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The algorithms based on the technique of optimal k -thresholding (OT) were recently proposed for signal recovery, and they are very different from the traditional family of hard thresholding methods. However, the computational cost for OT-based algorithms remains high at the current stage of their development. This stimulates the development of the so-called natural thresholding (NT) algorithm and its variants in this paper. The family of NT algorithms is developed through the first-order approximation of the so-called regularized optimal k -thresholding model, and thus the computational cost for this family of algorithms is significantly lower than that of the OT-based algorithms. 

Recently, self-supervised learning (SSL) from unlabelled speech data has gained increased attention in the automatic speech recognition (ASR) community. Typical SSL methods include autoregressive predictive coding (APC), Wav2vec2.0, and hidden unit BERT (HuBERT). However, SSL models are biased to the pretraining data. When SSL models are finetuned with data from another domain, domain shifting occurs and might cause limited knowledge transfer for downstream tasks.

Although supervised deep learning has revolutionized speech and audio processing, it has necessitated the building of specialist models for individual tasks and application scenarios. It is likewise difficult to apply this to dialects and languages for which only limited labeled data is available. Self-supervised representation learning methods promise a single universal model that would benefit a wide variety of tasks and domains. 

The papers in this special section focus on self-supervised learning for speech and audio processing. A current trend in the machine learning community is the adoption of self-supervised approaches to pretrain deep networks. Self-supervised learning utilizes proxy-supervised learning tasks (or pretext tasks) - for example, distinguishing parts of the input signal from distractors or reconstructing masked input segments conditioned on unmasked segments—to obtain training data from unlabeled corpora.