Title: Decomposing motor units through elimination for real-time intention driven assistive neurotechnology
Venue: NeurIPS 2025
Accepted: yes
Keywords: neurotechnology

motor unit decomposition

assistive technology

electromyography
Abstract: Extracting neural signals at the single motor neuron level provides an optimal control signal for neuroprosthetic applications. However, current algorithms to decompose motor units from high-density electromyography (HD-EMG) are time-consuming and inconsistent, limiting their application to controlled scenarios in a research setting. We introduce MUelim, an algorithm for efficient motor unit decomposition that uses approximate joint diagonalization with a subtractive approach to rapidly identify and refine candidate sources. The algorithm incorporates an extend-lag procedure to augment data for enhanced source separability prior to diagonalization. By systematically iterating and eliminating redundant or noisy sources, MUelim achieves high decomposition accuracy while significantly reducing computational complexity, making it well-suited for real-time applications. We validate MUelim by demonstrating its ability to extract motor units in both simulated and physiological HD-EMG grid data. Across six healthy participants performing ramp and maximum voluntary contraction paradigms, MUelim achieves up to a 36$\times$ speed increase compared to existing state-of-the-art methods while decomposing a similar number of high signal-to-noise sources. Furthermore, we showcase a real-world application of MUelim in a clinical setting in which an individual with spinal cord injury controlled an EMG-driven neuroprosthetic to perform functional tasks. We demonstrate the ability to decode motor intent in real-time using a spiking neural network trained on the decomposed motor unit spike trains to trigger functional electrical stimulation patterns that evoke hand movements during task practice therapy. We show that motor unit-based decoding enables nuanced motor control, highlighting the potential of MUelim to advance assistive neurotechnology and rehabilitation through precise, intention-driven neuroprosthetic systems.

Decomposing motor units through elimination for real-time intention driven assistive neurotechnology

Abstract

Extracting neural signals at the single motor neuron level provides an optimal control signal for neuroprosthetic applications. However, current algorithms to decompose motor units from high-density electromyography (HD-EMG) are timeconsuming and inconsistent, limiting their application to controlled scenarios in a research setting. We introduce MUelim, an algorithm for efficient motor unit decomposition that uses approximate joint diagonalization with a subtractive approach to rapidly identify and refine candidate sources. The algorithm incorporates an extend-lag procedure to augment data for enhanced source separability prior to diagonalization. By systematically iterating and eliminating redundant or noisy sources, MUelim achieves high decomposition accuracy while significantly reducing computational complexity, making it well-suited for real-time applications. We validate MUelim by demonstrating its ability to extract motor units in both simulated and physiological HD-EMG grid data. Across six healthy participants performing ramp and maximum voluntary contraction paradigms, MUelim achieves up to a 36 × speed increase compared to existing state-of-the-art methods while decomposing a similar number of high signal-to-noise sources. Furthermore, we showcase a real-world application of MUelim in a clinical setting in which an individual with spinal cord injury controlled an EMG-driven neuroprosthetic to perform functional tasks. We demonstrate the ability to decode motor intent in real-time using a spiking neural network trained on the decomposed motor unit spike trains to trigger functional electrical stimulation patterns that evoke hand movements during task practice therapy. We show that motor unit-based decoding enables nuanced motor control, highlighting the potential of MUelim to advance assistive neurotechnology and rehabilitation through precise, intention-driven neuroprosthetic systems.

1 Introduction

Electromyography (EMG) provides a natural motor interface for humans to interact with machines, capturing the electrical activity of muscles to facilitate intuitive control. At the core of physiological motor control is the motor unit, the smallest functional unit of muscle activation, consisting of a single motor neuron and the fibers it innervates [Heckman and Enoka, 2012]. EMG signals recorded at the periphery consist of a summation of motor unit action potentials and noise, with the input signal originating from the central nervous system, providing a direct link to neuromotor intent [Farina and Negro, 2015]. As a result, decomposing the physiological motor input to muscles via motor unit

activity may provide a more advanced and intuitive control signal for neuroproshetics [Tanzarella et al., 2023, Chen et al., 2020, Kapelner et al., 2019].

Recently, there have been significant advances in motor unit decomposition from non-invasive highdensity EMG (HD-EMG), leveraging swarm contrastive decomposition (SCD) [Grison et al., 2025], convolutive blind source separation (BSS) [Negro et al., 2016, Holobar et al., 2014], convolutional kernel compensation (CKC) [Holobar and Zazula, 2007], and deep learning-based approaches [Lin et al., 2024, Wen et al., 2023]. Open-source tools [Grison et al., 2025, Avrillon et al., 2024, Formento et al., 2021] have made it possible for researchers to analyze motor unit activity in controlled research settings during both isometric and dynamic movements [Osswald et al., 2025, Tanzarella et al., 2023, Chen et al., 2020]. However, these methods remain computationally intensive and inconsistent, often requiring significant processing time or manual intervention [Del Vecchio et al., 2020, Negro et al., 2016, Farina et al., 2014], prohibiting their use in real-time neuroprosthetic systems, where rapid and reliable decoding of motor intent is essential.

Existing decomposition methods typically use blind source separation (BSS), such as independent component analysis, in which the contrast functions used for source separation measure sparseness of spike trains, rather than independence [Negro et al., 2016]. While effective, these higher-order statistical methods are computationally demanding and sensitive to noise [Congedo et al., 2008]. Second-order statistical (SOS) methods [Belouchrani et al., 1997, Belouchrani and Amin, 1998] offer a more efficient alternative by leveraging spectral and temporal signatures of sources through joint diagonalization. However, SOS methods face two key challenges, namely joint diagonalization, a core component of SOS methods, has historically been computationally expensive, and SOS methods are constrained to decompose at most as many sources as there are recording channels [Congedo et al., 2008, Pham and Cardoso, 2001, Pham, 2001].

