Recovery of spatially varying acoustical properties via automated partial differential equation identification.

Observable dynamics, such as waves propagating on a surface, are generally governed by partial differential equations (PDEs), which are determined by the physical properties of the propagation media. The spatial variations of these properties lead to spatially dependent PDEs. It is useful in many fields to recover the variations from the observations of dynamical behaviors on the material. A method is proposed to form a map of the physical properties' spatial variations for a material via data-driven spatially dependent PDE identification and applied to recover acoustical properties (viscosity, attenuation, and phase speeds) for propagating waves. The proposed data-driven PDE identification scheme is based on ℓ1-norm minimization. It does not require any PDE term that is assumed active from the prior knowledge and is the first approach that is capable of identifying spatially dependent PDEs from measurements of phenomena. In addition, the method is efficient as a result of its non-iterative nature and can be robust against noise if used with an integration transformation technique. It is demonstrated in multiple experimental settings, including real laser measurements of a vibrating aluminum plate. Codes and data are available online at https://tinyurl.com/4wza8vxs.

A Sparse Conjugate Gradient Adaptive Filter.

In this letter, we propose a novel conjugate gradient (CG) adaptive filtering algorithm for online estimation of system responses that admit sparsity. Specifically, the Sparsity-promoting Conjugate Gradient (SCG) algorithm is developed based on iterative reweighting methods popular in the sparse signal recovery area. We propose an affine scaling transformation strategy within the reweighting framework, leading to an algorithm that allows the usage of a zero sparsity regularization coefficient. This enables SCG to leverage the sparsity of the system response if it already exists, while not compromising the optimization process. Simulation results show that SCG demonstrates improved convergence and steady-state properties over existing methods.

Nuisance effects and the limitations of nuisance regression in dynamic functional connectivity fMRI.

In resting-state fMRI, dynamic functional connectivity (DFC) measures are used to characterize temporal changes in the brain's intrinsic functional connectivity. A widely used approach for DFC estimation is the computation of the sliding window correlation between blood oxygenation level dependent (BOLD) signals from different brain regions. Although the source of temporal fluctuations in DFC estimates remains largely unknown, there is growing evidence that they may reflect dynamic shifts between functional brain networks. At the same time, recent findings suggest that DFC estimates might be prone to the influence of nuisance factors such as the physiological modulation of the BOLD signal. Therefore, nuisance regression is used in many DFC studies to regress out the effects of nuisance terms prior to the computation of DFC estimates. In this work we examined the relationship between seed-specific sliding window correlation-based DFC estimates and nuisance factors. We found that DFC estimates were significantly correlated with temporal fluctuations in the magnitude (norm) of various nuisance regressors. Strong correlations between the DFC estimates and nuisance regressor norms were found even when the underlying correlations between the nuisance and fMRI time courses were relatively small. We then show that nuisance regression does not necessarily eliminate the relationship between DFC estimates and nuisance norms, with significant correlations observed between the DFC estimates and nuisance norms even after nuisance regression. We present theoretical bounds on the difference between DFC estimates obtained before and after nuisance regression and relate these bounds to limitations in the efficacy of nuisance regression with regards to DFC estimates.

Empirical Bayes based relative impulse response estimation.

Relative impulse responses (ReIRs) have several applications in speech enhancement, noise suppression and source localization for multi-channel speech processing in reverberant environments. Estimating the ReIRs can be reduced to a system identification problem. A system identification method using an empirical Bayes framework is proposed and its application for spatial source subtraction in audio signal processing is evaluated. The proposed estimator allows for incorporating prior structure information of the system into the estimation procedure, leading to an improved performance especially in the presence of noise. The estimator utilizes the sparse Bayesian learning algorithm with appropriate priors to characterize both the early reflections and reverberant tails. The mean squared error of the proposed estimator is studied and an extensive experimental study with real-world recordings is conducted to show the efficacy of the proposed approach over other competing approaches.

Rectified Gaussian Scale Mixtures and the Sparse Non-Negative Least Squares Problem.

