arXiv subjects

Peter Gerstoft

Publications and source records attributed to Peter Gerstoft.

At least 19 recordsLinked to original sources

arXiv2026

Mitigating Spectral Bias in Neural Operators for Underwater Transmission Loss Prediction

Predicting underwater acoustic transmission loss rapidly and accurately is crucial for real-time ocean acoustic applications. While Fourier Neural Operators (FNO) have emerged as powerful surrogate models due to their global receptive fields, they suffer from spectral bias. The frequency truncation mechanism in FNO filters out high-frequency components, resulting in over-smoothed predictions that fail to capture fine-grained interference patterns. To overcome this limitation, this paper proposes a Spectral-Spatial Residual Learning (S2RL) framework. S2RL decomposes the prediction task into a coarse-to-fine process: a spectral Global Propagator first generates a globally consistent prediction, and a spatial Local Refiner subsequently recovers the high-frequency residuals. Experimental results on a South China Sea dataset show that the proposed method significantly outperforms FNO baselines while maintaining millisecond-level inference speeds.

cs.SD↗

arXiv2026

Encoding and Decoding Temporal Signals with Spiking Bandpass Wavelets

Spike-based encodings are sparse and energy-efficient, but have largely been formulated probabilistically, disconnected from most signal processing literature. We recast spike encoders as time-causal wavelet frames with quantitative bandwidths and reconstruction error bounds. The proposed wavelets preserve the sparsity and locality of spiking representations, with reconstruction up to spike quantization and time discretization. We demonstrate reconstruction on ECG and audio datasets, achieving a normalized RMSE comparable to continuous wavelet transforms. The spiking wavelets map directly to neuromorphic hardware.

cs.NE↗

arXiv2026

Scale-covariant spiking wavelets

We establish a theoretical connection between wavelet transforms and spiking neural networks through scale-space theory. We rely on the scale-covariant guarantees in the leaky integrate-and-fire neurons to implement discrete mother wavelets that approximate continuous wavelets. A reconstruction experiment demonstrates the feasibility of the approach and warrants further analysis to mitigate current approximation errors. Our work suggests a novel spiking signal representation that could enable more energy-efficient signal processing algorithms.

cs.NE↗

arXiv2025

When Bayesian Tensor Completion Meets Multioutput Gaussian Processes: Functional Universality and Rank Learning

Functional tensor decomposition can analyze multi-dimensional data with real-valued indices, paving the path for applications in machine learning and signal processing. A limitation of existing approaches is the assumption that the tensor rank-a critical parameter governing model complexity-is known. However, determining the optimal rank is a non-deterministic polynomial-time hard (NP-hard) task and there is a limited understanding regarding the expressive power of functional low-rank tensor models for continuous signals. We propose a rank-revealing functional Bayesian tensor completion (RR-FBTC) method. Modeling the latent functions through carefully designed multioutput Gaussian processes, RR-FBTC handles tensors with real-valued indices while enabling automatic tensor rank determination during the inference process. We establish the universal approximation property of the model for continuous multi-dimensional signals, demonstrating its expressive power in a concise format. To learn this model, we employ the variational inference framework and derive an efficient algorithm with closed-form updates. Experiments on both synthetic and real-world datasets demonstrate the effectiveness and superiority of the RR-FBTC over state-of-the-art approaches. The code is available at https://github.com/OceanSTARLab/RR-FBTC.

cs.LG↗

arXiv2025

Hankel-FNO: Fast Underwater Acoustic Charting Via Physics-Encoded Fourier Neural Operator

Fast and accurate underwater acoustic charting is crucial for downstream tasks such as environment-aware sensor placement optimization and autonomous vehicle path planning. Conventional methods rely on computationally expensive while accurate numerical solvers, which are not scalable for large-scale or real-time applications. Although deep learning-based surrogate models can accelerate these computations, they often suffer from limitations such as fixed-resolution constraints or dependence on explicit partial differential equation formulations. These issues hinder their applicability and generalization across diverse environments. We propose Hankel-FNO, a Fourier Neural Operator (FNO)-based model for efficient and accurate acoustic charting. By incorporating sound propagation knowledge and bathymetry, our method has high accuracy while maintaining high computational speed. Results demonstrate that Hankel-FNO outperforms traditional solvers in speed and surpasses data-driven alternatives in accuracy, especially in long-range predictions. Experiments show the model's adaptability to diverse environments and sound source settings with minimal fine-tuning.

