Quaternion Matrix Factorization for Low-Rank Quaternion Matrix Completion

Chen, Jiang-Feng; Wang, Qingwen; Song, Guang-Jing; Li, Tao

doi:10.3390/math11092144

Cited by 3 publications

(1 citation statement)

References 28 publications

(34 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Given the great success of the nonlocal means (NLM) [27] method, a series of NSS prior-based methods have been developed successively and have shown impressive restoration effects. These approaches can be broadly summarized into three clusters, i.e., filter-based methods [27,29,30], patch group-based sparse representation methods [4,23,[31][32][33][34][35][36][37][38], and low-rank approximation-based methods [2,[39][40][41][42][43][44]. Apart from focusing on the internal NSS prior of the corrupted image, some recent approaches have paid attention to exploiting the external NSS prior learned from high-quality natural images [28,45,46].…”

Section: Introductionmentioning

confidence: 99%

Learning the Hybrid Nonlocal Self-Similarity Prior for Image Restoration

Yuan,

Liu,

Liang

et al. 2024

Mathematics

View full text Add to dashboard Cite

As an immensely important characteristic of natural images, the nonlocal self-similarity (NSS) prior has demonstrated great promise in a variety of inverse problems. Unfortunately, most current methods utilize either the internal or the external NSS prior learned from the degraded image or training images. The former is inevitably disturbed by degradation, while the latter is not adapted to the image to be restored. To mitigate such problems, this work proposes to learn a hybrid NSS prior from both internal images and external training images and employs it in image restoration tasks. To achieve our aims, we first learn internal and external NSS priors from the measured image and high-quality image sets, respectively. Then, with the learned priors, an efficient method, involving only singular value decomposition (SVD) and a simple weighting method, is developed to learn the HNSS prior for patch groups. Subsequently, taking the learned HNSS prior as the dictionary, we formulate a structural sparse representation model with adaptive regularization parameters called HNSS-SSR for image restoration, and a general and efficient image restoration algorithm is developed via an alternating minimization strategy. The experimental results indicate that the proposed HNSS-SSR-based restoration method exceeds many existing competition algorithms in PSNR and SSIM values.

show abstract