Neural signal compression using a minimum Euclidean or Manhattan distance cluster-based deterministic compressed sensing matrix

•We build the MDC matrix that has a simple structure to compress neural signals.•MDC matrix largely compresses neural signals and has a small reconstruction error.•MDC matrix obeys the RIP for the related vector under two prerequisites.•Basic pursuit and lasso algorithms are best for the reconstruction of the signal.•MDC matrix can be used over a large range of the sampling rate for compression.

Multichannel wireless neural signal recording systems are a prominent topic in biomedical research, but because of several limitations, such as power consumption, the device size, and enormous quantities of data, it is necessary to compress the recorded data. Compressed sensing theory can be employed to compress neural signals. However, a neural signal is usually not sparse in the time domain and contains a large number of similar non-zero points. In this article, we propose a new method for compressing not only a sparse signal but also a non-sparse signal that has identical points. First, several concepts about the identical items of the signal are introduced; thus, a method for constructing the Minimum Euclidean or Manhattan Distance Cluster-based (MDC) deterministic compressed sensing matrix is given. Moreover, the Restricted Isometry Property of the MDC matrix is supported. Third, three groups of real neural signals are used for validation. Six different random or deterministic sensing matrices under diverse reconstruction algorithms are used for the simulation. From the simulation results, it can be demonstrated that the MDC matrix can largely compress neural signals and also have a small reconstruction error. For a six-thousand-point signal, the compression rate can be up to 98%, whereas the reconstruction error is less than 0.1. In addition, from the simulation results, the MDC matrix is optimal for a signal that has an extended length. Finally, the MDC matrix can be constructed by zeros and ones; additionally, it has a simple construction structure that is highly practicable for the design of an implantable neural recording device.