Recently, many algorithms have been proposed to remove elusive non-brain signals (as known as "artifacts") from electroencephalogram (EEG). However, the limited memory of portable devices can reduce the capabilities of artifact removal algorithms. To address this challenge, we propose an HMO-ASR algorithm. The proposed HMO-ASR algorithm consists of (1) two-level window-based preprocessing including PCA-based and modified z-score-based preprocessing to clean the data in each window, (2) iterative mean, standard deviation, and covariance update using a parallel algorithm to achieve window-based processing, and (3) early eigenvector matrix determination to save the computation. The HMO-ASR method can be implemented with limited memory on mobile devices or application-specific integrated circuits using the three procedures described above. The study results showed that the proposed HMO-ASR algorithm can achieve comparable performance to those obtained by the offline ASR algorithm with 99.34% memory size reduction.