Robust Sparse Representation in Quaternion Space
| Autor: | Kit Ian Kou, Cuiming Zou, Yulong Wang, Yuan Yan Tang |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Signal processing
Mean squared error Computer science MathematicsofComputing_NUMERICALANALYSIS ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION Robust statistics Estimator 02 engineering and technology Sparse approximation Computer Graphics and Computer-Aided Design Robustness (computer science) 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing Quaternion Algorithm Software ComputingMethodologies_COMPUTERGRAPHICS Sparse matrix |
| Zdroj: | IEEE transactions on image processing : a publication of the IEEE Signal Processing Society. 30 |
| ISSN: | 1941-0042 |
| Popis: | 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 limit 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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