Recent advancements in joint diagonalization techniques have significantly improved computational efficiency [de Vlaming and Slob, 2021, Ablin et al., 2018], making SOS methods more practical for real-world applications. To address the challenge of limited source separability, we propose using strategies based on existing decomposition methods [Grison et al., 2025, Negro et al., 2016] and electroencephalography data augmentation techniques [Carrara and Papadopoulo, 2024] to add time-delayed extensions prior to joint diagonalization. This augmentation increases the effective dimensionality and enhances source separability by capturing temporal dynamics, improving the conditioning of the source separation problem. Taking inspiration from compressive sensing [Candès et al., 2006, Donoho et al., 2005], we further accelerate the identification of candidate sources by leveraging the sparsity of motor unit source activity contained within symmetric positive definite (SPD) matrices. By randomly sampling SPD matrices for joint diagonalization, we can perform an iterative BSS to find unique sources while significantly reducing computational overhead.

With these considerations in mind, we propose MUelim, a motor unit decomposition algorithm that leverages approximate joint diagonalization to extract many candidate motor unit sources all at once and then eliminates suspected noise sources. We validate MUelim on both simulated and physiological HD-EMG datasets, demonstrating its ability to extract motor units with high accuracy and speed. Furthermore, we showcase its application in a clinical setting, where it enables a spinal cord injury (SCI) participant to control a neuroprosthetic device in real time, highlighting its potential to advance assistive neurotechnology and rehabilitation.

2 Methods

2.1 Overview of EMG decomposition as a blind source separation problem

EMG signals represent the summation of motor unit action potentials (MUAPs) and noise (Figure 1A). These signals can be modeled as a linear instantaneous mixture of sparse sources, where each source corresponds to the discharge timings of a motor unit. The observed EMG signals X ∈ R C × N , where C is the number of channels and N is the number of samples, can be expressed as:

where H ∈ R C × M is the mixing matrix with M motor unit sources, S ( t ) ∈ R M × N represents the spike trains, and N ( t ) is additive noise. The goal of EMG decomposition is to estimate the spike trains S ( t ) from the observed signals X ( t ) .

Motor unit decomposition can be framed as a BSS problem, where the objective is to estimate the separating matrix B ∈ R M × C such that:

where ˆ S ( t ) is the estimated motor unit source activity.

2.2 MUelim algorithm

2.2.1 Preprocessing and data augmentation

The input EMG data X is first divided into non-overlapping windows of size L for SPD matrix computation. The windowed data is represented as X binned ∈ R W × C × L , where W is the number of windows.

To incorporate temporal information, the data is extended using lagged versions of each channel. This augmentation creates an extended dataset X ext ∈ R W × ( C · R ) × L , where R is the extension factor. The extend-lag procedure increases the ratio of observations to sources, improving the conditioning of the source separation problem [Holobar and Zazula, 2007]. By embedding the data into a higherdimensional space, this approach captures both spatial and temporal dependencies, which are critical for resolving sources with overlapping activity.

The extend-lag procedure is inspired by the success in decoding from the tangent space of augmented covariance matrices [Carrara and Papadopoulo, 2024]. The augmented covariance matrix combines spatial covariance with temporal information, effectively embedding the original dataset into a higherdimensional space. This embedding enhances the separability of sources by capturing their nonlinear dynamics [Takens, 2006]:

where τ is the lag parameter, and R is the extension factor.

2.2.2 Iterative blind source separation (BSS)

MUelim employs an iterative BSS approach to identify and refine sources. The algorithm assumes that the sources are sparse in the transformed domain. The iterative process continues until a stopping criterion is met, such as reaching the maximum number of iterations, finding the maximum number of sources, or failing to identify a minimum number of new sources.

SPD matrix computation In each iteration, the extended dataset is sampled ( X ′ ext ) for SPD matrix computation. Depending on the characteristics of the data and the assumptions about the sources, several types of SPD matrix estimators can be used. Simple covariance matrices, channelwise kernels, such as linear, polynomial, or laplacian kernels, and cospectral matrices can be used to capture nonlinear dynamics of the system [Congedo et al., 2008, Belouchrani and Amin, 1998, Belouchrani et al., 1997].

In this study, cospectral matrices are used as the primary estimator due to their ability to capture both spatial and spectral dependencies. For each frequency f in the range [ f min , f max ] , the Fast Fourier transform is applied to each window of the extended data to compute the cospectral matrix C f :

where H denotes the Hermitian transpose. The diagonal elements of C f represent the power (autospectra) of each channel, while the off-diagonal elements represent the in-phase SOS dependency [Congedo et al., 2008].

Whitening To improve the numerical conditioning of the SPD matrices, whitening is applied. Whitening ensures that the mean SPD matrix ¯ C has an identity covariance structure, simplifying the subsequent diagonalization step. This is achieved through eigenvalue decomposition:

where V and Λ are the eigenvectors and eigenvalues of ¯ C .

