Feature-specific imaging (FSI) refers to any imaging system that directly measures linear projections of an object irradiance distribution. Numerous reports of FSI (also called compressive imaging) using static projections can be found in the literature. In this paper we will present adaptive methods of FSI suitable for the applications of (a) image reconstruction and (b) target detection. Adaptive FSI for image reconstruction is based on Principal Component and Hadamard features. The adaptive algorithm employs an updated training set in order to determine the optimal projection vector after each measurement. Adaptive FSI for detection is based on a sequential hypothesis testing framework. The probability of each hypothesis is updated after each measurement and in turn defines a new optimal projection vector. Both of these new adaptive methods will be compared with static FSI. Adaptive FSI for detection will also be compared with conventional imaging.