Methods and apparatuses for compressive sensing that enable efficient recovery of features in an input signal based on acquiring a few measurements corresponding to the input signal. One method of compressive sensing includes folding an image to generate first and second folds, and recovering a feature of the image based on the first and second folds without reconstructing the image. One example of a compressive sensing apparatus includes a lens, a focal plane array coupled to the lens and configured to generate first and second folds based on the image, and a decoder configured to receive the first and second folds and to recover a feature of the image without reconstructing the image. The feature may be a local geometric feature or a corner. Compressive sensing methods and apparatuses for determining translation and rotation between two images are also disclosed.