arXiv subjects

Xianrui Wang

Publications and source records attributed to Xianrui Wang.

5 recordsLinked to original sources

arXiv2026

Variable-Coefficient Parabolic Equations and Finite-Horizon Hamilton--Jacobi--Bellman Equations in Augmented Spectral Barron Spaces

We establish a whole-space solution framework in augmented spectral Barron spaces for uniformly elliptic parabolic equations with state-dependent principal coefficients. A frozen-symbol parametrix yields bounded Green and terminal operators and a one-derivative smoothing estimate on arbitrary finite horizons, without requiring the spatial variation of the principal coefficient to be perturbatively small. We then apply this linear framework to a finite-horizon Hamilton--Jacobi--Bellman equation. A semi-explicit gradient iteration converges on sufficiently short horizons at a Gamma-factorial rate in a whole-space augmented Barron norm, and its limit is identified with the stochastic-control value function. Finally, temporal Jackson approximation and spatial spectral Barron approximation give joint shallow cosine-network approximations in space and time for the value function and the optimal feedback, with quantitative error and neuron-count bounds. Taken together, these results connect variable-coefficient parabolic well-posedness and smoothing in augmented spectral Barron spaces with nonlinear HJB solvability and quantitative neural-network approximation.

math.OC↗

arXiv2026

Robust Online Overdetermined Independent Vector Analysis Based on Bilinear Decomposition

Online blind source separation is essential for both speech communication and human-machine interaction. Among existing approaches, overdetermined independent vector analysis (OverIVA) delivers strong performance by exploiting the statistical independence of source signals and the orthogonality between source and noise subspaces. However, when applied to large microphone arrays, the number of parameters grows rapidly, which can degrade online estimation accuracy. To overcome this challenge, we propose decomposing each long separation filter into a bilinear form of two shorter filters, thereby reducing the number of parameters. Because the two filters are closely coupled, we design an alternating iterative projection algorithm to update them in turn. Simulation results show that, with far fewer parameters, the proposed method achieves improved performance and robustness.

eess.AS↗

arXiv2025

Accelerated Convolutive Transfer Function-Based Multichannel NMF Using Iterative Source Steering

Among numerous blind source separation (BSS) methods, convolutive transfer function-based multichannel non-negative matrix factorization (CTF-MNMF) has demonstrated strong performance in highly reverberant environments by modeling multi-frame correlations of delayed source signals. However, its practical deployment is hindered by the high computational cost associated with the iterative projection (IP) update rule, which requires matrix inversion for each source. To address this issue, we propose an efficient variant of CTF-MNMF that integrates iterative source steering (ISS), a matrix inversion-free update rule for separation filters. Experimental results show that the proposed method achieves comparable or superior separation performance to the original CTF-MNMF, while significantly reducing the computational complexity.

cs.SD↗

arXiv2024

Low algorithmic delay implementation of convolutional beamformer for online joint source separation and dereverberation

Blind-audio-source-separation (BASS) techniques, particularly those with low latency, play an important role in a wide range of real-time systems, e.g., hearing aids, in-car hand-free voice communication, real-time human-machine interaction, etc. Most existing BASS algorithms are deduced to run on batch mode, and therefore large latency is unavoidable. Recently, some online algorithms were developed, which achieve separation on a frame-by-frame basis in the short-time-Fourier-transform (STFT) domain and the latency is significantly reduced as compared to those batch methods. However, the latency with these algorithms may still be too long for many real-time systems to bear. To further reduce latency while achieving good separation performance, we propose in this work to integrate a weighted prediction error (WPE) module into a non-causal sample-truncating-based independent vector analysis (NST-IVA). The resulting algorithm can maintain the algorithmic delay as NST-IVA if the delay with WPE is appropriately controlled while achieving significantly better performance, which is validated by simulations.

eess.AS↗

arXiv2023

A computationally efficient semi-blind source separation based approach for nonlinear echo cancellation based on an element-wise iterative source steering

While the semi-blind source separation-based acoustic echo cancellation (SBSS-AEC) has received much research attention due to its promising performance during double-talk compared to the traditional adaptive algorithms, it suffers from system latency and nonlinear distortions. To circumvent these drawbacks, the recently developed ideas on convolutive transfer function (CTF) approximation and nonlinear expansion have been used in the iterative projection (IP)-based semi-blind source separation (SBSS) algorithm. However, because of the introduction of CTF approximation and nonlinear expansion, this algorithm becomes computationally very expensive, which makes it difficult to implement in embedded systems. Thus, we attempt in this paper to improve this IP-based algorithm, thereby developing an element-wise iterative source steering (EISS) algorithm. In comparison with the IP-based SBSS algorithm, the proposed algorithm is computationally much more efficient, especially when the nonlinear expansion order is high and the length of the CTF filter is long. Meanwhile, its AEC performance is as good as that of IP-based SBSS.

eess.AS↗