Approximate joint diagonalization The separation of non-stationary signals can be achieved by joint diagonalization of a set of autocorrelation matrices [Belouchrani and Amin, 1998, Belouchrani et al., 1997]. In the context of MUelim, we consider a set of n SPD matrices { C 1 , . . . , C n } of size p × p , where each matrix C i represents a whitened SPD matrix computed from the extended EMG data (Eq. 4). The goal of joint diagonalization is to find a matrix B ∈ R p × p such that the transformed set { BC 1 B ⊤ , . . . , BC n B ⊤ } contains matrices that are as diagonal as possible. This is achieved by minimizing the following joint diagonalization criterion:

where diag( · ) extracts the diagonal elements of a matrix, and det( · ) denotes the determinant. This criterion, introduced by Pham [2001], is derived as the negative log-likelihood of a source separation model for Gaussian stationary sources.

After solving the joint diagonalization problem, the forward and backward filters are computed. The forward filters W forward are used to project the extended EMG data into the source space, while the backward filters W backward are used to reconstruct the original signals from the source space. Let W whiten and W -1 whiten represent the whitening and inverse whitening filters, respectively. The forward and backward filters are computed as:

Peak detection and source refinement After obtaining the forward filters from the joint diagonalization step, the full extended dataset is transformed into the source domain. For each source, the source power γ j ( k ) is computed as:

Peaks are detected in the source power to refine each source filter w j as the mean of the corresponding impulse indices:

The updated filter is then orthogonalized and normalized with respect to the previously identified filters to ensure independence:

This process is repeated iteratively until convergence, ensuring that the filters are optimized for the identified sources. During this improvement iteration step, k-means clustering is used to separate signal peaks from noise peaks detected in the source power. The silhouette score (SIL) for each source is then calculated from the detected peaks. Sources that do not converge or that have a low SIL are eliminated from the final forward filters ( W forward ).

Unique source identification Newly identified spatial filters per BSS iteration are compared with previously found filters to ensure uniqueness. Spatial similarity is assessed using the cosine similarity between filters. Temporal similarity between spike trains is evaluated based on the percentage of coincident spike timings between motor unit spike trains. Newly identified candidate sources that exceed predefined similarity thresholds are discarded.

Optionally, to remove the influence of already identified sources, existing sources can be peeled off from the data [Chen and Zhou, 2015]. This step may improve the detection of weaker sources in subsequent iterations by removing the contribution of already-identified sources. Refer to Supplementary Algorithm 1 for pseudocode and Supplementary Figure 1 for an overview of the algorithm.

2.2.3 Computational complexity

MUelim's computational complexity is primarily determined by the joint diagonalization step, which is performed on the extended data matrix. The data is extended using R lagged versions of each channel, resulting in C × R extended channels, where C is the number of original channels and R is the extension factor. The per-iteration computational cost is O ( K ( C × R ) 2 +( C × R ) 3 ) , where K is the number of matrices being diagonalized. For large C × R , the ( C × R ) 3 term dominates, so the complexity is approximately O (( C × R ) 3 ) per iteration. This scaling arises because the most expensive operation is matrix multiplications of size ( C × R ) × ( C × R ) . As channels or extension factor increases, decomposition time increases accordingly. However, MUelim's advantage becomes more pronounced with more motor unit sources, as it efficiently extracts many sources simultaneously rather than incrementally.

2.3 Algorithm evaluation

To validate the proposed algorithm, we tested the decomposition method on simulated EMG data. The simulated EMG signals were generated using a Poisson neuron model to create spike trains, which were then convolved with a MUAP template to produce signals across multiple channels. Random noise and amplitude modulation were incorporated to mimic the variability and complexity of real physiological signals. We tested MUelim, SCD [Grison et al., 2025], and MUEdit [Avrillon et al., 2024] on identical simulated datasets to enable direct comparison of decomposition performance.

We evaluated two channel configurations spanning the physiologically realistic range for motor unit decomposition: 32 channels with 5, 10, and 15 motor unit sources, and 64 channels with 5, 10, 15, 20, 25, and 30 motor unit sources. These configurations test up to N/ 2 sources across all three methods. Signals were generated using a sampling rate of 2,048 Hz with average motor unit firing rate of 10 Hz for 30 s total. We assessed decomposition accuracy by comparing detected spike timings with ground truth within a 25 ms window, and calculated false positive and false negative rates for each method.

To assess the feasibility of using the MUelim algorithm in application, we decomposed motor units from a 8x8 HD-EMG grid (GR10MM0808; 64 monopolar EMG channels) and Quattrocento amplifier (OT Bioelettronica) across different parameters. EMG signals were recorded from the flexor digitorum superficialis muscle in six healthy participants (N=6). Participants performed two experimental paradigms: a ramped contraction for 45 s , with the first 15 s ramping up, the next 15 s plateaued at approximately 30% of the maximum voluntary contraction, and the last 15 s ramping down, and a maximum voluntary contraction (MVC) sustained for 10 s . EMG measurements were taken at a sampling rate of 2,048 Hz . An initial bandpass filter for the incoming signal was set at 10-900 Hz for each recording, and then an offline filter of 20-500 Hz was applied to the recordings. Force measurements were taken using a digital hand dynamometer at 10 Hz and was synced with the EMG signal offline.

Following decomposition, we plotted spike trains superimposed over target and force trajectories. We extracted MUAP waveforms using spike-triggered averaging (STA), which averages the EMG signal around detected spike times to isolate the waveform associated with each motor unit. For each spike timing, we extracted a 30 ms window centered on the spike impulse. To reduce cross-contamination, we reconstructed the EMG signal from source space using the BSS inverse filters while suppressing other motor unit sources. Waveforms were aligned to their global maxima across channels to handle temporal jitter before averaging. We extracted waveforms from all channels and displayed results from the 5 most active channels based on signal amplitude. Individual traces show the average computed over a sliding window spanning one fifth of all detected MUAPs, with a stride equal to one sixth of the window length. Subsequent inverse spatial filters were mapped to the 2D grid to visualize source activity dipoles.

