A weighted discriminative approach for image denoising with overcomplete representations

We present a novel weighted approach for shrinkage functions learning in image denoising. The proposed approach optimizes the shape of the shrinkage functions and maximizes denoising performance by emphasizing the contribution of sparse overcomplete representation components. In contrast to previous work, we apply the weights in the overcomplete domain and formulate the restored image as a weighted combination of the post-shrinkage overcomplete representations. We further utilize this formulation in an offline Least Squares learning stage of the shrinkage functions, thus adapting their shape to the weighting process. The denoised image is reconstructed with the learned weighted shrinkage functions. Computer simulations demonstrate superior shrinkage-based denoising performance.