Matrix factorization techniques have been widely used in image completion to enhance the quality of incomplete images. In this article, we provide a comprehensive review of various matrix factorization methods, including Tucker decomposition, orthogonal tensor train (OTT), and non-negative matrix factorization (NMF). We also discuss their applications in image completion and highlight their advantages and limitations.
Tucker Decomposition
Tucker decomposition is a popular matrix factorization technique that decomposes a matrix into three matrices: a core matrix, a sparse matrix, and a low-rank matrix. In the context of image completion, Tucker decomposition can be used to estimate the missing pixels based on the observed pixels. The core matrix represents the underlying structure of the image, while the sparse matrix captures the details of the image.
Orthogonal Tensor Train (OTT)
OTTensor train (TT) is a generalization of the tensor product that can represent high-order tensors with a compact and efficient format. OTT is a variant of TT that is specifically designed for image completion tasks. OTT decomposes an image into a sequence of rank-one tensors, each of which represents a layer of the image. By recursively applying the decomposition to each layer, the missing pixels can be estimated with high accuracy.
Non-negative Matrix Factorization (NMF)
NMF is another popular matrix factorization technique that decomposes a matrix into two non-negative matrices. In the context of image completion, NMF can be used to estimate the missing pixels by finding the best fit between the observed pixels and a set of basis vectors. The basis vectors are non-negative and can be used to represent the image in a compact and efficient format.
Applications and Advantages
Matrix factorization techniques have numerous applications in image completion, including denoising, deblurring, and super-resolution. These techniques can also be used to improve the quality of images corrupted by various types of noise, such as additive white Gaussian noise (AWGN) or salt and pepper noise.
One of the main advantages of matrix factorization techniques is their ability to handle incomplete images with a large number of pixels. These techniques can also capture complex structures in the image, such as edges and textures, which are important for image completion.
Limitations and Future Directions
While matrix factorization techniques have shown promising results in image completion, they are not without limitations. One of the main challenges is choosing the appropriate rank parameter, which can significantly affect the quality of the estimated pixels. In addition, these techniques may not work well for images with complex structures or those that are severely corrupted.
In future research, it is important to develop new matrix factorization techniques that can handle more complex structures in images and provide better performance in various applications. Additionally, there is a need for more efficient algorithms that can handle large-scale image completion tasks.
Conclusion
Matrix factorization techniques have been widely used in image completion to enhance the quality of incomplete images. Tucker decomposition, OTT, and NMF are some of the popular matrix factorization methods reviewed in this article. These techniques have numerous applications in image completion and can capture complex structures in the image. However, there are still challenges and limitations associated with these techniques, which require further research to overcome.
