Sequential Sensing with Model Mismatch

Sequential compressed sensing is a promising new information acquisition and recovery technique to process big data that arise in various applications such as compressive imaging [2]-[4], power network monitoring [5], and large scale sensor networks [6]. The sequential nature of the problems arises either because the measurements are taken one after another, or due to the fact that the data is obtained in a streaming fashion so that it has to be processed in one pass. To harvest the benefits of adaptivity in sequential compressed sensing, various algorithms have been developed (see [1] for a review.) We may classify these algorithms as (1) being agnostic about the signal distribution and, hence, using random measurements [7]-[13]; (2) exploiting additional structure of the signal (such as graphical structure [14] and tree-sparse structure [15], [16]) to design measurements; (3) exploiting the distributional information of the signal in choosing the measurements possibly through maximizing mutual information: the seminal Bayesian compressive sensing work [17], Gaussian mixture models (GMM) [18], [19] and our earlier work [1] which presents a general framework for information guided sensing referred to as Info-Greedy Sensing. In this paper we consider the setup of Info-Greedy Sensing [1], as it provides certain optimality guarantees. Info-Greedy Sensing aims at designing subsequent measurements to maximize the mutual information conditioned on previous measurements.