A new result on recovery sparse signals using orthogonal matching pursuit

Figures & data

Table 1. Orthogonal matching pursuit.

Input:	$\mathrm{\Phi },y$, and maximum iteration number $k_{max}$
Initialize:	$k=0,r^0=y,T^0=\mathrm{\varnothing }$
while	$k<k_{max}$, do
	k = k + 1,
	$t^k=\arg \underset{1\le i\le n}{max}|〈r^{k-1},{\varphi }_i〉|,$
	$T^k=T^{k-1}\cup \left\{t^k\right\},$
	${\hat{x}}^k=\arg \underset{u\in {\mathbb{C}}^n:\mathrm{s}\mathrm{u}\mathrm{p}\mathrm{p}\left(u\right)\subset T^k}{min}\Vert y-\mathrm{\Phi }u{\Vert }_2,$
	$r^k=y-\mathrm{\Phi }{\hat{x}}^k.$
Output:	$T^k$ and ${\hat{x}}^k$

Figure 1. Performance of Theorem 2.1.