- The common approach in digital imaging follows the sample-then-compress framework. According to this approach, in the first step as many pixels as possible are captured and in the second step the captured image is compressed by digital means. The recently introduced theory of compressed sensing provides the mathematical foundation necessary to combine these two steps in a single one, that is, to compress the information optically before it is recorded. In this paper we overview and extend an optical implementation of compressed sensing theory that we have recently proposed. With this new imaging approach the compression is accomplished inherently in the optical acquisition step. The primary feature of this imaging approach is a randomly encoded aperture realized by means of a random phase screen. The randomly encoded aperture implements random projection of the object field in the image plane. Using a single exposure, a randomly encoded image is captured which can be decoded by proper decoding algorithm.