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Event-driven signal reconstruction through neuromorphic compressive sensing

Zeru Fang, Yanzhen Liu, Geoffrey Ye

arXiv:2609.28063v1eess.SP

TL;DR

Conventional compressive sensing uses dense, fixed-length measurements and reconstruction operations, limiting resource efficiency on constrained devices. This paper introduces spike-driven S-LISTA to represent measurements and reconstruction updates as events. Experiments report lower transmission and estimated reconstruction energy alongside competitive reconstruction and downstream performance.

  • Problem

    Conventional CS uses dense, fixed-length measurements and dense reconstruction operations, so communication and computational costs remain tied to system dimensions, limiting use on resource-constrained edge devices.

    Source: Introduction · p. 2

  • Method

    The framework represents compressed measurements and S-LISTA reconstruction updates as spikes, with joint training of the measurement network, reconstruction network, and dictionary.

    Source: Introduction · p. 3, Discussion · p. 12

  • Results

    Across synthetic, ECG, and event data, S-LISTA offers competitive reconstruction with substantially lower estimated energy; AER reduces transmitted bits by 96.1% on DVS-G and 96.5% on SHD versus ANN baselines with 8-bit quantized measurements.

    Source: Introduction · p. 3, Discussion · p. 12

  • Takeaways & Limitations

    Neuromorphic compressive sensing links sparse signal representations with sparse SNN activity as a promising approach to reconstruction on resource-constrained edge devices.

    Source: Discussion · p. 13

    Estimated energy covers sensing and reconstruction but excludes dictionary readout, communication, memory access, downstream task evaluation, and hardware control costs.

    Source: Experimental procedures and analytical… · p. 17

Abstract

from arXiv · show

Compressive sensing (CS) exploits intrinsic signal sparsity for efficient representation of high-dimensional data. However, conventional CS relies on fixed-length measurement representations and dense reconstruction operations, leaving communication and computational costs largely determined by system dimensions rather than signal sparsity. Here, we propose a neuromorphic CS framework centred on a spike-driven learned iterative shrinkage-thresholding algorithm (S-LISTA). By representing compressed measurements and reconstruction updates as sparse events, the framework links intrinsic signal sparsity to the spatiotemporal sparsity of spiking neural networks (SNNs), extending the benefits of sparsity across sensing, transmission and reconstruction. Communication and computational costs consequently depend on event activity, allowing sparse representations to translate into resource savings. Extensive experiments demonstrate substantial reductions in transmitted data volume and estimated reconstruction energy while maintaining competitive reconstruction and downstream task performance. The framework also exhibits robustness under challenging channel conditions. These findings establish neuromorphic CS as a promising paradigm for signal reconstruction in resource-constrained scenarios.

Introduction

Conventional compressive sensing uses dense measurements and reconstruction operations, limiting its resource efficiency on edge devices. The proposed framework uses spike events for measurement, transmission, and S-LISTA reconstruction, with synthetic-signal experiments showing lower estimated energy at comparable reconstruction error.

Introduction

  • Conventional CS uses dense, fixed-length measurements and dense reconstruction operations, leaving communication and computational costs tied to system dimensions and limiting edge-device use.SNN event-driven operation can reflect signal sparsity in computation, while LISTA's repeated dense residual corrections motivate a fixed-depth, event-driven alternative.Source: Introduction · p. 2

Neuromorphic compressive sensing architecture

  • The framework sends low-dimensional measurement spikes and reconstructs a sparse code by accumulating positive and negative spike updates, followed by continuous correction and dictionary readout.Joint training optimizes the measurement network, reconstruction network, and dictionary, with task supervision on the sparse code.Source: Neuromorphic compressive sensing… · pp. 3–4

S-LISTA enables energy-efficient sparse reconstruction

  • At comparable NMSE, S-LISTA reduces estimated energy consumption by up to 57.3% relative to ANN baselines on synthetic sparse signals.Increasing unfolded depth lowers reconstruction error with a moderate energy increase; ANN LISTA and LAMP achieve lower NMSE when more computation is available.Source: S-LISTA enables energy-efficient… · pp. 5–6
  • At measurement SNRs of 20 dB and below, S-LISTA achieves reconstruction performance similar to ANN baselines, although its NMSE rises by 4.24 dB at 20 dB relative to noiseless measurements.At 30 dB, NMSE rises by 0.54 dB relative to the noiseless condition.Source: S-LISTA enables energy-efficient… · p. 6
  • Continuous correction reduces example NMSE from −15.14 to −26.89 dB, but some small-magnitude coefficients remain unrecovered when membrane potentials do not reach the firing threshold.This thresholding can alter the sparse-code distribution, motivating a learnable dictionary adapted to S-LISTA codes.Source: S-LISTA enables energy-efficient… · p. 6

Learnable sensing and dictionaries improve ECG reconstruction

S-LISTA combines learned sensing and dictionaries with spike-driven reconstruction, targeting lower transmission and computation costs. Across ECG and event datasets, it reduces payload or estimated energy while maintaining competitive reconstruction and downstream task performance, including under challenging channels.

