Stable recovery of complex dictionary-sparse signals from phaseless measurements
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910986940710912 |
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| author | Xia, Lianxing Huo, Haiye |
| author_facet | Xia, Lianxing Huo, Haiye |
| contents | Dictionary-sparse phase retrieval, which is also known as phase retrieval with redundant dictionary, aims to reconstruct an original dictionary-sparse signal from its measurements without phase information. It is proved that if the measurement matrix $A$ satisfies null space property (NSP)/strong dictionary restricted isometry property (S-DRIP), then the dictionary-sparse signal can be exactly/stably recovered from its magnitude-only measurements up to a global phase. However, the S-DRIP holds only for real signals. Hence, in this paper, we mainly study the stability of the $\ell_1$-analysis minimization and its generalized $\ell_q\;(0<q\leq1)$-analysis minimization for the recovery of complex dictionary-sparse signals from phaseless measurements. First, we introduce a new $l_1$-dictionary restricted isometry property ($\ell_1$-DRIP) for rank-one and dictionary-sparse matrices, and show that complex dictionary-sparse signals can be stably recovered by magnitude-only measurements via $\ell_1$-analysis minimization provided that the quadratic measurement map $\mathcal{A}$ satisfies $\ell_1$-DRIP. Then, we generalized the $\ell_1$-DRIP condition under the framework of $\ell_q\;(0<q\leq1)$-analysis minimization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_03961 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stable recovery of complex dictionary-sparse signals from phaseless measurements Xia, Lianxing Huo, Haiye Information Theory Dictionary-sparse phase retrieval, which is also known as phase retrieval with redundant dictionary, aims to reconstruct an original dictionary-sparse signal from its measurements without phase information. It is proved that if the measurement matrix $A$ satisfies null space property (NSP)/strong dictionary restricted isometry property (S-DRIP), then the dictionary-sparse signal can be exactly/stably recovered from its magnitude-only measurements up to a global phase. However, the S-DRIP holds only for real signals. Hence, in this paper, we mainly study the stability of the $\ell_1$-analysis minimization and its generalized $\ell_q\;(0<q\leq1)$-analysis minimization for the recovery of complex dictionary-sparse signals from phaseless measurements. First, we introduce a new $l_1$-dictionary restricted isometry property ($\ell_1$-DRIP) for rank-one and dictionary-sparse matrices, and show that complex dictionary-sparse signals can be stably recovered by magnitude-only measurements via $\ell_1$-analysis minimization provided that the quadratic measurement map $\mathcal{A}$ satisfies $\ell_1$-DRIP. Then, we generalized the $\ell_1$-DRIP condition under the framework of $\ell_q\;(0<q\leq1)$-analysis minimization. |
| title | Stable recovery of complex dictionary-sparse signals from phaseless measurements |
| topic | Information Theory |
| url | https://arxiv.org/abs/2506.03961 |