Table 1 OMP algorithm

sensing matrix Φ

sparsity K.

Initialize:

iteration count k = 0

residual vector r⁰ = y

support set estimate $T^0=\mathrm{0̸}$.

While k < K

k = k + 1.

(Identify)       t^k= arg max _j |〈r^k-1,φ _j 〉|.

(Augment)    T^k= T^k-1∪ {t^k}.

(Estimate)    ${\widehat{x}}_{T^k}=\text{arg}\underset{x}{\text{min}}\parallel y-{\Phi }_{T^k}x{\parallel }_2$.

(Update)       $r^k=y-{\Phi }_{T^k}{\widehat{x}}_{T^k}.$.

End

Output:

$\widehat{x}=\text{arg}\underset{x:\mathsf{\text{supp}}\left(x\right)=T^K}{\text{min}}{∥y-\Phi x∥}_2.$