Training-free compressed sensing for wireless neural recording using analysis model and group weighted ℓ₁-minimization

Objective. Data compression is crucial for resource-constrained wireless neural recording applications with limited data bandwidth, and compressed sensing (CS) theory has successfully demonstrated its potential in neural recording applications. In this paper, an analytical, training-free CS recovery method, termed group weighted analysis -minimization (GWALM), is proposed for wireless neural recording. Approach. The GWALM method consists of three parts: (1) the analysis model is adopted to enforce sparsity of the neural signals, therefore overcoming the drawbacks of conventional synthesis models and enhancing the recovery performance. (2) A multi-fractional-order difference matrix is constructed as the analysis operator, thus avoiding the dictionary learning procedure and reducing the need for previously acquired data and computational complexities. (3) By exploiting the statistical properties of the analysis coefficients, a group weighting approach is developed to enhance the performance of analysis -minimization. Main results. Experimental results on synthetic and real datasets reveal that the proposed approach outperforms state-of-the-art CS-based methods in terms of both spike recovery quality and classification accuracy. Significance. Energy and area efficiency of the GWALM make it an ideal candidate for resource-constrained, large scale wireless neural recording applications. The training-free feature of the GWALM further improves its robustness to spike shape variation, thus making it more practical for long term wireless neural recording.