We conducted two tests to benchmark the number of decomposed sources and decomposition time across different parameters in a single representative participant. First, we assessed the influence of the extension factor and lag on decomposition performance. The extension factor was set between 1 and 6, with the lag between 1 and 10 for a total of 60 permutations. A cospectral estimator and bin size of 20 ms was used across all permutations. In the second test, we evaluated the influence of the SPD estimator, as well as the variability in bin size to compute SPD matrices. We evaluated a cospectral estimator and laplacian channelwise kernel over a range of bin sizes (10-2000 ms ) using open-source methods from pyRiemann [Barachant et al., 2025]. For all cospectral matrices, we

computed the FFT using a window size of 8 with 75% overlap between 0 and 60 Hz . For this test, we held the extension factor and lag constant at 2 extensions and 6 lag samples, respectively. For both tests, we ran each decomposition permutation over 5 seeds to determine the consistency of the algorithm with the given set of parameters. The average number of sources decomposed and decomposition time ± standard error of the mean are reported. A SIL threshold of 0.85 was used to determine high signal-to-noise sources. We found sources over 3 BSS iterations using a random sampling of 50% of the data for diagonalization of SPD matrices. For all tests, JADOC [de Vlaming and Slob, 2021] was used for joint diagonalization with a regularization strength of 0.85.

We then compared our results to current state-of-the-art open-source motor unit decomposition algorithms across all six participants, namely SCD [Grison et al., 2025] and MUEdit [Avrillon et al., 2024]. We assessed both number of sources decomposed and decomposition time. We held all other parameters constant based on the open-source implementations, with 0.85 SIL threshold used to determine acceptable sources. For SCD, we used the built-in GPU capability to increase decomposition speed. All tests were evaluated using a HP ZBook Power 15.6 inch G8 Mobile Workstation PC (Intel Core i7-11850H 2.50GHz, NVIDIA T1200 GPU, CUDA 12.2) python 3.11 or MATLAB 2021 for MUEdit.

2.4 Application: Intention driven neuroprosthetic

To demonstrate MUelim's utility in a realistic use-case, we evaluated its performance in an ongoing registered clinical trial (NCT06087445) in an individual with SCI. All study procedures were conducted under Institutional Review Board approval. The participant was informed of potential risks and monitored for adverse events throughout the study. In the study, a C3 incomplete SCI participant (ASIA D) used an EMG-based neuroprosthetic system to control movement-specific functional electrical stimulation (FES) patterns based on motor intent. The participant could partially open and close his hand, though not fully, and exhibited limited grip strength. Abnormal muscle synergies, particularly overactivity in the wrist flexors, limited his ability to achieve wrist extension. FES facilitated more complete hand opening, enhancing functional performance and reducing reliance on compensatory strategies. The complete training and inference workflow is illustrated in Supplementary Figure 3.

The neuroprosthetic system consists of 150 electrodes (75 bipolar EMG channels) embedded into a stretchable fabric. An operator manually calibrated FES patterns at the beginning of the session to evoke both hand open and hand close movements (Supplementary Video 1: Heatmap / Stim Patterns). A sinusoidal waveform with 20 Hz stimulation frequency was used for both patterns. Next, a block of operator-guided stimulation was used to find spatial filters for motor unit decomposition and train a spiking neural network (SNN) to decode motor intent from the decomposed motor unit spike trains. The operator manually cued the participant to perform different tasks guided by an occupational therapist (OT). The corresponding FES pattern was automatically stimulated with an offset of 1,000 ms to record intent with/without FES active. The BSS forward filters were computed in-session after collecting this training block (fit phase), then applied for real-time inference (transform phase), following standard scikit-learn convention (Supplementary Algorithm 1). EMG was recorded with a sampling rate of 3,000 Hz , collected in non-overlapping 100 ms bins to generate final predictions at 10 Hz used to switch/turn-off FES patterns when in inference mode.

Following this training block, EMG data was filtered for subsequent motor unit decomposition. First, FES artifact was removed using a template artifact filter, whereby a template of the artifact from the previous pulse window was subtracted from the current pulse window. Next, a 20 ms blanking window was used to blank out any remaining artifact in between FES pulses. The subsequent signal was then filtered using notch and bandpass filters similar to previous studies [Tacca et al., 2024, Meyers et al., 2024]. Following the preprocessing pipeline, motor units were decomposed using the proposed MUelim algorithm to compute the BSS forward filters from the training data. For enhanced speed and accuracy, motor unit spike trains were downsampled within a bin to five sub-bin splits, with a shape of n samp × n MUs × n splits . Next, the previous four bins were concatenated with the current bin to provide additional time information to the SNN. This was then fed into a fully-connected SNN developed using the LAVA framework. Hidden layers consisted of 1000 x 500 current based leaky integrate and fire neurons. Default neuron parameters from LAVA were used for training. A dropout of 40% was applied at each layer. The SNN was trained natively using the SLAYER module [Shrestha and Orchard, 2018] within LAVA for 15 epochs with batch size of 128 and an initial learning rate

of 0.001. The Adam optimizer with cosine annealing warm restarts was used to optimize the error function. The built-in spike rate error function with true rate of 0.8 and false rate of 0.001 was used to align the output SNN neuron activity with the three classes, namely Hand Open, Hand Close, and Rest. Both SNN training and inference utilized a GPU to enhance speed for application. All steps within the pipeline were wrapped in a sklearn transformer [Pedregosa et al., 2011] containing both fit and transform methods to be used in the existing clinical software.