Learnable sensing and dictionaries improve ECG reconstruction

  • With learned sensing and dictionaries, ECG S-LISTA reaches −20.92 dB NMSE, 5.81 dB better than ALISTA; estimated energy is 0.322 µJ/sample versus 1.378 for LAMP and 2.202 for ANN LISTA.Joint learning improves S-LISTA NMSE by 7.37 dB compared with fixed sensing and a Symlet-4 dictionary; energy excludes final dictionary readout.Source: Learnable sensing and dictionaries… · pp. 6–7, Figure 3 · p. 7
  • At 2 dB AWGN, S-LISTA has lower NMSE than LAMP; under unseen Rayleigh fading it leads all four methods from −5 to 9 dB, and at 156 bits/sample beats LAMP by 0.34 dB.At that bit budget, its NMSE trails ANN LISTA by 0.83 dB.Source: Learnable sensing and dictionaries… · p. 6, Figure 3 · p. 7

Neuromorphic compressive sensing reduces transmission cost on event data

  • Across DVS-G and SHD, S-LISTA transmits 87.5% fewer bits than ANN baselines; DVS-G task performance remains comparable, while SHD NMSE is −16.66 dB versus −16.45 dB for ANN LISTA, with accuracy about 3 points lower.Table 1 reports full-vector transmission under Rayleigh fading at 20 dB.Source: Neuromorphic compressive sensing… · p. 9, Table 1 · p. 10
  • On DVS-G, accuracy at 2 dB AWGN is 87.71% for S-LISTA versus 31.32% for ANN LISTA; under unseen Rayleigh fading, S-LISTA leads across tested SNRs on both datasets.On SHD, its NMSE is also lower than the vanilla SNN throughout the tested fading range, by at least approximately 4.49 dB.Source: Figure 4 · p. 8, Neuromorphic compressive sensing… · p. 9
  • At approximately 30 × 10^3 bits/sample on DVS-G, S-LISTA improves NMSE by 1.87 dB and accuracy by 4.31 points over the vanilla SNN; on SHD, it improves NMSE by 0.58 dB with both near 88% accuracy.These comparisons use AER transmission at comparable budgets.Source: Figure 4 · p. 8, Neuromorphic compressive sensing… · p. 9

Sample-wise performance and ablation analysis

Computational cost and estimated energy

The framework links signal sparsity to event-driven computation and communication, with estimated energy savings across sensing and reconstruction. Its discussion positions the approach for resource-constrained edge applications.

Computational cost and estimated energy

  • 19.5× on DVS-G and 10.9× on SHD: the framework reduces estimated sensing-stage energy relative to ANN methods.Table 3 reports computational cost and estimated energy per sample.Source: Computational cost and estimated energy · p. 11, Table 3 · p. 12
  • Approximately 3.99 mJ per sample on DVS-G and 6.93 µJ on SHD: combined sensing and reconstruction energy is reduced by approximately 95.6% and 98.4% relative to ANN LISTA.The paper links these savings to signal sparsity and computational sparsity in S-LISTA.Source: Computational cost and estimated energy · p. 12

Discussion

  • Experiments on synthetic sparse signals, ECG, and neuromorphic event datasets report lower estimated reconstruction energy than ANN baselines with competitive reconstruction quality.On visual and auditory event data, the complete framework reduces transmission cost with modest reconstruction and downstream-task trade-offs, and is evaluated under AWGN and unseen Rayleigh fading.Source: Discussion · p. 12
  • The paper identifies reconstruction and downstream analysis on resource-constrained edge devices as relevant application settings.Examples include accelerated MRI, biological microscopy, and event-based vision.Source: Discussion · p. 13

Neuromorphic sensing based on SNNs

  • A learnable mapping projects source observations from N dimensions to M-dimensional measurement currents, with M < N, which LIF neurons convert into binary spikes.The resulting framework represents compressed measurements and reconstruction updates as spikes, making communication and computation costs depend on event activity.Source: Discussion · p. 12, Neuromorphic sensing based on SNNs · p. 13

Wireless transmission and block-based AER

The transmission pipeline quantizes measurements and sends them as BPSK bits over AWGN or Rayleigh fading channels. Block-based AER transmits addresses for active events, reducing payload when address bits are fewer than full-vector bits.