In this paper, we develop a Bayesian evidence maximization framework to solve the sparse non-negative least squares problem (S-NNLS). We introduce a family of probability densities referred to as the Rectified Gaussian Scale Mixture (R-GSM), to model the sparsity enforcing prior distribution for the signal of interest. The R-GSM prior encompasses a variety of heavy-tailed distributions such as the rectified Laplacian and rectified Student-t distributions with a proper choice of the mixing density. We utilize the hierarchical representation induced by the R-GSM prior and develop an evidence maximization framework based on the Expectation-Maximization (EM) algorithm. Using the EM-based method, we estimate the hyper-parameters and obtain a point estimate for the solution of interest. We refer to this proposed method as rectified Sparse Bayesian Learning (R-SBL). We provide four EM-based R-SBL variants that offer a range of options to trade-off computational complexity to the quality of the E-step computation. These methods include the Markov Chain Monte Carlo EM, linear minimum mean square estimation, approximate message passing and a diagonal approximation. Using numerical experiments, we show that the proposed R-SBL method outperforms existing S-NNLS solvers in terms of both signal and support recovery, and is very robust against the structure of the design matrix.

A unified framework for sparse non-negative least squares using multiplicative updates and the non-negative matrix factorization problem.

We study the sparse non-negative least squares (S-NNLS) problem. S-NNLS occurs naturally in a wide variety of applications where an unknown, non-negative quantity must be recovered from linear measurements. We present a unified framework for S-NNLS based on a rectified power exponential scale mixture prior on the sparse codes. We show that the proposed framework encompasses a large class of S-NNLS algorithms and provide a computationally efficient inference procedure based on multiplicative update rules. Such update rules are convenient for solving large sets of S-NNLS problems simultaneously, which is required in contexts like sparse non-negative matrix factorization (S-NMF). We provide theoretical justification for the proposed approach by showing that the local minima of the objective function being optimized are sparse and the S-NNLS algorithms presented are guaranteed to converge to a set of stationary points of the objective function. We then extend our framework to S-NMF, showing that our framework leads to many well known S-NMF algorithms under specific choices of prior and providing a guarantee that a popular subclass of the proposed algorithms converges to a set of stationary points of the objective function. Finally, we study the performance of the proposed approaches on synthetic and real-world data.

Global signal regression acts as a temporal downweighting process in resting-state fMRI.

In resting-state functional MRI (rsfMRI), the correlation between blood oxygenation level dependent (BOLD) signals across different brain regions is used to estimate the functional connectivity of the brain. This approach has led to the identification of a number of resting-state networks, including the default mode network (DMN) and the task positive network (TPN). Global signal regression (GSR) is a widely used pre-processing step in rsfMRI that has been shown to improve the spatial specificity of the estimated resting-state networks. In GSR, a whole brain average time series, known as the global signal (GS), is regressed out of each voxel time series prior to the computation of the correlations. However, the use of GSR is controversial because it can introduce artifactual negative correlations. For example, it has been argued that anticorrelations observed between the DMN and TPN are primarily an artifact of GSR. Despite the concerns about GSR, there is currently no consensus regarding its use. In this paper, we introduce a new framework for understanding the effects of GSR. In particular, we show that the main effects of GSR can be well approximated as a temporal downweighting process in which the data from time points with relatively large GS magnitudes are greatly attenuated while data from time points with relatively small GS magnitudes are largely unaffected. Furthermore, we show that a limiting case of this downweighting process in which data from time points with large GS magnitudes are censored can also approximate the effects of GSR. In other words, the correlation maps obtained after GSR show a high degree of spatial similarity (including the presence of anticorrelations between the DMN and TPN) with maps obtained using only the uncensored (i.e. retained) time points. Since the data from these retained time points are unaffected by the censoring process, this finding suggests that the observed anticorrelations inherently exist in the data from time points with small GS magnitudes and are not simply an artifact of GSR.

Speech quality and stable gain trade-offs in adaptive feedback cancellation for hearing aids.

This paper addresses trade-offs in adaptive feedback cancellation (AFC) for hearing aids. Aggressive AFC for improved added stable gain (ASG) reduces speech quality. In this paper, the hearing-aid speech quality index (HASQI) is used to investigate AFC performance before the system becomes unstable. It is demonstrated that for a desired speech quality, multiple AFC algorithms can be evaluated for their ASG and computational efficiency. An example is presented with HASQI = 0.8, baseline AFC, and two advanced approaches. For the advanced AFCs, ASG gains of 4 and 7 dB were obtained at additional computational complexity of 8% and 11%, respectively.

Proportionate Adaptive Filtering Algorithms Derived Using an Iterative Reweighting Framework.

