Theoretical analysis for ℓ 1 - ℓ 2 minimization with partial support information

Haifeng Li; Leiyan Guo

Applications of Mathematics (2025)

  • Issue: 1, page 125-148
  • ISSN: 0862-7940

Abstract

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We investigate the recovery of k -sparse signals using the ℓ 1 - ℓ 2 minimization model with prior support set information. The prior support set information, which is believed to contain the indices of nonzero signal elements, significantly enhances the performance of compressive recovery by improving accuracy, efficiency, reducing complexity, expanding applicability, and enhancing robustness. We assume k -sparse signals 𝐱 with the prior support T which is composed of g true indices and b wrong indices, i.e., | T | = g + b ≤ k . First, we derive a new condition based on RIP of order 2 α ( α = k - g ) to guarantee signal recovery via ℓ 1 - ℓ 2 minimization with partial support information. Second, we also derive the high order RIP with t α for some t ≥ 3 to guarantee signal recovery via ℓ 1 - ℓ 2 minimization with partial support information.

How to cite

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Li, Haifeng, and Guo, Leiyan. "Theoretical analysis for $\ell _{1}$-$\ell _{2}$ minimization with partial support information." Applications of Mathematics (2025): 125-148. <http://eudml.org/doc/299909>.

@article{Li2025,
abstract = {We investigate the recovery of $k$-sparse signals using the $\ell _\{1\}$-$\ell _\{2\}$ minimization model with prior support set information. The prior support set information, which is believed to contain the indices of nonzero signal elements, significantly enhances the performance of compressive recovery by improving accuracy, efficiency, reducing complexity, expanding applicability, and enhancing robustness. We assume $k$-sparse signals $\{\bf x\}$ with the prior support $T$ which is composed of $g$ true indices and $b$ wrong indices, i.e., $|T|=g+b\le k$. First, we derive a new condition based on RIP of order $2\alpha $$(\alpha =k-g)$ to guarantee signal recovery via $\ell _\{1\}$-$\ell _\{2\}$ minimization with partial support information. Second, we also derive the high order RIP with $t\alpha $ for some $t\ge 3$ to guarantee signal recovery via $\ell _\{1\}$-$\ell _\{2\}$ minimization with partial support information.},
author = {Li, Haifeng, Guo, Leiyan},
journal = {Applications of Mathematics},
keywords = {compressed sensing; sparse optimization; algorithm},
language = {eng},
number = {1},
pages = {125-148},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Theoretical analysis for $\ell _\{1\}$-$\ell _\{2\}$ minimization with partial support information},
url = {http://eudml.org/doc/299909},
year = {2025},
}

TY - JOUR
AU - Li, Haifeng
AU - Guo, Leiyan
TI - Theoretical analysis for $\ell _{1}$-$\ell _{2}$ minimization with partial support information
JO - Applications of Mathematics
PY - 2025
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 125
EP - 148
AB - We investigate the recovery of $k$-sparse signals using the $\ell _{1}$-$\ell _{2}$ minimization model with prior support set information. The prior support set information, which is believed to contain the indices of nonzero signal elements, significantly enhances the performance of compressive recovery by improving accuracy, efficiency, reducing complexity, expanding applicability, and enhancing robustness. We assume $k$-sparse signals ${\bf x}$ with the prior support $T$ which is composed of $g$ true indices and $b$ wrong indices, i.e., $|T|=g+b\le k$. First, we derive a new condition based on RIP of order $2\alpha $$(\alpha =k-g)$ to guarantee signal recovery via $\ell _{1}$-$\ell _{2}$ minimization with partial support information. Second, we also derive the high order RIP with $t\alpha $ for some $t\ge 3$ to guarantee signal recovery via $\ell _{1}$-$\ell _{2}$ minimization with partial support information.
LA - eng
KW - compressed sensing; sparse optimization; algorithm
UR - http://eudml.org/doc/299909
ER -

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