The kernel technology of Compressed sensing theory is to find the sparsest representation to recover original signal data

in which the convex optimization algorithm of minimization the l

1

norm is a important method. At present

a key algorithm solved minimization the l

p

(p≤1)norm is iterative reweighted least squares algorithm（IRLS

－p

0

<

p≤1) with affine constraints

but a crucial question of the IRLS

－p

Algorithm is to iterate convergence and real time performances. Therefore

the EIRLS

－p

and  sEIRLS

－p

algorithms were proposed to extend IRLS

－p

as a family of algorithms for the matrix rank minimization problem

and to improve IRLS

－p

implementations performances of successive iterates convergence and real time. Validating results show that both EIRLS

－0

and sEIRLS

－0

perform better than singular value thresholding (SVT) algorithm. At the same time

it was observed that sEIRLS

－0

performs better than iterative hard thresholding algorithm(IHT) when there is no apriori information on the low rank solution.