An embodiment of the invention provides a method of detecting the position(s) where sensor(s) are activated on an interactive screen using sparse-activation compressive sensing. Sparse-activation compressive sensing makes use of the situation where the number of simultaneously activated sensors is substantially smaller than the number of sensors (nodes). Because the number of simultaneously activated sensors is substantially smaller than the number of sensors, the number of measurements required for determining which sensors are activated may also be reduced. Because fewer measurements are required when compared with full-scan techniques, less circuitry and power is required to detect the location(s) of activated sensors on an interactive screen.