cs.LG↗

arXiv2025

Differentiable physics for sound field reconstruction

Sound field reconstruction involves estimating sound fields from a limited number of spatially distributed observations. This work introduces a differentiable physics approach for sound field reconstruction, where the initial conditions of the wave equation are approximated with a neural network, and the differential operator is computed with a differentiable numerical solver. The use of a numerical solver enables a stable network training while enforcing the physics as a strong constraint, in contrast to conventional physics-informed neural networks, which include the physics as a constraint in the loss function. We introduce an additional sparsity-promoting constraint to achieve meaningful solutions even under severe undersampling conditions. Experiments demonstrate that the proposed approach can reconstruct sound fields under extreme data scarcity, achieving higher accuracy and better convergence compared to physics-informed neural networks.

eess.AS↗

arXiv2025

Real, Fake, or Manipulated? Detecting Machine-Influenced Text

Large Language Model (LLMs) can be used to write or modify documents, presenting a challenge for understanding the intent behind their use. For example, benign uses may involve using LLM on a human-written document to improve its grammar or to translate it into another language. However, a document entirely produced by a LLM may be more likely to be used to spread misinformation than simple translation (\eg, from use by malicious actors or simply by hallucinating). Prior works in Machine Generated Text (MGT) detection mostly focus on simply identifying whether a document was human or machine written, ignoring these fine-grained uses. In this paper, we introduce a HiErarchical, length-RObust machine-influenced text detector (HERO), which learns to separate text samples of varying lengths from four primary types: human-written, machine-generated, machine-polished, and machine-translated. HERO accomplishes this by combining predictions from length-specialist models that have been trained with Subcategory Guidance. Specifically, for categories that are easily confused (\eg, different source languages), our Subcategory Guidance module encourages separation of the fine-grained categories, boosting performance. Extensive experiments across five LLMs and six domains demonstrate the benefits of our HERO, outperforming the state-of-the-art by 2.5-3 mAP on average.

cs.CL↗

arXiv2025

Machine Learning in Acoustics: A Review and Open-Source Repository

Acoustic data provide scientific and engineering insights in fields ranging from bioacoustics and communications to ocean and earth sciences. In this review, we survey recent advances and the transformative potential of machine learning (ML) in acoustics, including deep learning (DL). Using the Python high-level programming language, we demonstrate a broad collection of ML techniques to detect and find patterns for classification, regression, and generation in acoustics data automatically. We have ML examples including acoustic data classification, generative modeling for spatial audio, and physics-informed neural networks. This work includes AcousticsML, a set of practical Jupyter notebook examples on GitHub demonstrating ML benefits and encouraging researchers and practitioners to apply reproducible data-driven approaches to acoustic challenges.

cs.SD↗

arXiv2025

Distributed acoustic sensing for ocean applications

Extensive monitoring of acoustic activities is important for many fields, including biology, security, oceanography, and Earth science. Distributed acoustic sensing (DAS) is an evolving technique for continuous, wide-coverage measurements of mechanical vibrations, which is suited to ocean applications. DAS illuminates an optical fiber with laser pulses and measures the backscattered wave due to small random variations in the refractive index of the material. External stimuli, such as mechanical strain due to acoustic wavefields impinging on the fiber-optic cable, modulate the backscattered wave. Continuous measurement of the backscattered signal provides a distributed sensing modality of the impinging wavefield. Considering the potential use of existing telecommunication fiber-optic cables deployed across the oceans, DAS has emerged as a promising technology for monitoring the underwater soundscape. This review presents advances in DAS in the last decade and details the underlying physics from electromagnetic to mechanical and eventually acoustic quantities. To guide the use of DAS for ocean applications, the effect of DAS acquisition parameters in signal processing is explained. Finally, DAS is demonstrated on data from the Ocean Observatories Initiative Regional Cabled Array for the detection of sound sources, such as whales, ships, and earthquakes.

