Sparse code shrinkage for image denoising

Sparse coding is a method for finding a representation of data in which each of the components of the representation is only rarely significantly active. Such a representation is closely related to redundancy reduction and independent component analysis, and has some neurophysiological plausibility. We show how sparse coding can be used for denoising. Using methods reminiscent of wavelet theory, we show how to apply a soft-thresholding operator on the components of sparse coding in order to reduce Gaussian noise. Our method has the important benefit over wavelet methods that the transformation is determined solely by the statistical properties of the data. The wavelet transformation, on the other hand, relies heavily on certain abstract mathematical properties that may be only weakly related to the properties of the natural data. Experiments on image data are reported.