Frontiers of Mathematics in China

, Volume 13, Issue 6, pp 1369–1396 | Cite as

Signal recovery under mutual incoherence property and oracle inequalities

  • Peng Li
  • Wengu ChenEmail author
Research Article


We consider the signal recovery through an unconstrained minimization in the framework of mutual incoherence property. A sufficient condition is provided to guarantee the stable recovery in the noisy case. Furthermore, oracle inequalities of both sparse signals and non-sparse signals are derived under the mutual incoherence condition in the case of Gaussian noises. Finally, we investigate the relationship between mutual incoherence property and robust null space property and find that robust null space property can be deduced from the mutual incoherence property.


Mutual incoherence property (MIP) Lasso Dantzig selector oracle inequality robust null space property (RNSP) 


65K05 90C25 92C55 94A12 


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This work was supported by the National Natural Science Foundation of China (Grant No. 11871109), NSAF (Grant No. U1830107), and the Science Challenge Project (TZ2018001).


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Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Graduate SchoolChina Academy of Engineering PhysicsBeijingChina
  2. 2.Institute of Applied Physics and Computational MathematicsBeijingChina

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