Exact recovery of sparse signals with side information

Abstract Compressed sensing has captured considerable attention of researchers in the past decades. In this paper, with aid powerful null space property, some deterministic recovery conditions are established for previous $$\ell _{1}$$ ℓ 1 – method and _{2}$$ 2 to guarantee exact sparse when side information desired signal is available. These obtained results provide a useful necessary complement investigation methods that based on statistical analysis. Moreover, one our theoretical findings also shows sharp previously classical remain suitable recovery. Numerical experiments both synthetic signals real-world images carried out further test performance above two methods.