Recovery analysis for block \(\ell_p-\ell_1\) minimization with prior support information. (English) Zbl 1493.90136
Summary: This paper provides a new theoretical support for block sparse recovery. By embedding prior support information into the block \(\ell_p- \ell_1\) minimization with \(0<p\leq 1\), we establish a sufficient condition on block \(p\)-restricted isometry property (RIP) to guarantee the stable and robust recovery of block sparse signals, as well as obtain a corresponding upper bound estimate of the error. The obtained result not only generalizes the existing ones, but also shows that the block \(\ell_p- \ell_1\) minimization with prior support information behaves robust and stable recovery performance under weaker condition than the analogous one for the block \(\ell_p-\ell_1\) minimization if more than 50% of the support information is accurate.
MSC:
| 90C25 | Convex programming |
| 94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |
| 47A52 | Linear operators and ill-posed problems, regularization |
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