PHAST-Net: Attention-Guided, Physics-Informed Network for Unified Estimation of Ideal Time-Frequency Representations

We introduce PHAST-Net, an attention-guided, physics-informed network for unified estimation of Ideal Time-Frequency Representations (ITFRs), spanning spectral, tempo-based, metrical, and harmonic representations such as Spectrograms, Tempograms, and Metrograms. PHAST-Net learns an application-general mapping from a constellation of wavelet transforms, the proposed Continuous Log-frequency Adaptive Wavelet Transform (CLAWT), to high-resolution, cross-term-suppressed time-frequency (T-F) representations. The proposed constellation of CLAWTs is selected through Cohen's class kernel analysis to maximise curvature coverage in a logarithmic-frequency T-F plane tailored to harmonic signal structure. PHAST-Net further incorporates a proposed physics-informed auxiliary reprojection loss designed to reconstruct the idealised observed CLAWT constellation from the predicted ITFR and the corresponding Cohen's class kernels during training. This auxiliary objective promotes transform consistency and energy conservation, mitigates pathological target sparsity, and enhances optimisation stability. Attention layers further promote effective cross-term suppression across the input constellation. The log-frequency formulation also enables Harmonic PHAST-Net, which estimates a Harmonic ITFR that isolates fundamental structure, supporting robust fundamental-only representations for speech and music, such as derived fundamental Tempograms and Metrograms. We further introduce Spline-PHAST-Net, which parameterises detected and associated T-F ridges as continuous spline trajectories, enabling arbitrary-grid re-rendering and signal reconstruction. Trained on an effectively unbounded procedurally generated dataset, PHAST-Net demonstrates improved accuracy over established approaches, providing a unified framework for high-resolution, cross-term-robust analysis of speech, music, and broader nonstationary signals.

Distributed Expectation Propagation for Multi-Object Tracking over Sensor Networks

In this paper, we present a novel distributed expectation propagation algorithm for multiple sensors, multiple objects tracking in cluttered environments. The proposed framework enables each sensor to operate locally while collaboratively exchanging moment estimates with other sensors, thus eliminating the need to transmit all data to a central processing node. Specifically, we introduce a fast and parallelisable Rao-Blackwellised Gibbs sampling scheme to approximate the tilted distributions, which enhances the accuracy and efficiency of expectation propagation updates. Results demonstrate that the proposed algorithm improves both communication and inference efficiency for multi-object tracking tasks with dynamic sensor connectivity and varying clutter levels.

Introducing RIFT: A Hierarchical Entropic Filtering Scheme for Ideal Time-Frequency Reconstruction

In this paper, we introduce the Reconstructive Ideal Fractional Transform (RIFT), an entropy-based probabilistic filtering algorithm formulated to reconstruct the Ideal Time-Frequency Representation (ITFR). RIFT surpasses the limitations imposed by the Gabor uncertainty principle for linear transforms, achieving the bilinear transform accuracy present in the Wigner-Ville Distribution (WVD) while effectively suppressing cross-terms. The algorithm utilises a hierarchical fractional wavelet-based scheme to account for localised time-frequency trajectory curvature. This scheme is optimised through an entropic-based filtering method that probabilistically extracts auto-terms while retaining the resolution of the WVD. This is achieved by employing a spatially varying, positively constrained deconvolution algorithm (Lucy-Richardson) with regularisation for adequate noise suppression. Additionally, the optimisation yields an Instantaneous Phase Direction field, which allows the localised curvature in speech or music extracts to be visualised and utilised within a Kalman tracking scheme, enabling the extraction of signal component trajectories. Evaluation demonstrates the algorithm's ability to eradicate cross-terms effectively and achieve superior time-frequency precision. This advance holds significant potential for a wide range of applications requiring high-resolution cross-term-free time-frequency analysis.