Robust Spare Representation in Quaternion Space

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	Robust Spare Representation in Quaternion Space
	Wang, Y.; Kou, K. I.; Zou, C.; Tang, Y.Y.
	2021-03-11
Source Publication	IEEE Transactions on Image Processing
ISSN	1941-0042
Pages	3637-3649
Abstract	Sparse representation has achieved great success across various fields including signal processing, machine learning, and computer vision. However, most existing sparse representation methods are confined to the real-valued data. This largely limits their applicability to the quaternion-valued data, which has been widely used in numerous applications such as color image processing. Another critical issue is that their performance may be severely hampered due to the data noise or outliers in practice. To tackle the problems above, in this work we propose a robust quaternion valued sparse representation (RQVSR) method in a fully quaternion-valued setting. To handle the quaternion noises, we first define a new robust estimator referred as quaternion Welsch estimator to measure the quaternion residual error. Compared to the conventional quaternion mean square error, it can largely suppress the impact of large data corruption and outliers. To implement RQVSR, we have overcome the difficulties raised by the noncommutativity of quaternion multiplication and developed an effective algorithm by leveraging the half-quadratic theory and the alternating direction method of multipliers framework. The experimental results show the effectiveness and robustness of the proposed method for quaternion sparse signal recovery and color image reconstruction.
Keyword	Quaternion Signal Recovery Quaternion Welsch Estimator Color Image Processing
Indexed By	SCIE
Language	英語English
The Source to Article	PB_Publication
Document Type	Journal article
Collection	DEPARTMENT OF MATHEMATICS
Corresponding Author	Kou, K. I.
Affiliation	University of Macau
Recommended Citation GB/T 7714	Wang, Y.,Kou, K. I.,Zou, C.,et al. Robust Spare Representation in Quaternion Space[J]. IEEE Transactions on Image Processing, 2021, 3637-3649.
APA	Wang, Y.., Kou, K. I.., Zou, C.., & Tang, Y.Y. (2021). Robust Spare Representation in Quaternion Space. IEEE Transactions on Image Processing, 3637-3649.
MLA	Wang, Y.,et al."Robust Spare Representation in Quaternion Space".IEEE Transactions on Image Processing (2021):3637-3649.

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