physics.geo-ph↗

arXiv2024

Scaling Continuous Kernels with Sparse Fourier Domain Learning

We address three key challenges in learning continuous kernel representations: computational efficiency, parameter efficiency, and spectral bias. Continuous kernels have shown significant potential, but their practical adoption is often limited by high computational and memory demands. Additionally, these methods are prone to spectral bias, which impedes their ability to capture high-frequency details. To overcome these limitations, we propose a novel approach that leverages sparse learning in the Fourier domain. Our method enables the efficient scaling of continuous kernels, drastically reduces computational and memory requirements, and mitigates spectral bias by exploiting the Gibbs phenomenon.

cs.LG↗

arXiv2024

Efficient Sound Field Reconstruction with Conditional Invertible Neural Networks

In this study, we introduce a method for estimating sound fields in reverberant environments using a conditional invertible neural network (CINN). Sound field reconstruction can be hindered by experimental errors, limited spatial data, model mismatches, and long inference times, leading to potentially flawed and prolonged characterizations. Further, the complexity of managing inherent uncertainties often escalates computational demands or is neglected in models. Our approach seeks to balance accuracy and computational efficiency, while incorporating uncertainty estimates to tailor reconstructions to specific needs. By training a CINN with Monte Carlo simulations of random wave fields, our method reduces the dependency on extensive datasets and enables inference from sparse experimental data. The CINN proves versatile at reconstructing Room Impulse Responses (RIRs), by acting either as a likelihood model for maximum a posteriori estimation or as an approximate posterior distribution through amortized Bayesian inference. Compared to traditional Bayesian methods, the CINN achieves similar accuracy with greater efficiency and without requiring its adaptation to distinct sound field conditions.

eess.AS↗

arXiv2024

Deep Learning-based Modulation Classification of Practical OFDM Signals for Spectrum Sensing

In this study, the modulation of symbols on OFDM subcarriers is classified for transmissions following Wi-Fi~6 and 5G downlink specifications. First, our approach estimates the OFDM symbol duration and cyclic prefix length based on the cyclic autocorrelation function. We propose a feature extraction algorithm characterizing the modulation of OFDM signals, which includes removing the effects of a synchronization error. The obtained feature is converted into a 2D histogram of phase and amplitude and this histogram is taken as input to a convolutional neural network (CNN)-based classifier. The classifier does not require prior knowledge of protocol-specific information such as Wi-Fi preamble or resource allocation of 5G physical channels. The classifier's performance, evaluated using synthetic and real-world measured over-the-air (OTA) datasets, achieves a minimum accuracy of 97\% accuracy with OTA data when SNR is above the value required for data transmission.

cs.NI↗

arXiv2024

Non-uniform Array and Frequency Spacing for Regularization-free Gridless DOA

Gridless direction-of-arrival (DOA) estimation with multiple frequencies can be applied in acoustics source localization problems. We formulate this as an atomic norm minimization (ANM) problem and derive an equivalent regularization-free semi-definite program (SDP) thereby avoiding regularization bias. The DOA is retrieved using a Vandermonde decomposition on the Toeplitz matrix obtained from the solution of the SDP. We also propose a fast SDP program to deal with non-uniform array and frequency spacing. For non-uniform spacings, the Toeplitz structure will not exist, but the DOA is retrieved via irregular Vandermonde decomposition (IVD), and we theoretically guarantee the existence of the IVD. We extend ANM to the multiple measurement vector (MMV) cases and derive its equivalent regularization-free SDP. Using multiple frequencies and the MMV model, we can resolve more sources than the number of physical sensors for a uniform linear array. Numerical results demonstrate that the regularization-free framework is robust to noise and aliasing, and it overcomes the regularization bias.

