In this paper, we develop the so-called variable projection support vector machine (VP-SVM) algorithm that is a generalization of the classical SVM. In fact, the VP block serves as an automatic feature extractor to the SVM, which are trained simultaneously. We consider the primal form of the arising optimization task and investigate the use of nonlinear kernels. We show that by choosing the so-called adaptive Hermite function system as the basis of the orthogonal projections in our classification scheme, several real-world signal processing problems can be successfully solved. In particular, we test the effectiveness of our method in two case studies corresponding to anomaly detection. First, we consider the detection of abnormal peaks in accelerometer data caused by sensor malfunction. Then, we show that the proposed classification algorithm can be used to detect abnormalities in ECG data. Our experiments show that the proposed method produces comparable results to the state-of-the-art while retaining desired properties of SVM classification such as light weight architecture and interpretability. We implement the proposed method on a microcontroller and demonstrate its ability to be used for real-time applications. To further minimize computational cost, discrete orthogonal adaptive Hermite functions are introduced for the first time.

Binaural hearing aids allow for a wireless exchange of microphone signals between a left and a right device. A significant noise reduction performance improvement can be achieved compared to a monaural configuration (a single device) or a bilateral configuration (in which the devices work independently). In addition, the binaural localization cues, i.e. the Interaural Time Differences and Interaural Level Differences , can also be better preserved in a binaural procedure. It was previously proven that a binaural noise reduction procedure based on the Speech Distortion Weighted Multi-channel Wiener Filter (SDW-MWF) indeed preserves the speech localization cues, if all microphone signals can be exchanged. However, in practice, it may not be feasible to exchange all microphone signals between the devices, so that reduced-bandwidth SDW-MWF schemes (where only filtered combinations of microphone signals are exchanged) have to be utilized. This paper demonstrates that a straightforward reduced-bandwidth SDW-MWF scheme still preserves the speech ITD cues, but distorts the speech ILD cues, in a single speech source scenario. Novel reduced-bandwidth SDW-MWF schemes, which make use of a common spectral postfilter, are therefore introduced. Experiments in a reverberant environment demonstrate that the novel schemes reduce the ILD distortion, without severely degrading the noise reduction performance.

The Speech Distortion Weighted Multichannel Wiener Filter (SDW-MWF) is a promising multi-microphone noise reduction technique, in particular for hearing aid applications. Its benefit over other techniques has been shown in several theoretical and experimental contributions. In theoretical studies, a single target speech source is commonly assumed, as this facilitates the analysis. In this contribution, we first prove that an algorithm, that implicitly assumes a single target speech source, is also more robust against estimation errors in the speech second order statistics, compared to a standard SDW-MWF algorithm. Secondly, as any SDW-MWF algorithm relies on a voice activity detector (VAD), a novel VAD-robust extension is also proposed. It is shown theoretically and through experiments with a realistic VAD that the new algorithm indeed achieves a good performance, even at low input SNR's where the VAD error rate is high.

The speech distortion weighted multichannel Wiener filter (SDW-MWF) is a promising multi-microphone noise reduction technique, in particular for hearing aid applications. Its benefit over other single- and multi-microphone techniques has been shown in several previous contributions, theoretically as well as experimentally. In theoretical studies, it is usually assumed that there is a single target speech source. The filter can then be decomposed into a conceptually interesting structure, i.e., into a spatial filter (related to other known techniques) and a single-channel postfilter, which then also allows for a performance analysis. Unfortunately, it is not straightforward to make a robust practical implementation based on this decomposition. Instead, a general SDW-MWF implementation, which only requires a (relatively easy) estimation of speech and noise correlation matrices, is mostly used in practice. This paper features a theoretical study and experimental validation on a binaural hearing aid setup of this standard SDW-MWF implementation, where the effect of estimation errors in the second-order statistics is analyzed. In this case, and for a single target speech source, the standard SDW-MWF implementation is found not to behave as predicted theoretically. Second, two recently introduced alternative filters, namely the rank-one SDW-MWF and the spatial prediction SDW-MWF, are also studied in the presence of estimation errors in the second-order statistics. These filters implicitly assume a single target speech source, but still only rely on the speech and noise correlation matrices. It is proven theoretically and illustrated through experiments that these alternative SDW-MWF implementations behave close to the theoretical optimum, and hence outperform the standard SDW-MWF implementation.

Binaural hearing aids use microphone signals from both left and right hearing aid to generate an output signal for each ear. The microphone signals can be processed by a procedure based on speech distortion weighted multichannel Wiener filtering (SDW-MWF) to achieve significant noise reduction in a speech + noise scenario. In binaural procedures, it is also desirable to preserve binaural cues, in particular the interaural time difference (ITD) and interaural level difference (ILD), which are used to localize sounds. It has been shown in previous work that the binaural SDW-MWF procedure only preserves these binaural cues for the desired speech source, but distorts the noise binaural cues. Two extensions of the binaural SDW-MWF have therefore been proposed to improve the binaural cue preservation, namely the MWF with partial noise estimation (MWF-eta) and MWF with interaural transfer function extension (MWF-ITF). In this paper, the binaural cue preservation of these extensions is analyzed theoretically and tested based on objective performance measures. Both extensions are able to preserve binaural cues for the speech and noise sources, while still achieving significant noise reduction performance.

In this paper two multichannel noise reduction strategies are compared in the context of binaural hearing aids. Recently a novel noise reduction method based on spatial-temporal prediction (STP) was introduced which showed an improvement over methods based on multichannel Wiener filtering, although at the cost of a higher computational complexity. Whereas this newmethod operates in the time domain, hearing aids typically demand faster frequency domain implementations. In this paper we therefore propose a frequency domain equivalent of the STP method. The performance of the new so-called spatial prediction (SP) method will be compared to a frequency domain implementation of the speech distortion weighted multichannel Wiener filter (SDW-MWF), theoretically as well as based on simulations with a binaural hearing aid configuration. It will be shown that the frequency domain SP method still achieves some improvement over the SDW-MWF, at the cost of higher computational complexity.