Info-Greedy sequential adaptive compressed sensing

Often these techniques are sequential in that the measurements are taken one after another. Hence information gained in the past can be used to guide an adaptive design of subsequent measurements, which naturally leads to the notion of sequential adaptive sensing. At the same time, a path to efficient sensing of big data is compressive sensing [4]-[6], which exploits low-dimensional structures to recover signals from a number of measurements much smaller than the ambient dimension of the signals. Early compressed sensing works mainly focus on nonadaptive and one-shot measurement schemes. Recently there has also been much interest in sequential adaptive compressed sensing, which measures noisy linear combinations of the entries (this is different from the direct adaptive sensing, which measures signal entries directly [7]-[10]). Although in the seminal work of [11], it was shown under fairly general assumptions that "adaptivity does not help much", i.e., sequential adaptive compressed sensing does not improve the order of the min-max bounds obtained by algorithms, these limitations are restricted to certain performance metrics. It has also been recognized (see, e.g., [12]-[14]) that adaptive compressed sensing offers several benefits with respect to other performance metrics, such as the reduction in the signalto-noise ratio (SNR) to recover the signal.