eess.SP↗

arXiv2023

Deep Learning based Spatially Dependent Acoustical Properties Recovery

The physics-informed neural network (PINN) is capable of recovering partial differential equation (PDE) coefficients that remain constant throughout the spatial domain directly from physical measurements. In this work, we propose a spatially dependent physics-informed neural network (SD-PINN), which enables the recovery of coefficients in spatially-dependent PDEs using a single neural network, eliminating the requirement for domain-specific physical expertise. We apply the SD-PINN to spatially-dependent wave equation coefficients recovery to reveal the spatial distribution of acoustical properties in the inhomogeneous medium. The proposed method exhibits robustness to noise owing to the incorporation of a loss function for the physical constraint that the assumed PDE must be satisfied. For the coefficients recovery of spatially two-dimensional PDEs, we store the PDE coefficients at all locations in the 2D region of interest into a matrix and incorporate the low-rank assumption for such a matrix to recover the coefficients at locations without available measurements.

cs.LG↗

arXiv2023

Spoofing Attack Detection in the Physical Layer with Robustness to User Movement

In a spoofing attack, an attacker impersonates a legitimate user to access or modify data belonging to the latter. Typical approaches for spoofing detection in the physical layer declare an attack when a change is observed in certain channel features, such as the received signal strength (RSS) measured by spatially distributed receivers. However, since channels change over time, for example due to user movement, such approaches are impractical. To sidestep this limitation, this paper proposes a scheme that combines the decisions of a position-change detector based on a deep neural network to distinguish spoofing from movement. Building upon community detection on graphs, the sequence of received frames is partitioned into subsequences to detect concurrent transmissions from distinct locations. The scheme can be easily deployed in practice since it just involves collecting a small dataset of measurements at a few tens of locations that need not even be computed or recorded. The scheme is evaluated on real data collected for this purpose.

eess.SP↗

arXiv2023

Robust and Sparse M-Estimation of DOA

A robust and sparse Direction of Arrival (DOA) estimator is derived for array data that follows a Complex Elliptically Symmetric (CES) distribution with zero-mean and finite second-order moments. The derivation allows to choose the loss function and four loss functions are discussed in detail: the Gauss loss which is the Maximum-Likelihood (ML) loss for the circularly symmetric complex Gaussian distribution, the ML-loss for the complex multivariate $t$-distribution (MVT) with $\nu$ degrees of freedom, as well as Huber and Tyler loss functions. For Gauss loss, the method reduces to Sparse Bayesian Learning (SBL). The root mean square DOA error of the derived estimators is discussed for Gaussian, MVT, and $\epsilon$-contaminated data. The robust SBL estimators perform well for all cases and nearly identical with classical SBL for Gaussian noise.

math.ST↗

arXiv2022

Spoofing Attack Detection in the Physical Layer with Commutative Neural Networks

In a spoofing attack, an attacker impersonates a legitimate user to access or tamper with data intended for or produced by the legitimate user. In wireless communication systems, these attacks may be detected by relying on features of the channel and transmitter radios. In this context, a popular approach is to exploit the dependence of the received signal strength (RSS) at multiple receivers or access points with respect to the spatial location of the transmitter. Existing schemes rely on long-term estimates, which makes it difficult to distinguish spoofing from movement of a legitimate user. This limitation is here addressed by means of a deep neural network that implicitly learns the distribution of pairs of short-term RSS vector estimates. The adopted network architecture imposes the invariance to permutations of the input (commutativity) that the decision problem exhibits. The merits of the proposed algorithm are corroborated on a data set that we collected.

cs.LG↗

arXiv2022

Deep Learning Object Detection Approaches to Signal Identification

Traditionally source identification is solved using threshold based energy detection algorithms. These algorithms frequently sum up the activity in regions, and consider regions above a specific activity threshold to be sources. While these algorithms work for the majority of cases, they often fail to detect signals that occupy small frequency bands, fail to distinguish sources with overlapping frequency bands, and cannot detect any signals under a specified signal to noise ratio. Through the conversion of raw signal data to spectrogram, source identification can be framed as an object detection problem. By leveraging modern advancements in deep learning based object detection, we propose a system that manages to alleviate the failure cases encountered when using traditional source identification algorithms. Our contributions include framing source identification as an object detection problem, the publication of a spectrogram object detection dataset, and evaluation of the RetinaNet and YOLOv5 object detection models trained on the dataset. Our final models achieve Mean Average Precisions of up to 0.906. With such a high Mean Average Precision, these models are sufficiently robust for use in real world applications.

cs.SD↗