Compressive sampling is a novel framework that exploits sparsity of a signal in a transform domain to perform sampling below the Nyquist rate. In this paper, we apply compressive sampling to reduce the sampling rate of binary images. A system is proposed whereby the image is split into non-overlapping blocks of equal size and compressive sampling is performed on selected blocks only using the orthogonal matching pursuit technique. The remaining blocks are sampled fully. This way, the complexity and the required sampling time is reduced since the orthogonal matching pursuit operates on a smaller number of samples, and at the same time local sparsity within an image is exploited. Our simulation results show more than 20% saving in acquisition for several binary images.