An Improved Sparsity Adaptive Matching Pursuit Algorithm and Its Application in Shock Wave Testing

Algorithm 1

The SAMP algorithm.

Input: sensing matrix A, the measurement signal y, step-size S.
	Initialize: t = 0, r0 = y, Λ0 =  , L = S.
	Repeat
(1)	Jt = max {L}. Seek the index of the first L most matching atoms, where J is the pending candidate set of atoms.
(2)	Ct = Λt-1∪Jt. Construct the total candidate set of atoms.
(3)	. Solve the least-squares problem. And according to Ft = max {, L}, find the index of the first L best atoms from Ct, where F is the atom construction set.
(4)	. Calculate the residual.
(5)	If ║rt║2 < 1e − 6, the algorithm iteration stop condition is satisfied, output ; otherwise, go to 6.
(6)	If ║rt║2 ≥ ║rt-1║2, Stage = Stage + 1, L = Stage × S, go to 1; otherwise, Λt = Ft, rt − 1 = rt, t = t + 1, go to 1.
Until iteration stop condition is true.
Output: estimated sparse signal ; estimated signal sparsity .