Real-time robotic control relies on high-speed tactile arrays, but increasing the number of sensing pixels to cover large areas often leads to greater scanning delays, with readout speeds for large arrays rarely exceeding 100 Hz. To overcome this restriction, we developed compressive tactile subsampling methods that take advantage of spatial patterns in tactile data. By sampling fewer pixels in each frame and reconstructing the tactile signal using a learned tactile dictionary, these methods enable quicker readout. Using a$32\times 32$tactile sensor array, we evaluated classification accuracy and reconstruction error for tactile interactions with 30 daily and 3D printed objects using a robotic arm. Compared to traditional raster scanning, our method produced 18 times faster frame rates while maintaining minimal reconstruction and classification error. By implementing this scalable technique into software, low-cost tactile arrays may be transformed and robots can attain high-resolution, high-speed touch sensing across their bodies. More details in our preprint [1].