Dictionary learning and shift-invariant sparse coding denoising for controlled-source electromagnetic data combined with complementary ensemble empirical mode decomposition

Controlled-source electromagnetic (CSEM) data recorded in industrialized areas are inevitably contaminated by strong cultural noise. Traditional noise attenuation methods are often ineffective for intricate aperiodic noise. To address the abovementioned problem, we have developed a novel noise isolation method based on the fast Fourier transform, complementary ensemble empirical mode decomposition (CEEMD), and shift-invariant sparse coding (SISC, an unsupervised machine-learning algorithm under a data-driven framework). First, large powerline noise is accurately subtracted in the frequency domain. Then, the CEEMD-based algorithm is used to correct the large baseline drift. Finally, taking advantage of the sparsity of periodic signals, SISC is applied to autonomously learn a feature atom (the useful signal with a length of one period) from the detrended signal and recover the CSEM signal with high accuracy. We determine the performance of the SISC by comparing it with three other promising signal processing methods, such as the mathematic morphology filtering, soft-threshold wavelet filtering, and K-singular-value decomposition (another dictionary learning method) sparse decomposition. Experimental results illustrate that SISC provides the best performance. Robustness test results indicate that SISC can increase the signal-to-noise ratio of noisy signal from 0 to more than 15 dB. Case studies of synthetic and real data collected in the Chinese provinces of Sichuan and Yunnan indicate that our method is capable of effectively recovering the useful signal from the observed data contaminated with different kinds of strong ambient noise. The curves of U/I and apparent resistivity after applying our method improved greatly. Moreover, our method performs better than the robust estimation method based on correlation analysis.