Multichannel sparse recovery of complex-valued signals using Huber's criterion
This work addresses robust signal recovery in sensor array applications like source localization, but it is incremental as it builds on existing SNIHT methods.
The paper tackles the problem of robust multichannel sparse recovery for complex-valued signals under heavy-tailed non-Gaussian noise by generalizing Huber's criterion and proposing the HUB-SNIHT algorithm, which shows negligible performance loss compared to conventional methods under Gaussian noise.
In this paper, we generalize Huber's criterion to multichannel sparse recovery problem of complex-valued measurements where the objective is to find good recovery of jointly sparse unknown signal vectors from the given multiple measurement vectors which are different linear combinations of the same known elementary vectors. This requires careful characterization of robust complex-valued loss functions as well as Huber's criterion function for the multivariate sparse regression problem. We devise a greedy algorithm based on simultaneous normalized iterative hard thresholding (SNIHT) algorithm. Unlike the conventional SNIHT method, our algorithm, referred to as HUB-SNIHT, is robust under heavy-tailed non-Gaussian noise conditions, yet has a negligible performance loss compared to SNIHT under Gaussian noise. Usefulness of the method is illustrated in source localization application with sensor arrays.