Wireless transmission and block-based AER

  • Measurements are uniformly quantized to q bits, represented as full binary vectors or AER addresses, and transmitted using BPSK over AWGN or Rayleigh fading.At the receiver, detected bits are converted back into quantized measurements or decoded spike states and AER addresses.Source: Wireless transmission and block-based… · pp. 13–14
  • The channel model assumes independent complex Gaussian noise, with h = 1 for AWGN and h drawn from CN(0, 1) for Rayleigh fading.Under quasi-static fading, h remains constant across one sample’s transmissions; the receiver has perfect channel state information and the transmitter has none.Source: Wireless transmission and block-based… · pp. 13–14
  • For block-based AER, each non-empty block sends its block address once, followed by the local addresses of its active events.The payload counts block-address and local-address bits and excludes framing and synchronization overhead.Source: Wireless transmission and block-based… · p. 14
  • AER reduces payload when its address bits require fewer bits than full-vector transmission; local-address errors displace events within a block, while block-address errors redirect all events in that block.Events decoded to the same coordinate are merged into one spike.Source: Wireless transmission and block-based… · p. 14

S-LISTA architecture

S-LISTA implements unfolded sparse recovery with spiking dynamics: it embeds received measurements, accumulates signed spike updates across layers, then applies a continuous correction and soft threshold before dictionary reconstruction.

S-LISTA architecture

  • S-LISTA follows the measurement-embedding and residual-correction structure of unfolded sparse recovery, accumulating spike updates across L layers.Each layer’s membrane state persists across time, while code accumulation proceeds across layers within each time step.Source: S-LISTA architecture · p. 14
  • The first layer receives current from the learnable measurement-embedding operator, and each layer integrates its input, generates signed spikes, and updates the sparse code.Layer membrane potential is initialized at the start of a sequence.Source: S-LISTA architecture · pp. 14–15
  • After the final layer, residual membrane potential corrects the accumulated code at its nonzero coordinates before an output soft threshold and dictionary reconstruction.Setting the output threshold λout to zero leaves the corrected code unchanged.Source: S-LISTA architecture · p. 15

Training objective and gradient estimation

Joint training optimizes sensing, S-LISTA, the dictionary, and an auxiliary classifier using reconstruction, sparsity, measurement-spike-rate, and task terms. Continuous gradient approximations support training despite hard spike generation.

Training objective and gradient estimation

  • The joint objective combines reconstruction error, sparse-code regularization, measurement spike rate, and task supervision from an auxiliary classifier applied to sparse codes.The reported downstream task performance is evaluated separately using reconstructed signals.Source: Training objective and gradient… · pp. 15–16
  • Because hard spike generation is non-differentiable, the sensing network uses a continuous approximation for gradient estimation during training.The temperature decreases so the approximation approaches the hard threshold; forward passes use hard spikes and backward passes use relaxed-probability gradients under a straight-through estimator.Source: Training objective and gradient… · p. 16
  • For full-vector binary transmission, the backward pass uses the probability that a received bit equals 1, incorporating bit-error probability; block-based AER uses differentiable address mapping based on block and local address error probabilities.Forward inference retains hard address decoding and hard bit decisions.Source: Training objective and gradient… · p. 16

Experimental procedures and analytical energy estimates

Experiments span synthetic sparse signals, ECG, and neuromorphic event streams, with matched measurement dimensions and channel conditions for ANN and vanilla SNN comparisons. Energy estimates count sensing and reconstruction operations, while availability information identifies public code and datasets.

