A method for approximating a plurality of digital signals or images using compressed sensing. In a scheme where a common component x.sub.c of said plurality of digital signals or images an innovative component x.sub.i of each of said plurality of digital signals each are represented as a vector with m entries, the method comprises the steps of making a measurement y.sub.c, where y.sub.c comprises a vector with only n.sub.i entries, where n.sub.i is less than m, making a measurement y.sub.i for each of said correlated digital signals, where y.sub.i comprises a vector with only n.sub.i entries, where n.sub.i is less than m, and from each said innovation components y.sub.i, producing an approximate reconstruction of each m-vector x.sub.i using said common component y.sub.c and said innovative component y.sub.i.