Robust Sensor Selection By Deep Unfolding

The challenge of sensor selection involves choosing a subset of the available measurements to estimate data while aiming to minimize estimation errors. Traditionally, convex relaxation methods with solvers like the projected subgradient (PSG) algorithm have been employed to address this problem. However, they are computationally intensive due to the large number of iterations involved and necessitate accurate apriori knowledge of the noise statistics, which may be unavailable. Moreover, in the case of linear measurements, the cost functions involved are data-independent, which makes them non-adaptive. In this paper, we tackle these challenges by introducing two deep neural networks that unfold the PSG algorithm. These networks are trained on observations where knowledge of noise statistics and the parameters to estimate are implicit. This makes the approach data-adaptive without needing any priors. Moreover, in comparison to the conventional PSG algorithm, the unfoldings require fewer iterations. Experimental results demonstrate that these networks achieve a lower mean-squared error by 4 10 dB compared to the standard PSG algorithm or random selection.