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The image nonlocal self-similarity (NSS) prior refers to the fact that a local patch often has many nonlocal similar patches to it across the image and has been widely applied in many recently proposed machining learning algorithms for image processing. However, there is no theoretical analysis on its working principle in the literature. In this paper, we discover a potential causality between NSS and low-rank property of color images, which is also available to grey images. A new patch group based NSS prior scheme is proposed to learn explicit NSS models of natural color images. The numerical low-rank property of patched matrices is also rigorously proved. The NSS-based QMC algorithm computes an optimal low-rank approximation to the high-rank color image, resulting in high PSNR and SSIM measures and particularly the better visual quality. A new tensor NSS-based QMC method is also presented to solve the color video inpainting problem based on quaternion tensor representation. The numerical experiments on color images and videos indicate the advantages of NSS-based QMC over the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Although image denoising as a basic task of image restoration has been widely studied in the past decades, there are not many studies on mixed noise denoising. In this paper, we propose two structured dictionary learning models to recover images corrupted by mixed Gaussian and impulse noise. These two models can be merged as $\ell _{p}$ -norm fidelity plus $\ell _{q}$ -norm regularization. The fidelity term is used to fit image patches and the regularization term is employed for sparse coding. Particularly, we utilize proximal (and proximal linearized) alternating minimization methods as the main solvers to deal with these two models. We remove the Gaussian noise under the assumption that the uncorrupted image can be approximated with a linear representation under an appropriate orthogonal basis. We use different ways to remove impulse noise for these two models. The experimental results are reported to compare the existing methods and demonstrate the performance of the proposed denoising model is better than the other existing methods in terms of some quality assessment metrics. [ABSTRACT FROM AUTHOR]

Heterogeneous transfer learning has recently gained much attention as a new machine learning paradigm in which the knowledge can be transferred from source domains to target domains in different feature spaces. Existing works usually assume that source domains can provide accurate and useful knowledge to be transferred to target domains for learning. In practice, there may be noise appearing in given source (text) and target (image) domains data, and thus, the performance of transfer learning can be seriously degraded. In this paper, we propose a robust and non-negative collective matrix factorization model to handle noise in text-to-image transfer learning, and make a reliable bridge to transfer accurate and useful knowledge from the text domain to the image domain. The proposed matrix factorization model can be solved by an efficient iterative method, and the convergence of the iterative method can be shown. Extensive experiments on real data sets suggest that the proposed model is able to effectively perform transfer learning in noisy text and image domains, and it is superior to the popular existing methods for text-to-image transfer learning. [ABSTRACT FROM AUTHOR]