A de-noising algorithm that obtains an estimate of a noise-free portion of
a noise-containing digital signal by applying a set of M linear
transforms to the noise-containing digital signal, determining M initial
de-noised estimates of each digital element of the digital signal,
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 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. The combination of weight factors is an
optimal combination that is derived such that a conditional mean squared
error with respect to the initial de-noised estimates is minimized. The
optimal determination is further determined based on a scaling factor
that removes explicit dependence to noise variance and on one of several
matrices.