Color Image Recovery Using Low-Rank Quaternion Matrix Completion Algorithm

Miao, Jifei; Kou, Kit Ian

doi:10.1109/tip.2021.3128321

Cited by 43 publications

(13 citation statements)

References 46 publications

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“…The clustering does not depend on the selection of center points and the number of clusters. Moreover, we provide a new method to solve the rank minimization problem [43], [44], [45], [46].…”

Section: Methodsmentioning

confidence: 99%

Image Segmentation Based on Fuzzy Low-Rank Structural Clustering

Song

Jia

Yang

et al. 2023

IEEE Trans. Fuzzy Syst.

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Fuzzy clustering is an essential algorithm in image segmentation, and most of them are fuzzy c-mean (FCM) algorithms. However, it is sensitive to noise, center point selection, cluster number, and distance metric. To address this problem, we propose a new fuzzy clustering method based on low-rank representation (LRR) for image segmentation, which integrates low-rank structure with fuzzy theory. First, we improve the morphological reconstruction super-pixel method based on edge detection by introducing anisotropy to enhance the image edge. Thus, on the one hand, the improved morphological reconstruction super-pixel method can improve its noise-resistance performance; on the other hand, the complexity of the subsequent low-rank computation can be reduced by enhancing the superpixels constructed by the edges. Second, inspired by the fact that rank can represent correlation, we propose the concept of fuzzy low-rank structure, where fuzzy means not dealing with data directly but with the relationship between data. Specifically, we perform rank minimization on the constructed membership matrix to obtain the optimal matrix. To obtain better clustering results, we added the Frobenius norm of the fuzzy matrix as a fuzzy regularization term in the LRR model to achieve global convergence and obtain a membership matrix with a strong element correlation. Finally, we obtain the final clustering results by clustering the processed membership matrix using a subspace clustering with a low-rank structure constraint. Experiments performed on artificial and real-world images show that the proposed method is effective and efficient, which is more competitive than state-of-the-art methods.

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Section: Methodsmentioning

confidence: 99%

Image Segmentation Based on Fuzzy Low-Rank Structural Clustering

Song

Jia

Yang

et al. 2023

IEEE Trans. Fuzzy Syst.

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“…To avoid scaling confusion we assume Tr W = ||W || nu = i λ i (W ) = 3, which means assigning a total weight 3 to three channels for diagonal W , and note that when W = I 3 (3.5) reduces to the commonly used quadratic loss [13,22,29,31,53]. In accordance to the weight W we require a prior estimation on the weighted max norm…”

Section: Lemma 3 Assumementioning

confidence: 99%

Color Image Inpainting via Robust Pure Quaternion Matrix Completion: Error Bound and Weighted Loss

Chen,

2022

Preprint

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In this paper, we study color image inpainting as a pure quaternion matrix completion problem. In the literature, the theoretical guarantee for quaternion matrix completion is not well-established. Our main aim is to propose a new minimization problem with an objective combining nuclear norm and a quadratic loss weighted among three channels. To fill the theoretical vacancy, we obtain the error bound in both clean and corrupted regimes, which relies on some new results of quaternion matrices. A general Gaussian noise is considered in robust completion where all observations are corrupted. Motivated by the error bound, we propose to handle unbalanced or correlated noise via a crosschannel weight in the quadratic loss, with the main purpose of rebalancing noise level, or removing noise correlation. Extensive experimental results on synthetic and color image data are presented to confirm and demonstrate our theoretical findings.

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“…In 1843, Hamilton introduced the concept of real quaternions, which are defined by [1] H = {q = q 0 + q 1 i + q 2 j + q 3 k : i 2 = j 2 = k 2 = −1, ijk = −1, q 0 , q 1 , q 2 , q 3 ∈ R}, which is a four-dimensional noncommutative associative algebra over real number field. Quaternions have been used in many areas, such as statistic of quaternion random signals [2], color image processing [3], and face recognition [4]. The non-commutative nature of quaternion multiplication introduces numerous challenges and difficulties when dealing with real quaternions.…”

Section: Introductionmentioning

confidence: 99%

The Hermitian Solution to a New System of Commutative Quaternion Matrix Equations

Zhang,

Wang,

Xie

2024

Symmetry

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This paper considers the Hermitian solutions of a new system of commutative quaternion matrix equations, where we establish both necessary and sufficient conditions for the existence of solutions. Furthermore, we derive an explicit general expression when it is solvable. In addition, we also provide the least squares Hermitian solution in cases where the system of matrix equations is not consistent. To illustrate our main findings, in this paper we present two numerical algorithms and examples.

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Color Image Recovery Using Low-Rank Quaternion Matrix Completion Algorithm

Cited by 43 publications

References 46 publications

Image Segmentation Based on Fuzzy Low-Rank Structural Clustering

Image Segmentation Based on Fuzzy Low-Rank Structural Clustering

Color Image Inpainting via Robust Pure Quaternion Matrix Completion: Error Bound and Weighted Loss

The Hermitian Solution to a New System of Commutative Quaternion Matrix Equations

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