Experimental procedures and analytical energy estimates

  • Experiments cover synthetic sparse signals, ECG, and neuromorphic event streams, with ANN and vanilla SNN comparisons matched on measurement dimensions and channel conditions.Experiments use NVIDIA H100 NVL GPUs; wireless transmission is trained with AWGN and evaluated with AWGN and Rayleigh fading, with five random seeds.Source: Experimental procedures and analytical… · pp. 16–17
  • Energy per sample is estimated by counting MAC and accumulate operations across all sample time steps, with dense matrix computations counted as MACs and spike-triggered weight additions as ACs.The estimates use 4.6 pJ per MAC and 0.9 pJ per AC, and exclude dictionary readout, communication, memory access, downstream evaluation, and hardware control costs.Source: Experimental procedures and analytical… · p. 17

Data availability

  • The MIT-BIH, DVS-Gesture, and Spiking Heidelberg Digits datasets are publicly available, and code for generating synthetic data is available online.The source code is publicly available at the project repository.Source: Data availability · p. 17, Code availability · p. 17

Competing interests

The authors report no competing interests. Supplementary Note 1 describes S-LISTA as a layered, spike-driven procedure that embeds received measurements, updates sparse codes, corrects residuals, and reconstructs the output.

Competing interests

Supplementary Note 1: S-LISTA algorithm

  • S-LISTA retains LISTA’s measurement embedding, residual correction, and sparse-code updating, processing received measurement sequences through unfolded layers with membrane states retained across time steps.Source: Supplementary Note 1: S-LISTA algorithm · p. 22
  • A learnable measurement-embedding operator maps received measurements into the sparse-code dimension, and its result is reused by subsequent layers at each time step.Source: Supplementary Note 1: S-LISTA algorithm · p. 22
  • Signed threshold crossings increase or decrease code coefficients, while spike accumulation replaces LISTA’s continuous soft-threshold update and the post-reset membrane potential retains unexpressed input.Source: Supplementary Note 1: S-LISTA algorithm · p. 22
  • Each layer uses the accumulated code to correct its input; after the final layer, the code selects support for continuous amplitude refinement, thresholding, and dictionary-based reconstruction.Source: Supplementary Note 1: S-LISTA algorithm · pp. 22–23

Datasets and network configurations

The experiments use synthetic sparse vectors, ECG heartbeats, and two event datasets, with dataset-specific processing and model configurations. The supplementary architecture table defines the network components and layer types used in the experiments.

Synthetic signals

  • Synthetic signals have 256 coordinates, 14, 28, or 42 nonzero entries, and 141 measurements; independent sets of 1,536, 6,000, and 10,000 signals support checkpoint selection, hyperparameter selection, and testing.Synthetic data are generated online; ANN depths are 2–5 and S-LISTA depths are 5, 10, 15, and 20 for reconstruction-error versus estimated-energy comparisons.Source: Datasets and network configurations · p. 23

Electrocardiogram (ECG) signals

  • ECG inputs are MIT-BIH heartbeats resampled to 256 points, using modified limb lead II and excluding paced records 102, 104, 107, and 217.DS1 is split by record for training and validation, while DS2 supplies 49,691 test heartbeats; models use 78 measurements and 256-dimensional codes.Source: Datasets and network configurations · pp. 23–24

Event datasets

  • DVS-Gesture events are integrated into 16 approximately equal-event-count segments and transformed with log(1 + x), then normalized within each sample.Source: Datasets and network configurations · p. 24
  • SHD event counts are binned into 25 intervals of 40 ms across 700 channels, retained without clipping or normalization; its provided test split is used for model selection and evaluation in the main results.Supplementary results additionally use held-out validation subsets and official test sets exclusively for evaluation.Source: Datasets and network configurations · p. 24

Network architectures

  • The supplementary architecture table specifies fully connected, convolutional, and transposed-convolutional layers, alongside LIF, ReLU, and LSTM components.LISTA input mappings and update components are listed separately, with connections following Methods.Source: Table 1 · p. 24, Datasets and network configurations · p. 24

Training and transmission settings

Training uses Adam with cosine learning-rate annealing and dataset-specific schedules, losses, and supervision. Transmission evaluations vary quantization or channel conditions, while event streams use binary spikes without an additional polarity bit.

Training settings

  • Training uses Adam with cosine learning-rate annealing, with dataset-specific batch sizes, update or epoch schedules, and minimum learning rates.Synthetic training uses 1,024-signal batches and two stages of 5,000 and 15,000 updates; final S-LISTA training uses 200 ECG epochs, 150 DVS-G epochs, and 100 SHD epochs.Source: Training and transmission settings · pp. 24–25
  • Synthetic models minimize normalized squared error, while ECG, DVS-G, and SHD use mean-squared error with dataset-specific sparse-code regularization; DVS-G and SHD also use task supervision.For ECG, checkpoint selection uses the DS1 validation subset, and DS2 is reserved for final evaluation.Source: Training and transmission settings · p. 25
  • Evaluation classifiers for DVS-G and SHD are trained separately for each method with sensing and reconstruction frozen, using AWGN at 10 dB.Source: Training and transmission settings · p. 25

