This paper deals with the study of multi-channel adaptive noise cancellation with a focus on its application in electromagnetic (EM) telemetry. We presented new variable step-size least mean square (LMS) techniques: regularized variable step-size LMS and regularized sigmoid variable size LMS, for electromagnetic telemetry data processing. Considering the complexity and spatial distribution of environmental noise, algorithms with multiple reference signals were used to retrieve transmitted EM signals. The feasibility of the regularized variable step size LMS algorithms with numerical simulation was analyzed and presented. The adaptive processing techniques were applied in the recovery of frequency and binary phase shift key modulated signal. The proposed multi-channel adaptive technique achieves fast convergence speed, low mean squared error and is shown to have good convergence characteristics compared to conventional methods. In addition to attaining good results from the multi-channel adaptive filter and performing the signal analysis in real-time, we implemented combined fast effective impulse noise removal techniques. The combination of median and mean filters was effective in removing a wide range of impulsive noises without distorting any other data points. Further, electromagnetic telemetry data were acquired during a drilling operation in Sichuan province, China, for real field application. Data processing workflow was designed for EM telemetry data processing based on the noise characteristics, simulation results and expected result for demodulation. To establish a comprehensive overview, a performance comparison of the acquisition array system is also provided. Conclusively, the introduced multichannel adaptive noise canceling techniques are very effective in recovering transmitted EM telemetry signals. [ABSTRACT FROM AUTHOR]