1. A method for measuring and recovering sparse signals comprising: a. performing a linear measurement to a length-N sparse signal vector x={x i } with a M×N measurement matrix A to obtain a length-M measurement vector y, wherein the measurement matrix A is denoted by: A = [ A 1 Π 1 ⋮ A d Π d ⋮ A D Π D ] wherein A d Π d is a sub-matrix of the measurement matrix A, for d=1˜D, Π d is a N×N random permutation matrix, and A d is an J×N matrix which is denoted by: A d = [ a 1 , 1 ( d ) ⋯ a 1 , L ( d ) 0 ⋱ 0 a J , 1 ( d ) ⋯ a J , L ( d ) ] wherein M<<N, J*L=N, the measurement symbols generated from the same permutation matrix are referred to as one dimension, and the D is the total dimension number; and b. recovering the length-N sparse signal vector x={x i } from the length-M measurement vector y.