Meta-AF: Meta-Learning for Adaptive Filters

Abstract

Adaptive filtering algorithms are pervasive throughout signal processing and have had a material impact on a wide variety of domains including audio processing, telecommunications, biomedical sensing, astrophysics and cosmology, seismology, and many more. Adaptive filters typically operate via specialized online, iterative optimization methods such as least-mean squares or recursive least squares and aim to process signals in unknown or nonstationary environments. Such algorithms, however, can be slow and laborious to develop, require domain expertise to create, and necessitate mathematical insight for improvement. In this work, we seek to improve upon hand-derived adaptive filter algorithms and present a comprehensive framework for learning online, adaptive signal processing algorithms or update rules directly from data. To do so, we frame the development of adaptive filters as a metalearning problem in the context of deep learning and use a form of self-supervision to learn online iterative update rules for adaptive filters. To demonstrate our approach, we focus on audio applications and systematically develop meta-learned adaptive filters for five canonical audio problems including system identification, acoustic echo cancellation, blind equalization, multi-channel dereverberation, and beamforming. We compare our approach against common baselines and/or recent state-ofthe-art methods. We show we can learn high-performing adaptive filters that operate in real-time and, in most cases, significantly outperform each method we compare against -all using a single general-purpose configuration of our approach.

End-To-End Deep Learning-Based Adaptation Control for Frequency-Domain Adaptive System Identification

“…III-A) the narrowband step-size µ f,τ is computed only from statistics of the respective frequency band, i.e., without exploiting any inter-frequency dependencies. This motivates a decomposition of the general mapping g BB-DNN (•) in ( 14) into F narrowband mappings [26], [28], [29]…”

“…with d κ and dκ denoting the time-domain echo and estimated echo signals at sample index κ, respectively, and K, T denoting the number of time-domain samples and frames, respectively. It should be noted that while the frequencydomain loss (25) suggests an independent residual echo power minimization per frequency band, its time-domain counterpart (26) couples the frequency-wise echo estimates by the inverse STFT. In addition, we examine the negated logarithmic Echo Return Loss Enhancement (ERLE)-type losses…”

“…The various approaches differ in the echo estimation model, feature design, DNN integration and loss function design. While [23], [25]- [27] employ a time-domain Finite Impulse Response (FIR) echo estimation model which is optimized in the frequency domain, [24], [26], [28], [29] consider a Convolutive Transfer Function (CTF) model (cf. e.g.…”

“…Another key difference is given by the integration of the DNN into the filter update. In [26]- [28], it is proposed to directly estimate the gradient, or parts of it, by complex-valued DNNs. In contrast, [23]- [25], [29] propose to infer only parameters of traditional step-size estimators while keeping the gradient direction of the respective filter update unchanged.…”

“…In contrast, [23]- [25], [29] propose to infer only parameters of traditional step-size estimators while keeping the gradient direction of the respective filter update unchanged. Furthermore, various step-size inference architectures have been considered ranging from broadband approaches, which jointly estimate a frequency-selective step-size vector with a single DNN, [23]- [25], to narrowband approaches, which use individual DNNs per frequency band [26], [28], [29]. In addition, joint control of frequency groups has been investigated [27].…”