Union of Low-Rank Subspaces Detector

The problem of signal detection using a flexible and general model is considered. Due to applicability and flexibility of sparse signal representation and approximation, it has attracted a lot of attention in many signal processing areas. In this paper, we propose a new detection method based on sparse decomposition in a union of subspaces (UoS) model. Our proposed detector uses a dictionary that can be interpreted as a bank of matched subspaces. This improves the performance of signal detection, as it is a generalization for detectors. Low-rank assumption for the desired signals implies that the representations of these signals in terms of some proper bases would be sparse. Our proposed detector exploits sparsity in its decision rule. We demonstrate the high efficiency of our method in the cases of voice activity detection in speech processing

A Novel Detection Scheme with Multiple Observations for Sparse Signal Based on Likelihood Ratio Test with Sparse Estimation

Recently, the problem of detecting unknown and arbitrary sparse signals has attracted much attention from researchers in various fields. However, there remains a peck of difficulties and challenges as the key information is only contained in a small fraction of the signal and due to the absence of prior information. In this paper, we consider a more general and practical scenario of multiple observations with no prior information except for the sparsity of the signal. A new detection scheme referred to as the likelihood ratio test with sparse estimation (LRT-SE) is presented. Under the Neyman-Pearson testing framework, LRT-SE estimates the unknown signal by employing the l1-minimization technique from compressive sensing theory. The detection performance of LRT-SE is preliminarily analyzed in terms of error probabilities in finite size and Chernoff consistency in high dimensional condition. The error exponent is introduced to describe the decay rate of the error probability as observations number grows. Finally, these properties of LRT-SE are demonstrated based on the experimental results of synthetic sparse signals and sparse signals from real satellite telemetry data. It could be concluded that the proposed detection scheme performs very close to the optimal detector