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The images collected by many remote sensing systems need to be transmitted wirelessly to the ground station for further analysis. These small, battery-powered remote sensing systems suffer from limited communication bandwidth and computational resources. To address these two limitations, we have developed a novel compression technique by combining Compressive Sensing (CS), Vector Quantization (VQ) and Arithmetic Coding (AC). We have applied it to compress images and videos, and compared its performance with the industry standard JPEG/MPEG compression schemes. Our results indicate that our algorithm provides better quality images at the same compression rate and eleven times faster compression of images on the transmit side as compared to JPEG/MPEG techniques. The details of our algorithm and comparison results with JPEG are provided in this paper.