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Keywords:
compressed sensing; sparse optimization; algorithm
compressed sensing; sparse optimization; algorithm
Summary:
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., $|T|=g+b\leq k$. 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 $t\geq 3$ to guarantee signal recovery via $\ell _{1}$-$\ell _{2}$ minimization with partial support information.
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