Information estimations and acquisition costs for quantized compressive sensing

According to the amount of information content to be estimated, there are three kinds of information estimation problems in compressive sensing (CS), i.e., signal estimation (SigE), support estimation (SupE), and sparsity order estimation (SOE). In this work, we study all these three estimation problems with consideration of quantization effects. Although the quantization effect does degrade the performance of all these three estimation problems, SOE outperforms SupE which is then better than SigE in terms of achieving the better estimation performance given the same acquisition costs or consuming the smaller number of measurements required to reach the same estimation probability. This is due to an important fact that SOE needs to retrieve the least amount of information content compared with SupE and SigE, which therefore alludes to its highest estimation performance and acquisition efficiency. Such an observation can shed lights on the implementation of practical CS-based applications, in which one can decide the acquisition costs based on the amount of information needed to be recovered.