In this paper, based on sparsity-promoting regularization techniques from the sparse signal recovery (SSR) area, least mean square (LMS)-type sparse adaptive filtering algorithms are derived. The approach mimics the iterative reweighted ℓ 2 and ℓ 1 SSR methods that majorize the regularized objective function during the optimization process. We show that introducing the majorizers leads to the same algorithm as simply using the gradient update of the regularized objective function, as is done in existing approaches. Different from the past works, the reweighting formulation naturally leads to an affine scaling transformation (AST) strategy, which effectively introduces a diagonal weighting on the gradient, giving rise to new algorithms that demonstrate improved convergence properties. Interestingly, setting the regularization coefficient to zero in the proposed AST-based framework leads to the Sparsity-promoting LMS (SLMS) and Sparsity-promoting Normalized LMS (SNLMS) algorithms, which exploit but do not strictly enforce the sparsity of the system response if it already exists. The SLMS and SNLMS realize proportionate adaptation for convergence speedup should sparsity be present in the underlying system response. In this manner, we develop a new way for rigorously deriving a large class of proportionate algorithms, and also explain why they are useful in applications where the underlying systems admit certain sparsity, e.g., in acoustic echo and feedback cancellation.

ResNEsts and DenseNEsts: Block-based DNN Models with Improved Representation Guarantees.

Models recently used in the literature proving residual networks (ResNets) are better than linear predictors are actually different from standard ResNets that have been widely used in computer vision. In addition to the assumptions such as scalar-valued output or single residual block, the models fundamentally considered in the literature have no nonlinearities at the final residual representation that feeds into the final affine layer. To codify such a difference in nonlinearities and reveal a linear estimation property, we define ResNEsts, i.e., Residual Nonlinear Estimators, by simply dropping nonlinearities at the last residual representation from standard ResNets. We show that wide ResNEsts with bottleneck blocks can always guarantee a very desirable training property that standard ResNets aim to achieve, i.e., adding more blocks does not decrease performance given the same set of basis elements. To prove that, we first recognize ResNEsts are basis function models that are limited by a coupling problem in basis learning and linear prediction. Then, to decouple prediction weights from basis learning, we construct a special architecture termed augmented ResNEst (A-ResNEst) that always guarantees no worse performance with the addition of a block. As a result, such an A-ResNEst establishes empirical risk lower bounds for a ResNEst using corresponding bases. Our results demonstrate ResNEsts indeed have a problem of diminishing feature reuse; however, it can be avoided by sufficiently expanding or widening the input space, leading to the above-mentioned desirable property. Inspired by the densely connected networks (DenseNets) that have been shown to outperform ResNets, we also propose a corresponding new model called Densely connected Nonlinear Estimator (DenseNEst). We show that any DenseNEst can be represented as a wide ResNEst with bottleneck blocks. Unlike ResNEsts, DenseNEsts exhibit the desirable property without any special architectural re-design.

SSGD: SPARSITY-PROMOTING STOCHASTIC GRADIENT DESCENT ALGORITHM FOR UNBIASED DNN PRUNING.

While deep neural networks (DNNs) have achieved state-of-the-art results in many fields, they are typically over-parameterized. Parameter redundancy, in turn, leads to inefficiency. Sparse signal recovery (SSR) techniques, on the other hand, find compact solutions to overcomplete linear problems. Therefore, a logical step is to draw the connection between SSR and DNNs. In this paper, we explore the application of iterative reweighting methods popular in SSR to learning efficient DNNs. By efficient, we mean sparse networks that require less computation and storage than the original, dense network. We propose a reweighting framework to learn sparse connections within a given architecture without biasing the optimization process, by utilizing the affine scaling transformation strategy. The resulting algorithm, referred to as Sparsity-promoting Stochastic Gradient Descent (SSGD), has simple gradient-based updates which can be easily implemented in existing deep learning libraries. We demonstrate the sparsification ability of SSGD on image classification tasks and show that it outperforms existing methods on the MNIST and CIFAR-10 datasets.

Jointly Leveraging Decorrelation and Sparsity for Improved Feedback Cancellation in Hearing Aids.

