The localization of sound sources with delay-and-sum (DAS) beamforming is limited by a poor spatial resolution-particularly at low frequencies. Various methods based on deconvolution are examined to improve the resolution of the beamforming map, which can be modeled by a convolution of the unknown acoustic source distribution and the beamformer's response to a point source, i.e., point-spread function. A significant limitation of deconvolution is, however, an additional computational effort compared to beamforming. In this paper, computationally efficient deconvolution algorithms are examined with computer simulations and experimental data. Specifically, the deconvolution problem is solved with a fast gradient projection method called Fast Iterative Shrikage-Thresholding Algorithm (FISTA), and compared with a Fourier-based non-negative least squares algorithm. The results indicate that FISTA tends to provide an improved spatial resolution and is up to 30% faster and more robust to noise. In the spirit of reproducible research, the source code is available online.

Abstract-Feedback oscillation is one of the major issues with hearing aids. An effective way of feedback suppression is adaptive feedback cancellation, which uses an adaptive filter to estimate the feedback path. However, when the external input signal is correlated with the receiver input signal, the estimate of the feedback path is biased. This so-called "bias problem" results in a large modeling error and a cancellation of the desired signal. This paper proposes a band-limited linear predictive coding based approach to reduce the bias. The idea is to replace the hearing-aid output with a synthesized signal, which sounds perceptually the same as or similar to the original signal but is statistically uncorrelated with the external input signal at high frequencies where feedback oscillation usually occurs. Simulation results show that the proposed algorithm can effectively reduce the bias and the misalignment between the real and the estimated feedback path. When combined with filtered-X adaptation in the feedback canceller, this approach reduces the misalignment even further. Index Terms-Adaptive feedback cancellation (AFC), hearing aids, linear predictive coding (LPC).

Feedback whistling is a severe problem with hearing aids. A typical acoustical feedback path represents a wave propagation path from the receiver to the microphone and includes many complicated effects among which some are invariant or nearly invariant for all users and in all acoustical environments given a specific type of hearing aids. Based on this observation, a feedback path model that consists of an invariant model and a variant model is proposed. A common-acoustical-pole and zero model-based approach and an iterative least-square search-based approach are used to extract the invariant model from a set of impulse responses of the feedback paths. A hybrid approach combining the two methods is also proposed. The general properties of the three methods are studied using artificial datasets, and the methods are cross-validated using the measured feedback paths. The results show that the proposed hybrid method gives the best overall performance, and the extracted invariant model is effective in modeling the feedback path.

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