Image denoising using learned overcomplete representations

We describe a method for learning sparse multiscale image representations using a sparse prior distribution over the basis function coefficients. The prior consists of a mixture of a Gaussian and a Dirac delta function, and thus encourages coefficients to have exact zero values. Coefficients for an image are computed by sampling from the resulting posterior distribution with a Gibbs sampler. Denoising using the learned image model is demonstrated for some standard test images, with results that compare favorably with other denoising methods.