Traditionally, image compression algorithms, such as JPEG, have been designed for human viewers' satisfaction. Increasingly however, more and more images are being viewed by computers, for performing computer vision tasks such as object detection. Image compression and object detection have largely been independent areas of research so far. However, several applications such as surveillance and medical imaging impose severe bandwidth and power restrictions. These constraints make the quality and/or size of the compressed image a critical factor in object detection performance. My works presents three compressed image representations that enable fast and accurate object detection. The first representation is a saliency guided wavelet representation which modifies traditional wavelet compression using the knowledge of saliency to improve both compression and detection performance compared to JPEG images. The second representation, called event stream representation, comes directly from the new DVS sensor which has ultra-low bandwidth and power requirements. We show, for the first time, high speed video reconstruction, and direct detection, on the event data. We achieve detection performance comparable to that on conventional JPEG images. Finally, we explore an abstract compressed representation called patch-wise binary representation, which represents an image (patch-wise) as a collection of short binary strings. We demonstrate two ways of generating these binary strings, called hashing and feature binarization, which enable 10x faster detection. We show promising detection and reconstruction results for both these approaches.