Transcranial focused ultrasound is a promising therapeutic modality. It consists in placing transducers around the skull and emitting shaped ultrasound waves that propagate through the skull and then concentrate on one particular location within the brain. However, the skull bone is known to distort the ultrasound beam. In order to compensate for such distortions, a number of techniques have been proposed recently, for instance using Magnetic Resonance Imaging (MRI) feedback. In order to fully determine the focusing distortion due to the skull, such methods usually require as many calibration signals as transducers, resulting in a lengthy calibration process. In this paper, we investigate how the number of calibration sequences can be signicantly reduced, based on random measurements and optimization techniques. Experimental data with six human skulls demonstrate that the number of measurements can be up to three times lower than with the standard methods, while restoring 90% of the focusing eciency.