1. A method for obtaining an estimate of a noise-free portion of a noise-containing digital signal, comprising the steps of: (a) applying a set of M linear transforms to the noise-containing digital signal; (b) determining M initial de-noised estimates of each digital element of the digital signal; (c) deriving a combination of weight factors for the M initial de-noised estimates of each digital element by formulating the combination as a linear estimation problem and solving it for the individual weight factors; and (d) formulating a final de-noised estimate of each digital element based on the corresponding M initial de-noised estimates and the combination of weight factors determined in steps (b) and (c) respectively.