Article

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

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## Abstract

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.

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Compressive sampling offers a new paradigm for acquiring signals that are compressible with respect to an orthonormal basis. The major algorithmic challenge in compressive sampling is to approximate a compressible signal from noisy samples. This paper describes a new iterative recovery algorithm called CoSaMP that delivers the same guarantees as the best optimization-based approaches. Moreover, this algorithm offers rigorous bounds on computational cost and storage. It is likely to be extremely efficient for practical problems because it requires only matrix–vector multiplies with the sampling matrix. For compressible signals, the running time is just O(Nlog2N), where N is the length of the signal.
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There is an enduring quest for technologies that provide – temporally and spatially – highly resolved information on electric neuronal or cardiac activity in functional tissues or cell cultures. Here, we present a planar high-density, low-noise microelectrode system realized in microelectronics technology that features 11,011 microelectrodes (3,150 electrodes per mm2), 126 of which can be arbitrarily selected and can, via a reconfigurable routing scheme, be connected to on-chip recording and stimulation circuits. This device enables long-term extracellular electrical-activity recordings at subcellular spatial resolution and microsecond temporal resolution to capture the entire dynamics of the cellular electrical signals. To illustrate the device performance, extracellular potentials of Purkinje cells (PCs) in acute slices of the cerebellum have been analyzed. A detailed and comprehensive picture of the distribution and dynamics of action potentials (APs) in the somatic and dendritic regions of a single cell was obtained from the recordings by applying spike sorting and spike-triggered averaging methods to the collected data. An analysis of the measured local current densities revealed a reproducible sink/source pattern within a single cell during an AP. The experimental data substantiated compartmental models and can be used to extend those models to better understand extracellular single-cell potential patterns and their contributions to the population activity. The presented devices can be conveniently applied to a broad variety of biological preparations, i.e., neural or cardiac tissues, slices, or cell cultures can be grown or placed directly atop of the chips for fundamental mechanistic or pharmacological studies.
Article
Compressed sensing is a novel technique to acquire sparse signals with few measurements. Normally, compressed sensing uses random projections as measurements. Here we design deterministic measurements and an algorithm to accomplish signal recovery with computational efficiency. A measurement matrix is designed with chirp sequences forming the columns. Chirps are used since an efficient method using FFTs can recover the parameters of a small superposition. We show that this type of matrix is valid as compressed sensing measurements. This is done by bounding the eigenvalues of sub-matrices, as well as an empirical comparison with random projections. Further, by implementing our algorithm, simulations show successful recovery of signals with sparsity levels similar to those possible by matching pursuit with random measurements. For sufficiently sparse signals, our algorithm recovers the signal with computational complexity O(KlogK) for K measurements. This is a significant improvement over existing algorithms.
Article
Microelectrode arrays (MEAs) offer a powerful tool to both record activity and deliver electrical microstimulations to neural networks either in vitro or in vivo. Microelectronics microfabrication technologies now allow building high-density MEAs containing several hundreds of microelectrodes. However, dense arrays of 3D micro-needle electrodes, providing closer contact with the neural tissue than planar electrodes, are not achievable using conventional isotropic etching processes. Moreover, increasing the number of electrodes using conventional electronics is difficult to achieve into compact devices addressing all channels independently for simultaneous recording and stimulation. Here, we present a full modular and versatile 256-channel MEA system based on integrated electronics. First, transparent high-density arrays of 3D-shaped microelectrodes were realized by deep reactive ion etching techniques of a silicon substrate reported on glass. This approach allowed achieving high electrode aspect ratios, and different shapes of tip electrodes. Next, we developed a dedicated analog 64-channel Application Specific Integrated Circuit (ASIC) including one amplification stage and one current generator per channel, and analog output multiplexing. A full modular system, called BIOMEA, has been designed, allowing connecting different types of MEAs (64, 128, or 256 electrodes) to different numbers of ASICs for simultaneous recording and/or stimulation on all channels. Finally, this system has been validated experimentally by recording and electrically eliciting low-amplitude spontaneous rhythmic activity (both LFPs and spikes) in the developing mouse CNS. The availability of high-density MEA systems with integrated electronics will offer new possibilities for both in vitro and in vivo studies of large neural networks.
