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Erschienen in:

09.06.2024

Recovery Conditions in Weighted Sparse Phase Retrieval via Weighted \(\ell _q\, (0<q\le 1)\) Minimization

verfasst von: Haiye Huo, Li Xiao

Erschienen in: Circuits, Systems, and Signal Processing | Ausgabe 9/2024

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Abstract

In this paper, we generalize the conditions for the exact or stable recovery of weighted k-sparse signals in weighted sparse phase retrieval in our previous work [11] from the weighted \(\ell _1\) minimization to the weighted \(\ell _q\, (0<q\le 1)\) minimization in a broad sense. Specifically, we first present that the weighted null space property (WNSP) is a sufficient and necessary condition to guarantee the exact recovery of a weighted k-sparse signal from its noiseless phaseless measurements via the weighted \(\ell _q\, (0<q\le 1)\) minimization in both the real and complex cases. In addition, we establish a general strong weighted restricted isometry property (SWRIP) condition for the stable recovery of a weighted k-sparse signal from its noisy phaseless measurements via the weighted \(\ell _q\, (0<q\le 1)\) minimization in the real case.

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Literatur
1.
2.
Zurück zum Zitat M. Cao, W. Huang, Sparse phase retrieval via \(\ell _p (0<p\le 1)\) minimization. Int. J. Wavelets Multiresolut. Inf. Process. 20(1), 2150034 (2022)CrossRef M. Cao, W. Huang, Sparse phase retrieval via \(\ell _p (0<p\le 1)\) minimization. Int. J. Wavelets Multiresolut. Inf. Process. 20(1), 2150034 (2022)CrossRef
3.
Zurück zum Zitat R. Chartrand, W. Yin, Iterative reweighted algorithms for compressive sensing. Proc. International Conference on Acoustics, Speech, and Signal Processing, IEEE, Las Vegas, NV, USA, 3869–3872 (2008) R. Chartrand, W. Yin, Iterative reweighted algorithms for compressive sensing. Proc. International Conference on Acoustics, Speech, and Signal Processing, IEEE, Las Vegas, NV, USA, 3869–3872 (2008)
4.
Zurück zum Zitat T. Chen, W. Sun, Linear phaseless retrieval of functions in spline spaces with arbitrary knots. IEEE Trans. Inf. Theory 68(2), 1385–1396 (2022)MathSciNetCrossRef T. Chen, W. Sun, Linear phaseless retrieval of functions in spline spaces with arbitrary knots. IEEE Trans. Inf. Theory 68(2), 1385–1396 (2022)MathSciNetCrossRef
5.
Zurück zum Zitat W. Chen, Y. Li, Recovery of signals under the condition on RIC and ROC via prior support information. Appl. Comput. Harmon. Anal. 46(2), 417–430 (2019)MathSciNetCrossRef W. Chen, Y. Li, Recovery of signals under the condition on RIC and ROC via prior support information. Appl. Comput. Harmon. Anal. 46(2), 417–430 (2019)MathSciNetCrossRef
6.
Zurück zum Zitat Y. Chen, C. Cheng, Q. Sun, Phase retrieval of complex and vector-valued functions. J. Funct. Anal. 283(7), 109593 (2022)MathSciNetCrossRef Y. Chen, C. Cheng, Q. Sun, Phase retrieval of complex and vector-valued functions. J. Funct. Anal. 283(7), 109593 (2022)MathSciNetCrossRef
8.
