We have developed a novel approach to attenuate random noise based on local signal-and-noise orthogonalization. In this approach, we first removed from a seismic section using one of the conventional denoising operators and then applied a weighting operator to the initially denoised section to predict the signal-leakage energy, as well as retrieve it from the initial noise section. The weighting operator was obtained by solving a least-squares minimization problem via shaping regularization with a smoothness constraint. Next, the initially denoised section and the retrieved signal were combined to form the final denoised section. The proposed denoising approach corresponded to orthogonalizing the initially denoised signal and noise in a local manner. We evaluated the denoising performance using local similarity. To test the orthogonalization property of the estimated signal and noise, we calculated the local similarity map between the denoised signal section and removed noise section. Low values of local similarity indicated a good orthogonalization and thus a good denoising performance. Synthetic and field data examples revealed the effectiveness of the proposed approach in applications to noise attenuation for conventional and simultaneous-source seismic data.