Once a decoder was trained, the full pipeline was used in inference mode, allowing the participant to control FES based on motor intent decoded from the decomposed motor unit activity. The operator manually labeled the task as the participant performed it with guidance from the OT to assess decoder performance offline. Bin-wise accuracy was used to assess how many 100 ms bins matched the ground truth manually labeled by the operator. A live user-interface was generated to visualize EMG activity, motor unit activity, SNN neuron output activity, and MUAP waveform generation. A Unity-engine virtual hand shows the real-time predictions and active FES provided to the participant.

3 Results

3.1 MUelim decomposition validation

Representative decomposition results from simulated EMG data are shown in Figure 1B-D. MUelim successfully decomposed the simulated signals into the three ground truth motor unit sources. Peak detection in the source power domain (Figure 1B) identified spike timings that closely matched ground truth (Figure 1C). Reconstructing the EMG signal at these spike timings with other sources suppressed produced clear motor unit action potential waveforms (Figure 1D), demonstrating successful recovery of the simulated MUAP shapes.

A

B

Peakdetection

Source

1

N

2

Time (s)

E

Spike train

Ground Truth

Decomposed

Source

2

0

1

2

Time (s)

3

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5

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Waveformidentification

Motor Unit Action

Potentials

HD-EMG

Amplitude (mV)

2.3

2.4

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2.5

2.6

2.7

2.8

We compared MUelim against state-of-the-art decomposition methods on identical simulated EMG datasets. Across all simulation scenarios (32 and 64 channels with 5 to 30 motor units), all three methods successfully identified the correct number of sources. When comparing spike timings with ground truth, MUelim achieved 99.99 ± 0.01% accuracy with 0.99 ± 0.14 false positives per source and 0.03 ± 0.02 false negatives per source, closely matching SCD (99.99 ± 0.01% accuracy, 0.93 ± 0.13 FP per source, 0.03 ± 0.02 FN per source) and MUEdit (98.98 ± 0.07% accuracy, 0.00 ± 0.00 FP per source, 3.06 ± 0.20 FN per source) (Supplementary Table 1).

Next, motor units were decomposed from a HD-EMG grid as a healthy individual performed a ramped contraction (Figure 2). Varying parameters were used to assess the impact on the number of

sources decomposed and decomposition time (Supplementary Figure 2). Using an extension factor of 4 and lag of 6, 19 unique motor unit sources were found in just under 5 minutes that align closely to the force output (Figure 2A). Representative MUAP waveforms (Figure 2B) demonstrate clean action potentials, while the inverse spatial filters (Figure 2C) show the spatial localization of motor unit sources across the electrode grid.

20

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Across all six participants in both ramp and MVC paradigms, MUelim consistently decomposed motor units with substantially reduced computational time compared to alternative methods (Table 1). For ramp contractions, MUelim achieved up to a 36 × speed increase compared to MUEdit (3.1 vs 112.3 minutes, Supplementary Table 2). The motor unit yields observed are consistent with prior reports for high-density grids in hand and forearm muscles [Farina et al., 2008, Negro et al., 2016]. Full timing results from the parameter sweep in a single participant are shown in Supplementary Figure 2. Varying bin size for SPD matrix computation affected the number of sources decomposed, while having a minimal effect on decomposition time (Supplementary Figure 2A-B). The optimal bin size range to extract the most sources was 20-30 ms . When comparing SPD matrix estimators, cospectral matrices yielded more sources in the optimal bin size range, while taking less time to decompose than a laplacian kernel estimator.

Both extension factor and lag influenced the number of sources decomposed and decomposition time (Supplementary Figure 2C-D). The number of sources decomposed began to saturate with an extension factor greater than 2. A lag between 4-8 samples per extension yielded the most sources. Across all permutations, SIL was greater than 0.85 for every source with a grand average SIL of 0 . 955 ± 0 . 001 . The maximum decomposition time was just under eight minutes with extension factor of 6 and lag of 8 samples. Using a small extension factor and lag > 1 , a majority of sources can still be found in a fast decomposition time. For example, with an extension factor of 2 and lag of 5, there was an average of 15 . 4 ± 0 . 98 sources decomposed across the 5 iterations (81% of the peak number of sources). Decomposition time for this setting was only 1 . 47 ± 0 . 01 minutes.

3.2 Closed-loop control of a neuroprosthetic by a SCI user

To evaluate whether MUelim could be used to control a neuroprosthetic, we trained a SNN to decode motor intent from a SCI participant's motor unit activity to activate movement-specific FES patterns during task practice therapy. The SCI participant was successfully able to control the neuroprosthetic using the trained decoder (Figure 3 and Supplementary Video 1). The motor unit-based SNN decoder achieved 85% bin-wise accuracy during live control. For comparison, an offline analysis using standard root-mean-square (RMS) features with a neural network (NN) decoder achieved 86% accuracy on the same dataset. All of the intended movements of the 3 tasks were successfully activated by the participant. Discrepancies between manual labels and final FES predictions can be attributed to short delays in transition between movements and movement to rest (Figure 3B FES predictions above vs. lightly shaded labels on top of the motor unit spike train). Looking at the first transition from rest to hand open to grab the pipe, MUelim detected the initial motor intent, which triggered the hand open FES pattern to activate (Figure 3A). Following this, there was an initial break-in period of the template artifact filter, with subsequent peaks detected after the second FES pulse that oscillated with stimulation frequency. The user retained control of the device and was successfully able to transition between states to allow the FES to assist in completing the task. Waveforms generated from the spike triggered averaging of reconstructed EMG at detected spikes show clean action potentials (Figure 3D), demonstrating the ability of the algorithm to detect spikes in between FES pulses.