Zurück zum Zitat B. Du, A. Wan, Stable and robust recovery of approximately \(k\)-sparse signals with partial support information in noise settings via weighted \(\ell _p (0<p\le 1)\) minimization. J. Comput. Math. 41(6), 1137–1170 (2023)MathSciNetCrossRef B. Du, A. Wan, Stable and robust recovery of approximately \(k\)-sparse signals with partial support information in noise settings via weighted \(\ell _p (0<p\le 1)\) minimization. J. Comput. Math. 41(6), 1137–1170 (2023)MathSciNetCrossRef
9.
Zurück zum Zitat M.P. Friedlander, H. Mansour, R. Saab et al., Recovering compressively sampled signals using partial support information. IEEE Trans. Inf. Theory 58(2), 1122–1134 (2012)MathSciNetCrossRef M.P. Friedlander, H. Mansour, R. Saab et al., Recovering compressively sampled signals using partial support information. IEEE Trans. Inf. Theory 58(2), 1122–1134 (2012)MathSciNetCrossRef
10.
Zurück zum Zitat B. Gao, Y. Wang, Z. Xu, Stable signal recovery from phaseless measurements. J. Fourier Anal. Appl. 22(4), 787–808 (2016)MathSciNetCrossRef B. Gao, Y. Wang, Z. Xu, Stable signal recovery from phaseless measurements. J. Fourier Anal. Appl. 22(4), 787–808 (2016)MathSciNetCrossRef
11.
Zurück zum Zitat H. Huo, Stable recovery of weighted sparse signals from phaseless measurements via weighted \(\ell _1\) minimization. Math. Method. Appl. Sci. 45(9), 4929–4937 (2022)CrossRef H. Huo, Stable recovery of weighted sparse signals from phaseless measurements via weighted \(\ell _1\) minimization. Math. Method. Appl. Sci. 45(9), 4929–4937 (2022)CrossRef
12.
Zurück zum Zitat H. Huo, W. Sun, L. Xiao, New conditions on stable recovery of weighted sparse signals via weighted \(\ell _1\) minimization. Circuits Syst. Sign. Proc. 37(7), 2866–2883 (2018)CrossRef H. Huo, W. Sun, L. Xiao, New conditions on stable recovery of weighted sparse signals via weighted \(\ell _1\) minimization. Circuits Syst. Sign. Proc. 37(7), 2866–2883 (2018)CrossRef
13.
Zurück zum Zitat L. Jacques, A short note on compressed sensing with partially known signal support. Sign. Proc. 90(12), 3308–3312 (2010)CrossRef L. Jacques, A short note on compressed sensing with partially known signal support. Sign. Proc. 90(12), 3308–3312 (2010)CrossRef
14.
Zurück zum Zitat K. Jaganathan, S. Oymak, B. Hassibi, Sparse phase retrieval: uniqueness guarantees and recovery algorithms. IEEE Trans. Signal Process. 65(9), 2402–2410 (2017)MathSciNetCrossRef K. Jaganathan, S. Oymak, B. Hassibi, Sparse phase retrieval: uniqueness guarantees and recovery algorithms. IEEE Trans. Signal Process. 65(9), 2402–2410 (2017)MathSciNetCrossRef
15.
Zurück zum Zitat M. Lai, J. Wang, An unconstrained \(\ell _q\) minimization with \(0<q\le 1\) for sparse solution of underdetermined linear system. SIAM J. Optim. 21(1), 82–101 (2011)MathSciNetCrossRef M. Lai, J. Wang, An unconstrained \(\ell _q\) minimization with \(0<q\le 1\) for sparse solution of underdetermined linear system. SIAM J. Optim. 21(1), 82–101 (2011)MathSciNetCrossRef
16.
Zurück zum Zitat H. Li, S. Li, Y. Xia, Sampling complexity on phase retrieval from masked Fourier measurements via Wirtinger flow. Inverse Prob. 38(10), 105004 (2022)MathSciNetCrossRef H. Li, S. Li, Y. Xia, Sampling complexity on phase retrieval from masked Fourier measurements via Wirtinger flow. Inverse Prob. 38(10), 105004 (2022)MathSciNetCrossRef
17.
