In this paper, measuring dynamic signals at points of interest (POIs) using a mobile agent is considered, where the agent is required to repeatedly measure at and transit between the POIs. Dynamic field sensing is needed in areas ranging from nanomechanical mapping of live sample to crop monitoring. Existing work on mobile sensing, however, has been focused on cooperatively tracking one or few known or unknown POIs, whereas the dynamics of the signals is ignored. Challenges arise from capturing and recovering the dynamics at each POI by using the data intermittently measured by the mobile agent, resulting in temporal-spatial coupling in mobile sensing. Moreover, trade off between the sensing cost and the performance needs to be addressed. We propose a compressed-sensing based approach to tackle this problem. First, a check-and-removal process based on random permutation and partition of the measurement periods is developed to avoid the temporal-spatial coupling under the agent speed constraint. Then a shuffle-and-pair process based on the simulate-annealing is proposed to minimize the transition distance while preserving the performance. It is shown that the distribution of the measurement periods between the POIs converges. The proposed approach is illustrated through a simulation study of measuring the temperature-dependent nanomechanical variations of a polymer sample.