High-speed tactile arrays are essential for real-time robotic control in unstructured environments, but high pixel counts limit readout rates of most large tactile arrays to below 100Hz. We introduce ACTS - adaptive compressive tactile subsampling - a method that efficiently samples tactile matrices and reconstructs interactions using sparse recovery and a learned tactile dictionary. Tested on a 1024-pixel sensor array (32x32), ACTS increased frame rates by 18X compared to raster scanning, with minimal error. For the first time in large-area tactile skin, we demonstrate rapid object classification within 20ms of contact, high-speed projectile detection, ricochet angle estimation, and deformation tracking through enhanced spatiotemporal resolution. Our method can be implemented in firmware, upgrading existing low-cost, flexible, and robust tactile arrays into high-resolution systems for large-area spatiotemporal touch sensing.