To overcome the limited coverage in traditional wireless sensor networks, \emph{mobile crowd sensing} (MCS) has emerged as a new sensing paradigm. To achieve longer battery lives of user devices and incentive human involvement, this paper presents a novel approach that seamlessly integrates MCS with wireless power transfer, called \emph{wirelessly powered crowd sensing} (WPCS), for supporting crowd sensing with energy consumption and offering rewards as incentives. The optimization problem is formulated to simultaneously maximize the data utility and minimize the energy consumption for service operator, by jointly controlling wireless-power allocation at the \emph{access point} (AP) as well as sensing-data size, compression ratio, and sensor-transmission duration at \emph{mobile sensor} (MS). Given the fixed compression ratios, the optimal power allocation policy is shown to have a \emph{threshold}-based structure with respect to a defined \emph{crowd-sensing priority} function for each MS. Given fixed sensing-data utilities, the compression policy achieves the optimal compression ratio. Extensive simulations are also presented to verify the efficiency of the contributed mechanisms.