Transmission settings

  • Transmission settings include ECG uniform 8-bit quantization and separately trained 2-, 4-, 6-, and 8-bit models; wireless evaluation scans AWGN and Rayleigh fading from −5 to 20 dB.Main event results and AER ablations use Rayleigh fading at 20 dB; DVS-G and SHD transmit one binary spike stream without an added polarity bit, while ANN baselines use 8-bit measurements.Source: Training and transmission settings · p. 25

Evaluation metrics

This section defines evaluation conventions and presents theoretical guarantees for S-LISTA, including bounds on outputs, recovery error and noise sensitivity, and a link between signal sparsity and receiver spike activity. It also evaluates firing, reconstruction error, spike activity and estimated synaptic energy in the tested setting, including comparison with recurrent S-LCA.

Evaluation metrics

  • Evaluation uses T = 1 for synthetic signals and ECG, T = 16 for DVS-G, and T = 25 for SHD; downstream accuracy uses complete reconstructed sequences.Results are averaged over seeds 42–46 for synthetic signals, ECG, and event datasets; energy estimates use 4.6 pJ per MAC and 0.9 pJ per AC, with dataset-specific noise conditions.Source: Evaluation metrics · p. 26

Supplementary Note 3: Theoretical analysis of S-LISTA

3.1 Inverse problem formulation and assumptions

  • The recovery analysis models total input noise as transmission noise plus encoding noise, and does not require the noise to be Gaussian or independent of the source.Transmission noise reflects received-versus-transmitted measurements; encoding noise reflects deviation of spike measurements from the linear reference, including transmitter memory.Source: §3.1 · p. 26

3.2 Boundedness of membrane states and reconstruction outputs

  • With finite fixed parameters, depth L ≥2, and bounded input, S-LISTA’s membrane states and reconstruction outputs remain bounded independently of time.The reconstructed signal is bounded because the dictionary is fixed and finite.Source: §3.2 · pp. 27–28

3.3 Recovery error bounds of S-LISTA

  • The recovery-error bound remains on the same scale as observed squared errors across three synthetic-signal sparsity levels, while small enough input noise can preserve spikes and linearly bound output change.The noise condition depends on keeping perturbations below the distance of clean pre-reset potentials to their firing thresholds; the output bound includes a geometric factor across steps.Source: §3.3 · pp. 30–32, Figure 1 · p. 30

3.4 Sparsity analysis

  • The firing-rate bound links activity to true-code sparsity while accounting for spikes outside the support, including intermediate activity that may cancel in the final code.When accumulation stays within the true support, the ideal upper bound is proportional to the fraction of nonzero coefficients; otherwise, the additional term captures activity outside that support.Source: §3.4 · p. 33
  • Across tested sparsities, mean S-LISTA firing rate increased with s but stayed at or below the ideal s/(2N) bound.The analysis used a fixed trained model with L = 10 layers and 5,000 test samples at each sparsity level.Source: Figure 2 · p. 33, §3.4 · p. 33

Supplementary Note 4: Comparison with spiking LCA

Supplementary Note 5: Evaluation with an independent validation set

With independent validation splits, S-LISTA retained comparable DVS-G classification accuracy and achieved the lowest SHD NMSE, while using one-eighth the ANN transmission bits on both datasets.

Supplementary Note 5: Evaluation with an independent validation set

  • Approximately 20% of official training data was held out for validation, grouped by source recording on DVS-G and stratified by class on SHD; official test sets were unchanged.Models were selected using validation NMSE and accuracy under AWGN at 10 dB, then evaluated under Rayleigh fading at 20 dB.Source: Supplementary Note 5: Evaluation with… · p. 34
  • On DVS-G, classification accuracy is comparable; on SHD, S-LISTA has the lowest NMSE but trails ANN accuracy by 1.55–1.99 percentage points; both use one-eighth the ANN bits.Results use full-vector transmission under Rayleigh fading at 20 dB.Source: Supplementary Note 5: Evaluation with… · p. 35, Table 3 · p. 35
  • Supplementary Table 3 reports means ± standard deviations over seeds 42–46 using a fixed split for each dataset.The table covers full-vector transmission under Rayleigh fading at 20 dB.Source: Table 3 · p. 35

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