  Reliable and energy-efficient wireless data transmission remains a major
challenge in resource-constrained wireless neural recording tasks, where data
compression is generally adopted to relax the burdens on the wireless data
link. Recently, Compressed Sensing (CS) theory has successfully demonstrated
its potential in neural recording application. The main limitation of CS,
however, is that the neural signals have no good sparse representation with
commonly used dictionaries and learning a reliable dictionary is often data
dependent and computationally demanding. In this paper, a novel CS approach for
implantable neural recording is proposed. The main contributions are: 1) The
co-sparse analysis model is adopted to enforce co-sparsity of the neural
signals, therefore overcoming the drawbacks of conventional synthesis model and
enhancing the reconstruction performance. 2) A multi-fractional-order
difference matrix is constructed as the analysis dictionary, thus avoiding the
dictionary learning procedure and reducing the need for previously acquired
data and computational resources. 3) By exploiting the statistical priors of
the analysis coefficients, a weighted analysis $\ell_1$-minimization (WALM)
algorithm is proposed to reconstruct the neural signals. Experimental results
on Leicester neural signal database reveal that the proposed approach
outperforms the state-of-the-art CS-based methods. On the challenging high
compression ratio task, the proposed approach still achieves high
reconstruction performance and spike classification accuracy.
