SNN-Based Filtering

• SNN-based filtering is a neuromorphic technique that employs spiking neuron dynamics, such as LIF models, to implement adaptive temporal and spatial filters for noise reduction and signal enhancement.
• It integrates explicit pre-/post-processing modules and inherent neuron filter properties to achieve denoising, dynamic state estimation, and adversarial robustness in various applications.
• Hybrid schemes, including Spike-Kal approaches and on-sensor filtering, demonstrate significant improvements in estimation accuracy and energy efficiency while maintaining real-time performance.

Spiking Neural Network (SNN)-Based Filtering refers to the use of spiking neural architectures for explicit or implicit signal, noise, or data reduction tasks across analog, event-stream, or frame-based inputs. SNN-based filters can manifest at multiple levels: as explicit pre- or post-processing stages, as elements interleaved within network pipelines, or as intrinsic temporal/spatial filter dynamics realized by neuron and synapse models themselves. SNN filtering leverages the event-driven, temporally precise, and energy-efficient properties of spiking computation and has been demonstrated in contexts ranging from adversarial defense in neuromorphic vision to denoising, signal restoration, dynamic state estimation, and on-detector data reduction.

1. Principles of SNN Filtering: Dynamics and Theoretical Models

Spiking neurons and synapses inherently act as temporal filters. The Leaky Integrate-and-Fire (LIF) neuron, as the canonical computational unit, implements a low-pass filter on its synaptic input. Each synapse may further realize convolutional or Infinite Impulse Response (IIR) filter dynamics, imparting temporal memory and enabling spatial-temporal pattern separation. Formally, in discrete time, the subthreshold membrane voltage and postsynaptic potential updates can be cast as IIR operations:

$$V_i^l[t] = \lambda\,V_i^l[t-1] - V_{\rm th}\,R_i^l[t] + \sum_{j}w_{i,j}^l\,F_j^l[t]$$

$$F_j^l[t] = \sum_{p=1}^P \alpha_{p}^l\,F_j^l[t-p] + \sum_{q=0}^Q \beta_{q}^l\,O_j^{l-1}[t-q]$$

where $\{\alpha_p^l\}, \{\beta_q^l\}$ are trainable synaptic kernel coefficients, and the neuron output is obtained via a threshold function. SNNs thus form networks of adaptive spatial-temporal filters, and gradient-based learning can optimize both the connection weights and the filter parameters—including the full synaptic kernel and decay structure—yielding systems capable of sophisticated nonlinear filtering on dynamic inputs (Fang et al., 2020).

2. Explicit Filtering Modules: Spatio-Temporal and Signal-domain

SNN-based systems often employ explicit filtering modules, either as front-end denoising or as post-decoding enhancement layers. For event-camera (Dynamic Vision Sensor, DVS) data, a prototypical approach applies a spatio-temporal correlation filter before SNN processing. This filter maintains a timestamp-memory matrix and discards events that lack sufficient local spatial or temporal support, effectively removing isolated (noise) events and preserving only meaningful high-correlation structures:

• For an event $e_i=(x_i,y_i,t_i,p_i)$, neighboring memory cells are updated, and only events with local timestamp differences within a window $T$ are retained.
• Continuous formulations utilize spatial kernels $w(i',j')$ over a radius and temporal windows.
• Such filtering can be parameterized by spatial radius $s$ and temporal window $T$, with empirical search for optimal trade-off between noise rejection and information loss (Marchisio et al., 2021).

In low-level vision, SNN units themselves can function as high-pass filters. For image deraining, standard LIF neurons naturally fire preferentially on high-frequency (rain streak) features but exhibit frequency-domain saturation and lack spatial awareness. Visual LIF (VLIF) neurons extend the LIF by aggregating neighboring pixels via local convolutional patches, thus providing both frequency decomposition and spatial contextual filtering. Additional modules, such as the Spiking Decomposition and Enhancement Module (SDEM) and Spiking Multi-scale Unit (SMU), decompose inputs into high- and low-frequency streams and perform hierarchical multi-scale refinement (Chen et al., 1 Dec 2025).

3. Hybrid SNN-Filtering Schemes in State Estimation and Decoding

SNNs have been integrated as adaptive, learning-driven filters within classical signal processing frameworks. In the Spike-Kal algorithm for Kalman filtering, a two-layer LIF SNN replaces the analytic matrix inversion step by learning to approximate the optimal Kalman gain online. The SNN receives instantaneous, real-valued features (e.g., state estimation errors) as input and outputs a gain matrix, adapting in real time to varying noise statistics and obviating the need for explicit, model-derived noise covariances:

• The SNN is trained using reward-modulated spike-timing-dependent plasticity (R-STDP), with a “teacher” (standard Kalman filter) providing initialization targets.
• The architecture reduces parameter count and computational burden, with performance improvements of 18%–65% over previous SNN-based Kalman filter approaches while achieving real-time throughput on neuromorphic substrates (Xiao et al., 17 Apr 2025).