Article
We present a low-power complementary metal-oxide semiconductor (CMOS) analog integrated biopotential detector intended for neural recording in wireless multichannel implants. The proposed detector can achieve accurate automatic discrimination of action potential (APs) from the background activity by means of an energy-based preprocessor and a linear delay element. This strategy improves detected waveforms integrity and prompts for better performance in neural prostheses. The delay element is implemented with a low-power continuous-time filter using a ninth-order equiripple allpass transfer function. All circuit building blocks use subthreshold OTAs employing dedicated circuit techniques for achieving ultra low-power and high dynamic range. The proposed circuit function in the submicrowatt range as the implemented CMOS 0.18- microm chip dissipates 780 nW, and it features a size of 0.07 mm(2). So it is suitable for massive integration in a multichannel device with modest overhead. The fabricated detector succeeds to automatically detect APs from underlying background activity. Testbench validation results obtained with synthetic neural waveforms are presented.
Article
Microelectrode recording during deep brain stimulation surgery improves the likelihood of successful target localization and enables the electrophysiological characterization of human neural structures. Many clinical recording systems do not support the ability to capture research-quality recordings. Established clinical centers already using such equipment may be prevented from acquiring human intracranial data because of the need to completely change recording systems to obtain research-quality recordings. This technical note describes the novel design and implementation of a recording system that significantly improves research capabilities without disrupting the existing clinical setup. This design introduces a second recording system (including pre-amplifier, differential amplifier, analog-to-digital converter, and computer with analysis software) that divides the microelectrode signal into two independent streams. This design preserves the existing intraoperative recording setup, but significantly improves research-level recording, data storage, and analysis capabilities. We provide the first description of such a system using components that are all commercially available and relatively inexpensive. This approach presents an appealing alternative to the purchase of an entirely new system for surgical teams that already perform intraoperative recordings to assist in stereotactic target localization, yet wish to expand their neurophysiological recording capabilities.
Conference Paper
This paper proposes a deterministic compressed sensing matrix that comes by design with a very fast reconstruction algorithm, in the sense that its complexity depends only on the number of measurements n and not on the signal dimension N. The matrix construction is based on the second order Reed-Muller codes and associated functions. This matrix does not have RIP uniformly with respect to all kappa-sparse vectors, but it acts as a near isometry on kappa-sparse vectors with very high probability.
Article
This paper considers a natural error correcting problem with real valued input/output. We wish to recover an input vector f∈R<sup>n</sup> from corrupted measurements y=Af+e. Here, A is an m by n (coding) matrix and e is an arbitrary and unknown vector of errors. Is it possible to recover f exactly from the data y? We prove that under suitable conditions on the coding matrix A, the input f is the unique solution to the ℓ<sub>1</sub>-minimization problem (||x||<sub>ℓ1</sub>:=Σ<sub>i</sub>|x<sub>i</sub>|) min(g∈R<sup>n</sup>) ||y - Ag||<sub>ℓ1</sub> provided that the support of the vector of errors is not too large, ||e||<sub>ℓ0</sub>:=|{i:e<sub>i</sub> ≠ 0}|≤ρ·m for some ρ>0. In short, f can be recovered exactly by solving a simple convex optimization problem (which one can recast as a linear program). In addition, numerical experiments suggest that this recovery procedure works unreasonably well; f is recovered exactly even in situations where a significant fraction of the output is corrupted. This work is related to the problem of finding sparse solutions to vastly underdetermined systems of linear equations. There are also significant connections with the problem of recovering signals from highly incomplete measurements. In fact, the results introduced in this paper improve on our earlier work. Finally, underlying the success of ℓ<sub>1</sub> is a crucial property we call the uniform uncertainty principle that we shall describe in detail.