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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2309.11090 |
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| _version_ | 1866910400847544320 |
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| author | Zhang, Zirui Wu, Yiwen Liu, Yang Li, Siyu Li, Hong Liu, Hao |
| author_facet | Zhang, Zirui Wu, Yiwen Liu, Yang Li, Siyu Li, Hong Liu, Hao |
| contents | In this work, we investigate the optimal map-making technique for the linear system $d=Ax+n$ while carefully taking into account singularities that may come from either the covariance matrix $C = \langle nn^t \rangle$ or the main matrix $A$. We first describe the general optimal solution, which is quite complex, and then use the modified pseudo inverse to create a near-optimal solution, which is simple, robust, and can significantly alleviate the unwanted noise amplification during map-making. The effectiveness of the nearly optimal solution is then compared to that of the naive co-adding solution and the standard pseudo inverse solution, showing noticeable improvements. Interestingly, all one needs to get the near-optimal solution with singularity is just a tiny change to the classical solution, which is designed for the case without singularity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_11090 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Optimal map-making with singularities Zhang, Zirui Wu, Yiwen Liu, Yang Li, Siyu Li, Hong Liu, Hao Cosmology and Nongalactic Astrophysics Instrumentation and Methods for Astrophysics In this work, we investigate the optimal map-making technique for the linear system $d=Ax+n$ while carefully taking into account singularities that may come from either the covariance matrix $C = \langle nn^t \rangle$ or the main matrix $A$. We first describe the general optimal solution, which is quite complex, and then use the modified pseudo inverse to create a near-optimal solution, which is simple, robust, and can significantly alleviate the unwanted noise amplification during map-making. The effectiveness of the nearly optimal solution is then compared to that of the naive co-adding solution and the standard pseudo inverse solution, showing noticeable improvements. Interestingly, all one needs to get the near-optimal solution with singularity is just a tiny change to the classical solution, which is designed for the case without singularity. |
| title | Optimal map-making with singularities |
| topic | Cosmology and Nongalactic Astrophysics Instrumentation and Methods for Astrophysics |
| url | https://arxiv.org/abs/2309.11090 |