Sequential Sensing with Model Mismatch
This work addresses robustness in sequential sensing for signal processing applications, but it is incremental as it builds on existing Info-Greedy Sensing frameworks.
The paper tackles the problem of sequential sensing performance degradation due to model mismatch between true and assumed signal models, establishing performance bounds in terms of entropy gap and power requirements, and proposes initialization methods using sample covariance or sketching.
We characterize the performance of sequential information guided sensing, Info-Greedy Sensing, when there is a mismatch between the true signal model and the assumed model, which may be a sample estimate. In particular, we consider a setup where the signal is low-rank Gaussian and the measurements are taken in the directions of eigenvectors of the covariance matrix in a decreasing order of eigenvalues. We establish a set of performance bounds when a mismatched covariance matrix is used, in terms of the gap of signal posterior entropy, as well as the additional amount of power required to achieve the same signal recovery precision. Based on this, we further study how to choose an initialization for Info-Greedy Sensing using the sample covariance matrix, or using an efficient covariance sketching scheme.