ASNNwasable to dissociate between motor unit activity during the different movements independent of the task (Figure 3C). The prediction probability calculated from the output neuron firing rate is shown on top of the SNN output spike train. When there was no output neuron firing, the decoder defaulted to a rest prediction. Corresponding snapshots of the tasks are shown below the spike trains (Figure 3E). Refer to Supplementary Video 1 for the full live video demonstrating neuroprosthetic control.

Labels/Predictions

A

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MotorUnitSpikeTrain

Hand Open

Hand Close

Shifted cue/label

FES

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A. Zoom-in plot of raw EMG with spike train on top at the transition between rest and hand open. Spikes are detectable in a 50 ms window between FES pulses with 20 Hz stimulation frequency. B. Full spike train that was decomposed in real-time while using the EMG-FES system in task practice. Rectangles above the spike train indicate the final movement predicted that triggered the corresponding FES movement to evoke assistance. The lighter shaded rectangles across the full spike train indicate the ground truth manually labeled by the operator. C. Output of the SNN with 3 classes and the resulting prediction probability based on the output neuron firing rates. D. Sample motor unit action potential waveforms averaged across the five highest weighted channels. E. Snapshots of SCI participant performing the rehabilitation tasks. See Supplementary Video 1 for a real-time demo.

4 Discussion

We introduced an efficient method for motor unit decomposition that leverages approximate joint diagonalization for rapid extraction of motor units from HD-EMG. Our approach incorporates an extend-lag procedure, previously used in EEG and dynamical systems analysis [Carrara and Papadopoulo, 2024, Takens, 2006], to augment the data and enhance source separability prior to joint diagonalization. While the extend-lag procedure itself is not novel, its application in this context enhances source separability by capturing temporal dynamics and improves the conditioning of the source separation problem. MUelim builds on advances in convolutive BSS and joint diagonalization [Negro et al., 2016, Holobar and Zazula, 2007, Belouchrani et al., 1997, Pham, 2001], and addresses computational bottlenecks that have limited motor unit decomposition for real-time applications [Congedo et al., 2008, Grison et al., 2025].

Comprehensive validation on both simulated and physiological data demonstrated MUelim's effectiveness. Direct comparison on identical simulated datasets showed that MUelim achieved comparable decomposition accuracy to SCD and MUEdit. Validation across six healthy participants in both ramp and MVC contractions demonstrated consistent performance with up to 36 × speed improvements compared to open-source methods such as SCD [Grison et al., 2025] and MUEdit [Avrillon et al., 2024], while achieving similar or greater source yield. MUelim's substantially reduced BSS filter computation time (minutes vs up to hours) enables practical deployment in closed-loop neuroprosthetic systems where rapid session setup is required.

We demonstrated this feasibility in a clinical neuroprosthetic control application, in which we decoded motor intent from motor unit firing activity decomposed using MUelim to enable an individual with SCI to volitionally control FES movement patterns. The motor unit-based SNN decoder achieved comparable performance to an offline RMS-NN decoder (85% vs 86% accuracy), although direct comparison is difficult since FES was already triggered during data collection, affecting subsequent motor recruitment and EMG signals. Integrating MUelim with a SNN decoder enables spike-based decoding, which has the potential to be incorporated in neuromorphic hardware for low-power neuroprosthetics [Tanzarella et al., 2023, Chen et al., 2020].

There are several limitations to this work. MUelim was validated only on non-invasive HD-EMG and has not yet been tested on intramuscular EMG, which may present different decomposition challenges [Negro et al., 2016, Holobar et al., 2014]. Due to clinical trial constraints, the clinical evaluation period was limited. As a result, spatial filters may require adaptation for long-term or at-home use, as electrode shifts and signal quality changes can degrade performance over time [Del Vecchio et al., 2020, Farina et al., 2014]. Future work should perform more rigorous benchmarking of motor unitbased features against RMS and other standard EMG preprocessing approaches using open-source datasets, such as those used in EMGBench [Yang et al., 2024]. Broader validation across diverse user populations and movement tasks will also be important to establish generalizability of the approach [Osswald et al., 2025, Wen et al., 2023]. As with any assistive neurotechnology, there is a potential risk that MUelim could lead to unintended device actuation if motor units are incorrectly decomposed, or raise privacy concerns if EMG data are not handled securely. Nevertheless, MUelim provides a practical and efficient solution for real-time motor unit decomposition, supporting the development of robust, intention-driven assistive technologies.

5 Conclusion

This work presents MUelim, an efficient algorithm for motor unit decomposition from HD-EMG signals. By leveraging approximate joint diagonalization, MUelim achieves high decomposition accuracy while significantly reducing computational complexity, outperforming state-of-the-art methods with up to a 36 × speed improvement. Comprehensive validation on identical simulated datasets demonstrated that MUelim achieves comparable accuracy to existing methods. Validation across six healthy participants in both ramp and maximum voluntary contraction paradigms demonstrates its ability to extract motor units with high signal-to-noise ratios. Furthermore, we showcased its application in a clinical setting, where MUelim facilitated real-time decoding of motor intent to control a neuroprosthetic device by a SCI participant, highlighting its potential for advancing assistive neurotechnology.