Similarly, in implantable brain-machine interfaces, SNNs are paired with linear Bessel filters in post-processing, significantly boosting decoding accuracy and closing the performance gap with state-of-the-art recurrent networks. Block bidirectional Bessel filters offer a compromise between latency and accuracy, with over 5% absolute improvement in $R^2$ for SNN-based decoders at modest added compute cost (Zhou et al., 2023).

4. On-Sensor and Neuromorphic Filtering for Data Reduction

SNNs serve efficiently as real-time, compact “smart pixel” data reduction or filtering engines in high-throughput environments such as high-energy physics (HEP) detectors. In one implementation, analog charge waveforms from pixel sensors are transformed into asynchronous spike trains encoding rising and falling edges, which are then processed by a recurrent LIF SNN trained via evolutionary algorithms:

• Parameter-efficient (≤1k) SNNs achieve 91.9% signal efficiency and 26.5% data reduction, matching or exceeding much larger DNNs on the same hardware.
• Integer-weighted, low-precision architectures are robust to hardware-induced noise and enable sub-nanosecond, sub-microjoule operation (Kulkarni et al., 2023).

A crucial design insight is that SNN filtering can be tightly co-designed with data encoding, network structure, and hyperparameter selection, exploiting population-based evolutionary search to discover efficient, high-accuracy filter configurations under resource constraints.

5. Adversarial Robustness via SNN-Based Preprocessing

Adversarial perturbations can drastically reduce SNN classification accuracy on event-based vision tasks. Explicit spatio-temporal filtering before the SNN input robustifies the pipeline by removing low-correlation, attack-inserted events. The non-differentiable filtering operation (event keep-or-remove) impedes gradient-based adversarial attacks, even when attackers adapt their strategy to account for preprocessing modules. Empirically, applying tuned spatio-temporal filters restored DVS-Gesture and NMNIST classification accuracy from as low as 15.2%/4.0% under attack to ≥90.8%/94.0%, respectively (Marchisio et al., 2021).

Systematic filter design methodology involves:

1. Training a base SNN on clean data.
2. Searching for optimal filter parameters (spatial radius and temporal window) with respect to both attack robustness and unperturbed accuracy.
3. Validating across adversary models (with and without filter awareness).
4. Deploying the full DVS+filter+SNN pipeline in hardware or simulation.

6. Empirical Performance and Trade-Offs

Performance advances in SNN-based filtering have been observed across modalities:

• Spatio-temporal filters for DVS SNNs regain nearly all accuracy lost to adversarial event attacks, with minor impact on baseline accuracy at optimal parameter settings (Marchisio et al., 2021).
• SNN-assisted Kalman filtering achieves up to 65% reduction in estimation mean-squared error and 50% neuron reduction compared to prior SNN Kalman hybrid methods (Xiao et al., 17 Apr 2025).
• Neuromorphic HEP sensors filter at 4 ns latency and ~1k parameter footprint, under tight chip power/area constraints, with signal efficiency comparable to DNN classifiers (Kulkarni et al., 2023).
• SNN-based derainers achieve state-of-the-art PSNR and SSIM on multiple benchmarks with only 13% of the energy consumption of previous best SNNs and 1–2% of that of CNNs/Transformers (Chen et al., 1 Dec 2025).
• In neural decoding, the addition of a low-order Bessel filter boosts SNN regression $R^2$ by up to 8%, with negligible additional compute and real-time operation (Zhou et al., 2023).

Trade-offs include filtering aggressiveness (higher spatial/temporal windows or stricter thresholds may enhance noise rejection but reduce signal fidelity), and latency–accuracy trade-offs in post-processing filters (e.g., block bidirectional filtering for BMIs adds 32 ms latency but recovers full offline gains).

7. Limitations, Challenges, and Future Directions

While SNN-based filtering shows strong energy efficiency, low latency, and robustness advantages, current limitations include:

• Frequency-domain saturation and spatial locality in standard LIF neurons, addressed by context-aware or patch-wise generalized neurons (e.g., VLIF) (Chen et al., 1 Dec 2025).
• Partial SNN integration in classical filters (e.g., only Kalman gain estimation) with open prospects for end-to-end SNN-based filtering of prediction and covariance steps (Xiao et al., 17 Apr 2025).
• Latency incurred by post-processing filters, which may be prohibitive for ultra-low-latency applications (Zhou et al., 2023).
• Potential loss of clean accuracy with over-aggressive noise filtering, requiring parameterized tuning and validation (Marchisio et al., 2021).

Future work targets include analog hybrid filter/SNN implementations with sub-nW power, online adaptation to non-Gaussian or dynamically structured noise, scalable sparsity-preserving spiking architectures for high-dimensional filtering, and aggressive quantization/parameter reduction for embedded and neuromorphic deployment (Zhou et al., 2023, Chen et al., 1 Dec 2025). These advances suggest a broadening applicability of SNN-based filtering to any context where spatial-temporal filtering, energy efficiency, and event-driven computation are required.