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 todays 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 signals 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. 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