Disclaimer

The system used in the study referenced has not been approved or cleared as safe or effective by FDA. This device is limited by U.S. federal law to investigational use.

Acknowledgments

The authors would like to thank the broader Battelle development, quality, and management teams for their engineering work and general project support. Algorithm development, data analysis, and manuscript drafting were funded through Battelle Memorial Institute internal research and development funds.

The spinal cord injury trial was supported by the Assistant Secretary of Defense for Health Affairs endorsed by the Department of Defense, in the amount of $2,004,786, through the Spinal Cord Injury Research Program under Award No. W81XWH-22-1-1119 and W81XWH-22-1-1083. Opinions, interpretations, conclusions and recommendations are those of the author and are not necessarily endorsed by the Department of Defense.

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Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis manuscript introduces an approach MUEdit for decomposing motor unit action potentials from HD-sEMG. The proposed method uses a combination of joint diagonalization and expansion of the domain by time-lagging to identify motor unit sources and identify more sources than sEMG channels in a computationally efficient manner. They show successful recovery in synthetic data. They compare to a small set of alternative methods on a single subject, showing improvements in speed compared to alternative approaches. They show a demo using the extracted MUAPs to drive a spiking neural network in a spinal cord injury patient.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\nThe algorithm appears to be novel and show some advantages in speed/computation time compared to other approaches. \nThere are several contemporary alternative approaches benchmarked. \n\nWeaknesses\n* Evaluations and baselines are unconvincing and limited\n* The advantages of the algorithm is not made especially clear, and its performance in different data regimes (e.g. sparse, dense, scaling with channel counts) is not shown. There is not a set of ablations that makes clear how different algorithmic properties and features factor into computational savings and data quality (e.g. removing time lag, approximations of joint diagonalization).\n\nQUESTIONS:\n* The synthetic data experiments are too easy, as the algorithm achieves perfect performance. Competing methods are not benchmarked on synthetic data, which is the only regime that has a ground truth, so its unclear exactly how these are compared. \n\n* The proposed algorithm is benchmarked in Figure 2 with extensive hyperparameter tuning as shown in Supplementary Figure 3 and then compared to alternative algorithms using open source hyperparameters. Its not clear if these hyperparameters were tuned on the evaluation set, and how the competing algorithms would perform with additional hyperparameter tuning. \n\n* The evaluation and comparison is only on a single subject. It is unclear what degree of tuning is needed to deploy this to additional subjects which would impact computation time. \n\n* The spiking NN demo does not add much to the manuscript. It is unclear if similar results could be achieved with any spike extraction approach. \n\nMinor\n\n* Why is uncertainty only reported in Table 1 for 1 method?\n\n* Can you be more specific about how alternative methods were computationally optimized. \n\n* What is the time scaling of approaches with channels and additional motor units\n\n* Where does the assumption of sparsity in the BSS fail\n\n* Can you give more details about the extracted MUAPs? Are their qualitative features that can be used to further convince the reader that these are 'real'\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\n- The authors introduce a new algorithm MUelim for decomposing high-density surface EMG into the motor units that generated the signals.\n- The algorithm shows great speed improvements (up to 3700%) versus the current state-of-the-art methods\n- They demonstrated the usefulness of the decomposition by having a participant with SCI control their hand through FES by decoding the intention (hand open, close, rest) from the extracted MUAPs using a spiking neural network.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n- The presented algorithm works fast and builds on existing literature\n- Having a fast and accurate algorithm for MUAP decomposition can be very valuable for a number of other projects\n- They show that the method works in simulated data, which is key to understand the behavior of the novel method.\n- They test it on a real scenario and show that it works and can be useful to extract control signals in a participant with SCI.\n- Paper is well written and leads the reader nicely through the methods and the results.\n\nWeaknesses:\n- During simulation, it would be good to have a comparison with other methods, making sure that the results are similar. Also, please add a figure to the main text related to simulation: making sure that the novel method can detect all sources and has results similar to existing methods is a key results of the paper. Finally, you discuss that one of the key parts of the method allowed to get more sources than the available channels, but you do not test this in simulation.\n- You mention in the paper that you were able to use the method online in the clinical setting. However, the time for decomposition you showed was in minutes. Did you pre-compute the decomposition and then use the forward matrix online? This needs an important clarification, as one of your motivation points talks about being able to use this online, and this may not be a big difference with existing methods.\n- The task you tested in the clinical setting is probably not the best way to motivate this method: from the video in the supplemental, I can see the participant had quite a bit of residual movement, which means that you could do the same task just by processing the full EMG. The method would be better motivated in cases in which you are interested in the MUAPs individually: maybe more neuroscience related questions, or tasks in which participants are instructed to control specific MUAPs.\n\nQUESTIONS:\nMethods:\n1. Paragraph on how the MUAP waveforms are extracted (lines 181-186) is not very clear. Please add more details into how this process works.\n2. You mention in the introduction that the addition of time-delayed extensions prior to joint diagonalizations helps with potentially extracting more sources than channels. However, in section 2.3 you only evaluate cases in which there are many more channels than sources. What happens when the number of sources is higher than the number of channels? Also, please compare the simulation results you got with existing methods (such as MUedit and SCD). \n3. In section 2.4, please add how much residual movement the participant had available. Were they able to open and close their hand by themselves?\n4. The manuscript would greatly benefit from some diagram of the training procedure and inference during the neuroprosthetic experiment, potentially as an addition to Figure 3.\n5. Was the EMG decomposition done before starting the inference experiment? If so, how did you decompose the EMG signal in real-time? Please clarify. If you are pre-computing the forward filters, please clarify.\n\nResults:\n1. Please add a figure to the main text with the results from the simulation experiment, as it can give key insights into whether the proposed method is working as expected. At the beginning of the results section you cite Figure 1, but that doesn’t really contain simulation results.\n2. Make sure that the units of Figure 2B (especially the right plot) are correct. \n3. Figure 2C is not mentioned in the main text: what is the message you are trying to convey with it?\n4. In Table 1, why do you show variability for MUelim but not for the other methods? Also, add a discussion on what the expected number of motor units should be, to better understand the results.\n5. How does the per-bin accuracy looks like if you use the full non-decomposed EMG rather than motor units? I would imagine that it would be much higher performance, but that would depend on how much residual movement the participant may have. Please add a few sentences to the limitations paragraph related to this method in this participant.\n6. Mark the transition between rest and hand open in Figure 3A\n7. Figure 3D probably has wrong units.\n\nDiscussion:\n1. In lines 322-323 you claim “MUelim achieves similar or greater source yield with 323 substantially reduced computation time, supporting its use in closed-loop neuroprosthetic systems”. However, the computation times you show are in the order of minutes. If you are pre-computing the forward filters please clarify and tone down the claim.\n\nIf these comments and questions are addressed, I’ll increase my score.\n\nLIMITATIONS:\nLimitations are discussed in the manuscript and I have no ethical concerns with the submission.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 4, "DATE": "2025-07-03"}

