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Reliable and energy-efficient wireless data transmission remains a majorchallenge in resource-constrained wireless neural recording tasks, where datacompression is generally adopted to relax the burdens on the wireless datalink. Recently, Compressed Sensing (CS) theory has successfully demonstratedits potential in neural recording application. The main limitation of CS,however, is that the neural signals have no good sparse representation withcommonly used dictionaries and learning a reliable dictionary is often datadependent and computationally demanding. In this paper, a novel CS approach forimplantable neural recording is proposed. The main contributions are: 1) Theco-sparse analysis model is adopted to enforce co-sparsity of the neuralsignals, therefore overcoming the drawbacks of conventional synthesis model andenhancing the reconstruction performance. 2) A multi-fractional-orderdifference matrix is constructed as the analysis dictionary, thus avoiding thedictionary learning procedure and reducing the need for previously acquireddata and computational resources. 3) By exploiting the statistical priors ofthe analysis coefficients, a weighted analysis $\ell_1$-minimization (WALM)algorithm is proposed to reconstruct the neural signals. Experimental resultson Leicester neural signal database reveal that the proposed approachoutperforms the state-of-the-art CS-based methods. On the challenging highcompression ratio task, the proposed approach still achieves highreconstruction performance and spike classification accuracy.

Compressed Sensing for Implantable Neural Recordings Using Co-sparse Analysis Model and Weighted $\ell_1$-Optimization