In one embodiment, a management entity monitors for a change in a convergence rate of spatio-temporal compressive sensing measurements from a plurality of sensors in a sensor network operating according to a measurement matrix up to a halting criterion, and if the change is below a given threshold, determines whether the change is due to impulse noise or due to continued sensed measurements. If continued sensed measurements, the management entity initiates a single-dimensional compressive sensing in a spatial domain at regular time intervals, and identifies and tracks gradient clusters. In response to a change in joint spatio-temporal sparsity of tracked nodes of the gradient clusters, the management entity can then determine an updated measurement matrix based on the joint spatio-temporal sparsity of tracked nodes while satisfying one or more operating parameters, and directs at least certain sensors of the plurality of sensors to operate according to the updated measurement matrix.