A denoising mechanism uses chosen signal classes and selected analysis dictionaries. The chosen signal class includes a collection of signals. The analysis dictionaries describe signals. The embedding threshold value is initially determined for a training set of signals in the chosen signal class. The update signal is initialized with a signal corrupted by noise. The estimate calculated by: computing coefficients for the updated signal using the analysis dictionaries; computing an embedding index for each of the path(s); extracting a coefficient subset from coefficients for the path(s) whose embedding index exceeds an embedding threshold; adding a coefficient subset to a coefficient collection; generating a partial estimate using the coefficient collection; creating an attenuated partial estimate by attenuating the partial estimate by an attenuation factor; updating the updated signal by subtracting the attenuated partial estimate from the updated signal; and adding the attenuated partial estimate to the estimate.