Existing self-supervised pre-trained speech models have offered an effective way to leverage massive unannotated corpora to build good automatic speech recognition (ASR). However, many current models are trained on a clean corpus from a single source, which tends to do poorly when noise is present during testing. Nonetheless, it is crucial to overcome the adverse influence of noise for real-world applications. In this work, we propose a novel training framework, called deHuBERT, for noise reduction encoding inspired by H. Barlow's redundancy-reduction principle. The new framework improves the HuBERT training algorithm by introducing auxiliary losses that drive the self- and cross-correlation matrix between pairwise noise-distorted embeddings towards identity matrix. This encourages the model to produce noise-agnostic speech representations. With this method, we report improved robustness in noisy environments, including unseen noises, without impairing the performance on the clean set.