Denoising methods are usually imperfect, causing some signal leakage in the residual data. The local orthogonalization method is powerful for retrieving the leaked signal; however, its original implementation could not effectively retrieve weak residual because the residual data have weak similarity. We develop a process for extracting weak signal by the local orthogonalization method in the migrated domain and then eliminating artifacts and compensating amplitude with two more rounds of local orthogonalization in the original domain. In the migrated domain, the weak signal can be enhanced by energy focusing, but the random noise cannot be systematically enhanced, which allows us to retrieve most of the residual signal using local orthogonalization. After demigrating the retrieved weak signal back to the original domain, we may encounter artifacts caused by the false focus of random noise in the migrated domain. Therefore, we perform the second round of local orthogonalization between the current and initial denoised results to eliminate these artifacts. We further compensate for the amplitude loss caused by migration and demigration using the third round of local orthogonalization between the updated signal and noise sections. Numerical experiments illustrate the superiority of our method over existing methods for retrieving the weak signal for pre- and poststack seismic profiles and ground-penetrating radar data.

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