Image feature extraction and denoising by sparse coding

We show how sparse coding can be used to extract wavelet like features from natural image data. Sparse coding is a method for finding a representation of image windows in which each of the components of the representation is only rarely significantly active. Such a representation is closely related to the techniques of independent component analysis and blind source separa tion. As an application of the sparse coding scheme, we show how to apply a soft-thresholding operator on the components of sparse coded noisy image w indows in order to reduce Gaussian noise. The results outperform both Wiene r and median filtering. Compared to wavelet transforms, methods based on sp arse coding have the important benefit that the features are fully adapted to the training images and determined solely by their statistical propertie s, while the wavelet transformation relies heavily on certain abstract math ematical properties that may be only weakly related to the properties of th e natural data.