A Novel Adaptive Low-Rank Matrix Approximation Method for Image Compression and Reconstruction
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916814573797376 |
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| author | Xu, Weiwei Shen, Weijie Liu, Chang Jia, Zhigang |
| author_facet | Xu, Weiwei Shen, Weijie Liu, Chang Jia, Zhigang |
| contents | Low-rank matrix approximation plays an important role in various applications such as image processing, signal processing and data analysis. The existing methods require a guess of the ranks of matrices that represent images or involve additional costs to determine the ranks. A novel efficient orthogonal decomposition with automatic basis extraction (EOD-ABE) is proposed to compute the optimal low-rank matrix approximation with adaptive identification of the optimal rank. By introducing a randomized basis extraction mechanism, EOD-ABE eliminates the need for additional rank determination steps and can compute a rank-revealing approximation to a low-rank matrix. With a computational complexity of $O(mnr)$, where $m$ and $n$ are the dimensions of the matrix and $r$ is its rank, EOD-ABE achieves significant speedups compared to the state-of-the-art methods. Experimental results demonstrate the superior speed, accuracy and robustness of EOD-ABE and indicate that EOD-ABE is a powerful tool for fast image compression and reconstruction and hyperspectral image dimensionality reduction in large-scale applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22713 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Novel Adaptive Low-Rank Matrix Approximation Method for Image Compression and Reconstruction Xu, Weiwei Shen, Weijie Liu, Chang Jia, Zhigang Numerical Analysis Low-rank matrix approximation plays an important role in various applications such as image processing, signal processing and data analysis. The existing methods require a guess of the ranks of matrices that represent images or involve additional costs to determine the ranks. A novel efficient orthogonal decomposition with automatic basis extraction (EOD-ABE) is proposed to compute the optimal low-rank matrix approximation with adaptive identification of the optimal rank. By introducing a randomized basis extraction mechanism, EOD-ABE eliminates the need for additional rank determination steps and can compute a rank-revealing approximation to a low-rank matrix. With a computational complexity of $O(mnr)$, where $m$ and $n$ are the dimensions of the matrix and $r$ is its rank, EOD-ABE achieves significant speedups compared to the state-of-the-art methods. Experimental results demonstrate the superior speed, accuracy and robustness of EOD-ABE and indicate that EOD-ABE is a powerful tool for fast image compression and reconstruction and hyperspectral image dimensionality reduction in large-scale applications. |
| title | A Novel Adaptive Low-Rank Matrix Approximation Method for Image Compression and Reconstruction |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2506.22713 |