Digital filters for low-latency quantification of brain rhythms in real time

Abstract

Objective. The rapidly developing paradigm of closed-loop neuroscience has extensively employed brain rhythms as the signal forming real-time neurofeedback, triggering brain stimulation, or governing stimulus selection. However, the efficacy of brain rhythm contingent paradigms suffers from significant delays related to the process of extraction of oscillatory parameters from broad-band neural signals with conventional methods. To this end, real-time algorithms are needed that would shorten the delay while maintaining an acceptable speed-accuracy trade-off. Approach. Here we evaluated a family of techniques based on the application of the least-squares complex-valued filter (LSCF) design to real-time quantification of brain rhythms. These techniques allow for explicit optimization of the speed-accuracy trade-off when quantifying oscillatory patterns. We used EEG data collected from 10 human participants to systematically compare LSCF approach to the other commonly used algorithms. Each method being evaluated was optimized by scanning through the grid of its hyperparameters using independent data samples. Main results. When applied to the task of estimating oscillatory envelope and phase, the LSCF techniques outperformed in speed and accuracy both conventional Fourier transform and rectification based methods as well as more advanced techniques such as those that exploit autoregressive extrapolation of narrow-band filtered signals. When operating at zero latency, the weighted LSCF approach yielded 75% accuracy when detecting alpha-activity episodes, as defined by the amplitude crossing of the 95th-percentile threshold. Significance. The LSCF approaches are easily applicable to low-delay quantification of brain rhythms. As such, these methods are useful in a variety of neurofeedback, brain-computer-interface and other experimental paradigms that require rapid monitoring of brain rhythms.

Real-time estimation of phase and amplitude with application to neural data

“…The processing delay is only due to a causal filter if the latter is required, e.g., for brain activity data. To minimize the delay, one has to exploit specially designed filters 33 .…”

Short-Delay Neurofeedback Facilitates Training of the Parietal Alpha Rhythm

“…Such a low latency would enhance the sense of agency [14] and harness the power of automatic learning [30] by directly and specifically interacting with brain-state transitions. To achieve this desired latency decrease, more efficient signal processing pipelines are needed that use optimized hardware-software communication protocols, as well as more sophisticated signal processing pipelines for the extraction of oscillation parameters from brain activity [56,34,52]. curve prior and allows curves and the mean difference between the curves to be nonlinear.…”

“…In this method, the raw EEG signal is transformed into a narrowband analytic signal, a complex-valued function whose absolute value corresponds to an instantaneous amplitude(or envelope) of the rhythm. The cFIR method allows us to explicitly define NFB latency and obtain a more accurate envelope estimate for a specified latency compared to the other approaches frequently used for quantification of narrowband components in the EEG data, [56]. This speed-accuracy trade-off can be appreciated from the accuracy vs. processing delay curves presented in Figure 2 B for the cFIR and the commonly used approach based on narrow-band filtering followed by signal rectification.…”

“…Alpha-rhythm envelope was extracted with the cFIR approach [56] (Figure 2 A). In this method, the raw EEG signal is transformed into a narrowband analytic signal, a complex-valued function whose absolute value corresponds to an instantaneous amplitude(or envelope) of the rhythm.…”

“…This duration can be decreased by means of optimizing data acquisition and signal processing steps. To this end, we recently developed NFB-Lab software [57], where we implement a novel causal complex-valued finite impulse response (cFIR) approach for simultaneous narrow-band filtering and extracting the instantaneous power of an EEG rhythm [56]. This method allowed us to achieve high accuracy of narrow-band power estimation with the lag as short as 100 ms.…”