comments: SUMMARY:
This paper shows a method for accurate and efficient motor unit decomposition called MUelim. The authors demonstrate motor unit decomposition for simulated EMG data, an able-bodied individual, and an individual with spinal cord injury.

STRENGTHS AND WEAKNESSES:
Strengths
* Significant speed improvement of 3700% over an alternative method
* Evaluates motor unit decomposition with a user with spinal cord injury and uses this for real-time inference for FES
* Shows similar SNR and number of motor units decomposed as the baseline methods

Weaknesses
* Does not compare with public datasets for motor unit decomposition
* Limited machine learning evaluation. ML evaluation is with a single participant in what seems to be a single trial for three similar pick and place tasks task. 
* Even with an able-bodied individual, only a single individual is tested for motor unit decomposition 
* Does not compare with other machine learning preprocessing methods for ML task (e.g. classification on raw signals, RMS signals, or time-frequency transforms).

QUESTIONS:
* How do these motor unit decomposition methods perform with public datasets?
* How useful is motor unit decomposition for downstream tasks such as classification of hand open, hand close, and rest compared to other preprocessing methods?
* ASIA D usually means significant motor function is retained by the user. How much was the FES needed to restore function for this user for the pick and place tasks demonstrated?

LIMITATIONS:
yes
TITLE: Official Review
CLARITY: 3
IMPACT: 4
ORIGINALITY: 2
DATE: 2025-07-03

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper presents MUelim, a novel algorithm designed for real-time motor unit decomposition from high-density electromyography (HD-EMG) signals. The core contribution is an efficient method that leverages approximate joint diagonalization combined with a novel extend-lag data augmentation procedure to extract motor unit activity quickly and accurately. The method is validated on both simulated and physiological HD-EMG data and is shown to outperform state-of-the-art techniques in terms of decomposition speed—up to 3,700% faster—while maintaining comparable accuracy. MUelim is also demonstrated in a clinical setting, enabling an individual with spinal cord injury to control a neuroprosthetic device in real-time via decoded motor intent, showcasing its potential in assistive neurotechnology.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n1. Efficiency: MUelim offers significant speed improvements over current methods, making it suitable for real-time applications.\n2. Clinical relevance: Demonstrated utility in a real clinical trial, enabling intention-driven control of a neuroprosthetic device.\n3. High accuracy: Achieved nearly perfect spike timing detection in simulated data (99.93% accuracy).\n4. Robust evaluation pipeline: Includes parameter sweeps (extension factor, lag, estimator types), detailed algorithm validation, and real-world application.\n5. Integration with spiking neural networks: Enables low-power, event-driven decoding for future neuromorphic applications.\n\nWeaknesses:\n\n1. Limited dataset diversity: Only tested on non-invasive HD-EMG; not validated on intramuscular EMG or broader subject populations.\n2. Simplified tasks: Real-world clinical task is relatively simple, potentially limiting generalization to more complex motor intentions.\n3. Algorithmic novelty: While practical, the core techniques are adapted from prior work rather than invented anew.\n4. Lack of theoretical complexity analysis: No formal time/space complexity or asymptotic runtime characterization is provided.\n\nQUESTIONS:\n1. How do you choose the extension factor R?\nThe paper performs a parameter sweep across R (extension factor) and lag, reporting that R = 4 and lag = 6 provides the best balance between number of decomposed sources and computation time. However, the choice of R is empirical and may benefit from adaptive tuning strategies.\n\n2. The study compares MUelim against two open-source baselines: MUEdit and Swarm Contrastive Decomposition. Are there any more comparison methods available? Further comparisons with deep learning-based or RMS-feature-based EMG decoding methods would be necessary for broader benchmarking.\n\n3. I did not find an analysis of algorithm complexity in the article. The paper lacks a formal complexity analysis, which would be helpful in understanding scalability, especially for embedded or wearable systems.\n\n4. In Table 1, is the extension factor R seriously affecting the response time? Increasing R leads to longer or shorter decomposition time but also more decomposed sources?\n\n5. In equation (1), dimensions of each component do not correspond to each other.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-04"}