Denoising for airborne transient electromagnetic data using noise-whitening-based weighted nuclear norm minimization

Abstract

Recovering anomalous information covered under noise in late gates can enhance airborne transient electromagnetic (ATEM) detection. Conventional denoising mainly comprises filtering and gate correlation-based decomposition algorithms; the former fails to extract anomalies contaminated by noise and the latter relies on the correlation between gates, which may yield false late gate anomalies caused by early large-amplitude anomalies in early gates. In ATEM profiles, the correlation between anomalies in adjacent gates makes the anomalies to be measured to have low-rank characteristics relative to the noise-contaminated profiles; the noise is uniformly distributed in the profiles, which have nonlocal self-similarity. Therefore, the low-rank matrix approximation algorithm is applicable to ATEM data denoising. In this study, an algorithm—noise-whitening-based weighted nuclear norm minimization (NW-WNNM)—is designed to remove ATEM profile noise. First, we analyse the influence of patch size in block matching on anomalous and noisy patches and estimate the profile patch size adaptively. Then, we combine the estimation of noise variance in weighted nuclear norm minimization (WNNM) with the noise whitening of similar patch matrices to reduce the noise interference on the nuclear norm and add a whitening factor in the weight vector to make the soft-thresholding function applicable to the low-rank reconstruction of the whitened matrix. By analysing the reconstructed low-rank matrix and its feature distribution, compared with WNNM, NW-WNNM can detect the feature information more accurately and eliminate the influence of noise on the nuclear norm. Simulation and field profile results indicate that NW-WNNM is superior to comparison denoising methods.