1. A computer implemented method for designing special measurement matrices (CS-matrices) for use in compressed sensing, comprising the steps of: a processor generating a CS matrix A as a matrix product A=U B where B is p by m and U is n by p; a processor generating said matrix B with the property that, for objects of interest, Bx is sparse or is approximately a sparse vector, wherein B is an orthogonal matrix; and a processor generating said matrix U as an n by p matrix with the properties that: (1) the columns of U are of unit length in the Euclidean norm; (2) the square matrix G=U′U, where U′ denotes the transpose (real-valued matrix entries) or the conjugate transpose (complex-valued matrix entries), has its off-diagonal entries bounded in absolute value by the coherence parameter M; and a processor using said matrices to produce an approximate reconstruction of a digital signal or image.