Summary: Penumbral imaging is a technique which exploits the fact that spatial information can be recovered from the shadow or penumbra that an unknown source casts through a simple large circular aperture. Since the technique is based on linear deconvolution, it is sensitive to noise. In this paper, a two-step method is proposed for decoding penumbral images: first, a noise-reduction algorithm based on ICA-domain (independent component analysis-domain) shrinkage is applied to smooth the given noise; second, the conventional linear deconvolution follows. The simulation results show that the reconstructed image is dramatically improved in comparison to that without the noise-removing filters, and the proposed method is successfully applied to real experimental X-ray imaging.