Sparse Representation for Color Image Based on Geometric Algebra

Wang, Rui; Yu-jie, WU; Shen, Ming; Cao, Wenming

doi:10.1109/icme.2018.8486524

Cited by 3 publications

(3 citation statements)

References 11 publications

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“…where UU H = I M ×M , VV H = I N ×N , I is an identity matrix. Wang et al [11], [12] apply a new algorithm corresponding dictionary learning algorithm, namely K-GASVD, the details of K-GASVD algorithm are shown in Table 1. GA is used to map the color image into a high dimensional space for color image analysis and shows the superior performance compared with competing methods on color images.…”

Section: Applications To Signal and Image Processing A Applications To Sparse Representation Models For Image Processingmentioning

confidence: 99%

Geometric Algebra in Signal and Image Processing: A Survey

Wang

Cao

et al. 2019

IEEE Access

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Recently, Geometric Algebra (GA) has attracted more and more attention in the field of signal and image processing. GA can treat multi-dimensional signals in a holistic way to keep the correlations among multiple dimensions and avoid information loss. So when traditional signal and image processing algorithms are redefined in GA space, they will be more powerful and achieve better performance in multi-dimensional signal processing. In this paper, we provide a comprehensive survey covering various GA-based algorithms. In particular, we first review the mathematic theories of GA and Reduced Geometric Algebra (RGA). Then, advanced GA-based algorithms are elaborately analyzed and compared, including GA-based Sparse representation model, GA-based Dictionary Learning method, Clifford Support Vector Machine, GA-based Feature extraction algorithms, GA-based adaptive filtering algorithms, GA-based Fourier-type transform, and GA-based edge detection algorithm. Finally, we discuss several open issues and challenges of GA, and point out possible research directions in the future.INDEX TERMS Geometric algebra (GA), multivectors, multi-dimensional signals, image processing.

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Section: Applications To Signal and Image Processing A Applications To Sparse Representation Models For Image Processingmentioning

confidence: 99%

Geometric Algebra in Signal and Image Processing: A Survey

Wang

Cao

et al. 2019

IEEE Access

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“…When dealing with color image, the most urgent problem needed to be addressed is to avoid the loss of inherent relationship of RGB channels. Wang et al [19] applied geometric algebra to denote the structure of color information and map the color image into a high-dimensional space, and the model has been, until very recently, regarded as a powerful model for color image processing. Each color image patch can be represented as f = 0 + f 1 e 1 + f 2 e 2 + f 12 e 12 ∈ (G 2 ) N while applying GA, and the sparse representation model in G 2 has been given as…”

Section: Related Work a Review Of Current Sparse Representa-tion Modelsmentioning

confidence: 99%

“…Xu et al [18] provided an efficient color sparse representation model on account of the compatibility between quaternion matrix and color image to avoid losing the correlation of three color channels. Wang et al [19] applied geometric algebra to map the color image into a high-dimensional space to color image analysis and achieved high performance. To address the problem of high computational complexity owing to non-commutative multiplication, Shen et al [20] presented a novel theory of reduced geometric algebra (RGA) with commutative multiplication rules and a novel vector-valued sparse representation model for color image using RGA.…”

Section: Introductionmentioning

confidence: 99%

Multivector Sparse Representation for Multispectral Images Using Geometric Algebra

2019

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Multispectral images can provide more faithful representations for real scenes than the traditional images and improve the performance of image restoration tasks. In this paper, we propose a novel multivector sparse representation model for multispectral images using geometric algebra (GA), with the truth that GA is now well used in image processing and it gives a formidable way to represent multispectral images. The proposed model represents a multispectral image as a GA multivector by fully considering the spatial and spectral information, where a GA dictionary learning algorithm is presented using the K-GA-singular value decomposition (GASVD) (generalized K-means clustering for GASVD) method. Consequently, with the complete consideration of the relationship between spectral channels in multispectral images, artifacts and blurring effects can be successfully avoided. The experimental results demonstrate that the proposed sparse model surpasses the existing methods for multispectral images reconstruction and denoising tasks by capturing correlations between spectral channels thoroughly and shows its usefulness and effectiveness for multispectral images processing.INDEX TERMS Multivector, sparse representation, geometric algebra (GA), multispectral images, dictionary learning, K-GASVD.

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An Immune Clone Particle Swarm Optimization Algorithm for Sparse Representation of Hyperspectral Images

Wang

Liu

2021

Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering

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Sparse Representation for Color Image Based on Geometric Algebra

Cited by 3 publications

References 11 publications

Geometric Algebra in Signal and Image Processing: A Survey

Geometric Algebra in Signal and Image Processing: A Survey

Multivector Sparse Representation for Multispectral Images Using Geometric Algebra

An Immune Clone Particle Swarm Optimization Algorithm for Sparse Representation of Hyperspectral Images

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