Tensor-based multiple denoising via successive spatial smoothing, low-rank approximation and reconstruction for R-D sensor array processing

Abstract

The parameter estimation problem from noisy signal measurements plays a key role in several practical applications in the array signal processing area ranging from telecommunications and radar to biomedical and acoustics. The performance of parameter estimation techniques is sensitive to the signal-to-noise ratio (SNR) and severely degrades in noisy scenarios. Classical denoising using SVD low-rank approximation and its tensor counterpart known as higher order SVD (HOSVD) have been widely applied as a preprocessing step to improve the SNR of the received signal. In this paper, we propose the tensor-based multiple denoising (MuDe) approach that successively applies spatial smoothing, denoising and reconstruction to the noisy data. By taking into account the knowledge of the model order and by exploiting subarrays created by the spatial smoothing, we can successively denoise the data by means of HOSVD-based and SVD-based low-rank approximation for tensor and matrix data, respectively. We show that our proposed approach significantly reduces the noise level, allowing a more accurate estimation of parameters compared to state-of-the-art matrix-based and tensor-based techniques without decreasing the sensor array aperture.