Zurück zum Zitat A.I. Lvovsky, M.G. Raymer, Continuous-variable optical quantum-state tomography. Rev. Mod. Phys. 81(1), 299–332 (2009)CrossRef A.I. Lvovsky, M.G. Raymer, Continuous-variable optical quantum-state tomography. Rev. Mod. Phys. 81(1), 299–332 (2009)CrossRef
18.
Zurück zum Zitat R.P. Millane, Phase retrieval in crystallography and optics. J. Opt. Soc. Am. A 7(3), 394–411 (1990)CrossRef R.P. Millane, Phase retrieval in crystallography and optics. J. Opt. Soc. Am. A 7(3), 394–411 (1990)CrossRef
19.
Zurück zum Zitat H. Rauhut, R. Ward, Interpolation via weighted \(\ell _1\) minimization. Appl. Comput. Harmon. Anal. 40(2), 321–351 (2016)MathSciNetCrossRef H. Rauhut, R. Ward, Interpolation via weighted \(\ell _1\) minimization. Appl. Comput. Harmon. Anal. 40(2), 321–351 (2016)MathSciNetCrossRef
20.
Zurück zum Zitat Y. Shechtman, Y.C. Eldar, O. Cohen et al., Phase retrieval with application to optical imaging: a contemporary overview. IEEE Signal Process. Mag. 32(3), 87–109 (2015)CrossRef Y. Shechtman, Y.C. Eldar, O. Cohen et al., Phase retrieval with application to optical imaging: a contemporary overview. IEEE Signal Process. Mag. 32(3), 87–109 (2015)CrossRef
21.
Zurück zum Zitat N. Vaswani, W. Lu, Modified-CS: modifying compressive sensing for problems with partially known support. IEEE Trans. Sign. Process. 58(9), 4595–4607 (2010)MathSciNetCrossRef N. Vaswani, W. Lu, Modified-CS: modifying compressive sensing for problems with partially known support. IEEE Trans. Sign. Process. 58(9), 4595–4607 (2010)MathSciNetCrossRef
22.
Zurück zum Zitat V. Voroninski, Z. Xu, A strong restricted isometry property, with an application to phaseless compressed sensing. Appl. Comput. Harmon. Anal. 40(2), 386–395 (2016)MathSciNetCrossRef V. Voroninski, Z. Xu, A strong restricted isometry property, with an application to phaseless compressed sensing. Appl. Comput. Harmon. Anal. 40(2), 386–395 (2016)MathSciNetCrossRef
23.
24.
Zurück zum Zitat Y. Xia, Z. Xu, The recovery of complex sparse signals from few phaseless measurements. Appl. Comput. Harmon. Anal. 50, 1–15 (2021)MathSciNetCrossRef Y. Xia, Z. Xu, The recovery of complex sparse signals from few phaseless measurements. Appl. Comput. Harmon. Anal. 50, 1–15 (2021)MathSciNetCrossRef
25.
Zurück zum Zitat G. You, Z.-H. Huang, Y. Wang, A theoretical perspective of solving phaseless compressive sensing via its nonconvex relaxation. Inf. Sci. 415, 254–268 (2017)CrossRef G. You, Z.-H. Huang, Y. Wang, A theoretical perspective of solving phaseless compressive sensing via its nonconvex relaxation. Inf. Sci. 415, 254–268 (2017)CrossRef
26.
Zurück zum Zitat Z. Zhou, J. Yu, Phaseless compressive sensing using partial support information. Optim. Lett. 14, 1961–1973 (2020)MathSciNetCrossRef Z. Zhou, J. Yu, Phaseless compressive sensing using partial support information. Optim. Lett. 14, 1961–1973 (2020)MathSciNetCrossRef
Metadaten
Titel
Recovery Conditions in Weighted Sparse Phase Retrieval via Weighted Minimization
verfasst von
Haiye Huo
Li Xiao
Publikationsdatum
09.06.2024
Verlag
Springer US
Erschienen in
Circuits, Systems, and Signal Processing / Ausgabe 9/2024
Print ISSN: 0278-081X
Elektronische ISSN: 1531-5878
DOI
https://doi.org/10.1007/s00034-024-02735-w