We propose a new adaptive feedback cancellation (AFC) system in hearing aids (HAs) based on a well-posed optimization criterion that jointly considers both decorrelation of the signals and sparsity of the underlying channel. We show that the least squares criterion on subband errors regularized by a p-norm-like diversity measure can be used to simultaneously decorrelate the speech signals and exploit sparsity of the acoustic feedback path impulse response. Compared with traditional subband adaptive filters that are not appropriate for incorporating sparsity due to shorter sub-filters, our proposed framework is suitable for promoting sparse characteristics, as the update rule utilizing subband information actually operates in the fullband. Simulation results show that the normalized misalignment, added stable gain, and other objective metrics of the AFC are significantly improved by choosing a proper sparsity promoting factor and a suitable number of subbands. More importantly, the results indicate that the benefits of subband decomposition and sparsity promoting are complementary and additive for AFC in HAs.

Proportionate Adaptive Filters Based on Minimizing Diversity Measures for Promoting Sparsity.

In this paper, a novel way of deriving proportionate adaptive filters is proposed based on diversity measure minimization using the iterative reweighting techniques well-known in the sparse signal recovery (SSR) area. The resulting least mean square (LMS)-type and normalized LMS (NLMS)-type sparse adaptive filtering algorithms can incorporate various diversity measures that have proved effective in SSR. Furthermore, by setting the regularization coefficient of the diversity measure term to zero in the resulting algorithms, Sparsity promoting LMS (SLMS) and Sparsity promoting NLMS (SNLMS) are introduced, which exploit but do not strictly enforce the sparsity of the system response if it already exists. Moreover, unlike most existing proportionate algorithms that design the step-size control factors based on heuristics, our SSR-based framework leads to designing the factors in a more systematic way. Simulation results are presented to demonstrate the convergence behavior of the derived algorithms for systems with different sparsity levels.

A Generalized Proportionate-Type Normalized Subband Adaptive Filter.

We show that a new design criterion, i.e., the least squares on subband errors regularized by a weighted norm, can be used to generalize the proportionate-type normalized subband adaptive filtering (PtNSAF) framework. The new criterion directly penalizes subband errors and includes a sparsity penalty term which is minimized using the damped regularized Newton's method. The impact of the proposed generalized PtNSAF (GPtNSAF) is studied for the system identification problem via computer simulations. Specifically, we study the effects of using different numbers of subbands and various sparsity penalty terms for quasi-sparse, sparse, and dispersive systems. The results show that the benefit of increasing the number of subbands is larger than promoting sparsity of the estimated filter coefficients when the target system is quasi-sparse or dispersive. On the other hand, for sparse target systems, promoting sparsity becomes more important. More importantly, the two aspects provide complementary and additive benefits to the GPtNSAF for speeding up convergence.

On Mitigating Acoustic Feedback in Hearing Aids with Frequency Warping by All-Pass Networks.

Acoustic feedback control continues to be a challenging problem due to the emerging form factors in advanced hearing aids (HAs) and hearables. In this paper, we present a novel use of well-known all-pass filters in a network to perform frequency warping that we call "freping." Freping helps in breaking the Nyquist stability criterion and improves adaptive feedback cancellation (AFC). Based on informal subjective assessments, distortions due to freping are fairly benign. While common objective metrics like the perceptual evaluation of speech quality (PESQ) and the hearing-aid speech quality index (HASQI) may not adequately capture distortions due to freping and acoustic feedback artifacts from a perceptual perspective, they are still instructive in assessing the proposed method. We demonstrate quality improvements with freping for a basic AFC (PESQ: 2.56 to 3.52 and HASQI: 0.65 to 0.78) at a gain setting of 20; and an advanced AFC (PESQ: 2.75 to 3.17 and HASQI: 0.66 to 0.73) for a gain of 30. From our investigations, freping provides larger improvement for basic AFC, but still improves overall system performance for many AFC approaches.

A Wearable, Extensible, Open-Source Platform for Hearing Healthcare Research.

Hearing loss is one of the most common conditions affecting older adults worldwide. Frequent complaints from the users of modern hearing aids include poor speech intelligibility in noisy environments and high cost, among other issues. However, the signal processing and audiological research needed to address these problems has long been hampered by proprietary development systems, underpowered embedded processors, and the difficulty of performing tests in real-world acoustical environments. To facilitate existing research in hearing healthcare and enable new investigations beyond what is currently possible, we have developed a modern, open-source hearing research platform, Open Speech Platform (OSP). This paper presents the system design of the complete OSP wearable platform, from hardware through firmware and software to user applications. The platform provides a complete suite of basic and advanced hearing aid features which can be adapted by researchers. It serves web apps directly from a hotspot on the wearable hardware, enabling users and researchers to control the system in real time. In addition, it can simultaneously acquire high-quality electroencephalography (EEG) or other electrophysiological signals closely synchronized to the audio. All of these features are provided in a wearable form factor with enough battery life for hours of operation in the field.

