conference on computer vision and pattern recognition. IEEE, 2012.[20] W. Dong, G. Shi, and X. Li, Nonlocal image restoration with bilateral variance estimation: a low-rank approach, IEEE Transactions on Image Processing, vol. 22, no. 2, pp. 700 711, 2013.[21] Y. Hu, D. Zhang, J. Ye, X. Li, X. He, Fast and accurate matrix completion via truncated nuclear norm regularization, IEEE Trans. Pattern Anal. Mach. Intell. 35 (9) (2013) 2117 2130.[22] R. Chartrand and W. Yin, Iteratively reweighted algorithms for compressive sensing, in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 38693872, IEEE, Las Vegas, NV, USA, MarchApril 2008.[23] Yakhnenko and V. Honavar, Multi-instance multi-label learning for image classification with large vocabularies, in Proc. Brit. Mach. Vis. Conf., 2011, pp. 112[24] B. Goldberg, X. Zhu, B. Recht, J. ming Xu, and R. Nowak, Transduction with matrix completion: Three birds with one stone, in Proc. Adv. Neural Inf. Process. Syst., 2010, pp. 757765.[25] Z. Harchaoui, M. Douze, M. Paulin, M. Dudik, and J. Malick, Large-scale image classification with trace-norm regularization, in Proc. IEEE Conf. Comput. Vis. Pattern Recog., 2012, pp. 33863393[26] S. Chen, X. Hu, and S. Peng, Hyperspectral imagery denoising using a spatial-spectral domain mixing prior, J. Comput. Sci. Technol., vol. 27, no. 4, pp. 851861, Jul. 2012.[27] Sun, Airong, Yihua Tan, and Jinwen Tian. "Hyperspectral image segmentation using spectral-spatial constrained conditional random field." MIPPR 2011: Multispectral Image Acquisition, Processing, and Analysis. Vol. 8002. SPIE, 2011.[28] Chen, Shao-Lin, Xi-Yuan Hu, and Si-Long Peng. "Hyperspectral imagery denoising using a spatial-spectral domain mixing prior." Journal of computer science and technology 27.4 (2012): 851-861.
2. 研究的基本内容、问题解决措施及方案
毕 业 设 计（论 文）开 题 报 告 本课题要研究或解决的问题和拟采用的研究手段（途径）： Research Methods:The recovery of unknown measurements is the goal of the low-rank matrix recovery problem. This problem has different types of applications. The interdependence between elements imposed by the low-rank structure are used in this matrix completion and low-rank approximation techniques. This study is very important. In this project, the main goal and purpose are to recover low-rank matrices and applications in image restoration. For this task, we are using the non-local gradual reweighted regularization method (NGRR). That will use for Low-rank matrix recovery (LRMR) and also apply the other method for image restoration, that things we will use this algorithm in low matrix data recovery (LRMR) and application in image restoration. non-local gradual reweighted regularization algorithm is the main algorithm in our task. It presents a theoretical framework and mathematical model for the processes involved in our issue, namely Low-rank matrix recovery and applications in image restoration. These methods are frequently used in situations where the observations are derived through a counting procedure. Many situations benefit from the ability to recover (or de-noise) a low-rank signal from noisy, count-based observations. For this main algorithm, we need to complete pseudocode for Low rank matrix recovery and also image restoration.To focusing this algorithm, this method needs also the block matching and grouping Block matching and group block helps to understand this algorithm. For a picture block situated in the limit of region with data misfortune, we can get a decent gauge through over four stages. Be that as it may, for picture block situated inside region with data misfortune, since there is no solid data for comparative block coordinating, the assessment in light of above handling isn't exact. To tackle this issue, we utilize emphasis dispersion to spread picture data into the objective region. In other words, the past result of picture rebuilding is utilized as theInstatement of next emphasis. With the increment of number of cycles, picture blocks situated inside region with data misfortune will be slowly topped off with its encompassing data bit by bit. The most important part is in project, we are adding four algorithms that are truncated nuclear norm minimization, Weighted nuclear norm minimization, Beta process factor analysis and non-gradual reweighted regularization. non-gradual reweighted regularization will compared other three baseline algorithms And for images calculation, we need to add peak signal to noise ratio because that will help us to to get every image missing ratio. The equation are:PSNR=10 〖log〗_10 (〖255〗^2/(1/NΣ_(J=1)^N 〖(x_j-x _j)〗^2 ))Describes x_j and x _j are the real and estimated images at pixel j, respectively.All techniques will be executed utilizing MATLAB programming with a grayscale going from 0 to 255. In an examination of various image reclamation strategies. Research Plans:According to the proposed algorithm, the most challenging part is removing masked using algorithms. Matlab will be use in this experiment. To begin using Matlab, we must first choose or select the programming file that we want to use. Either the data or the Matlab cannot be read. For this task, we need to take grayscale image, we have pixel values going from 0 to 255. The more modest numbers more like zero address the hazier shade while the bigger numbers more like 255 address the lighter or the white shade. To confirm the presence of the proposed technique in picture reclamation, we apply it to different regular pictures in various errands: rebuilding pictures with irregular loss of pixels. The technique of (NGRR) algorithm is checked on test pictures displayed in contrasting it and some exemplary picture rebuilding strategies, including BPFA, TNNR, and WNNM. All techniques are executed utilizing MATLAB programming with a grayscale going from 0 to 255. In an examination of various image reclamation strategies.After comparing algorithms, we need to also use PSNR (peak signal noise ratio),that i mentioned in other section, to calculate missing ratio. Missing ratio can told us, our proposed algorithm is correct or not. And missing ratio should be write dB values.毕 业 设 计（论 文）开 题 报 告指导教师意见： 对文献综述的评语：2．对本课题的深度、广度及工作量的意见和对设计（论文）结果的预测： 指导教师：年月日所在专业审查意见： 负责人： 年月日
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