One of the major issues in multifunction radar is the allocation of time resources to maximize the ability of the radar. If jet engine modulation (JEM) is analyzed correctly in an insufficient dwell time environment, the remaining time can be allocated for other tasks. This paper presents effective reconstruction of insufficient JEM signals based on compressed sensing (CS) method. The CS method was employed to extract a refined spectrum from insufficient JEM signals. In the process of applying the CS method to JEM signals, we utilized the modified linear programming (LP) standard form of an optimization method. The approach proposed in this paper is significant because it enables reliable estimation in spite of the insufficient JEM signal. Its application to insufficient JEM signals demonstrated that the reconstruction method presented in this paper improved the accuracy of JEM analysis and is expected to be effective from the perspective of radar resource management.