Bone-Conduction Sensor Assisted Noise Estimation for Improved Speech Enhancement.

State-of-the-art noise power spectral density (PSD) estimation techniques for speech enhancement utilize the so-called speech presence probability (SPP). However, in highly non-stationary environments, SPP-based techniques could still suffer from inaccurate estimation, leading to significant amount of residual noise or speech distortion. In this paper, we propose to improve speech enhancement by deploying the bone-conduction (BC) sensor, which is known to be relatively insensitive to the environmental noise compared to the regular air-conduction (AC) microphone. A strategy is suggested to utilized the BC sensor characteristics for assisting the AC microphone in better SPP-based noise estimation. To our knowledge, no previous work has incorporated the BC sensor in this noise estimation aspect. Consequently, the proposed strategy can possibly be combined with other BC sensor assisted speech enhancement techniques. We show the feasibility and potential of the proposed method for improving the enhanced speech quality by both objective and subjective tests.

A Wearable Platform for Research in Augmented Hearing.

We have previously reported a realtime, open-source speech-processing platform (OSP) for hearing aids (HAs) research. In this contribution, we describe a wearable version of this platform to facilitate audiological studies in the lab and in the field. The system is based on smartphone chipsets to leverage power efficiency in terms of FLOPS/watt and economies of scale. We present the system architecture and discuss salient design elements in support of HA research. The ear-level assemblies support up to 4 microphones on each ear, with 96 kHz, 24 bit codecs. The wearable unit runs OSP Release 2018c on top of 64-bit Debian Linux for binaural HA with an overall latency of 5.6 ms. The wearable unit also hosts an embedded web server (EWS) to monitor and control the HA state in realtime. We describe three example web apps in support of typical audiological studies they enable. Finally, we describe a baseline speech enhancement module included with Release 2018c, and describe extensions to the algorithms as future work.

A Realtime, Open-Source Speech-Processing Platform for Research in Hearing Loss Compensation.

We are developing a realtime, wearable, open-source speech-processing platform (OSP) that can be configured at compile and run times by audiologists and hearing aid (HA) researchers to investigate advanced HA algorithms in lab and field studies. The goals of this contribution are to present the current system and propose areas for enhancements and extensions. We identify (i) basic and (ii) advanced features in commercial HAs and describe current signal processing libraries and reference designs to build a functional HA. We present performance of this system and compare with commercial HAs using "Specification of Hearing Aid Characteristics," the ANSI 3.22 standard. We then describe a wireless protocol stack for remote control of the HA parameters and uploading media and HA status for offline research. The proposed architecture enables advanced research to compensate for hearing loss by offloading processing from ear-level-assemblies, thereby eliminating the bottlenecks of CPU and communication between left and right HAs.

Spatiotemporal sparse Bayesian learning with applications to compressed sensing of multichannel physiological signals.

Energy consumption is an important issue in continuous wireless telemonitoring of physiological signals. Compressed sensing (CS) is a promising framework to address it, due to its energy-efficient data compression procedure. However, most CS algorithms have difficulty in data recovery due to nonsparsity characteristic of many physiological signals. Block sparse Bayesian learning (BSBL) is an effective approach to recover such signals with satisfactory recovery quality. However, it is time-consuming in recovering multichannel signals, since its computational load almost linearly increases with the number of channels. This work proposes a spatiotemporal sparse Bayesian learning algorithm to recover multichannel signals simultaneously. It not only exploits temporal correlation within each channel signal, but also exploits inter-channel correlation among different channel signals. Furthermore, its computational load is not significantly affected by the number of channels. The proposed algorithm was applied to brain computer interface (BCI) and EEG-based driver's drowsiness estimation. Results showed that the algorithm had both better recovery performance and much higher speed than BSBL. Particularly, the proposed algorithm ensured that the BCI classification and the drowsiness estimation had little degradation even when data were compressed by 80%, making it very suitable for continuous wireless telemonitoring of multichannel signals.