Low-Earth-orbit (LEO) satellites assist observation satellites (OSs) to compress and backhaul more time-determined images (TDI) has become a new paradigm, which is used to enhance the timeout caused by the limited computing resources of OSs. However, how to capture the time-varying and dynamic characteristics of multi-dimensional resources is challenging for efficient collaborative scheduling. Motivated by this factor, we design a highly succinct multi-dimensional resource time-expanded graph (MDR-TEG) modell. Specifically, by employing a slots division mechanism and introducing an external virtual node, the time-varying communication, caching, and computing (3C) resources are depicted in low complexity by the link weights within, between, and outside the slots. Based on the MDR-TEG, the maximizing successful transmission ratio of TDI (MSTR-TDI) is modeled as a mixed integer linear programming (MILP) problem. Which further relaxed decomposed into two tractable sub-problems: maximizing the successful transmission rate of images (MSTRI) and ensuring the timeliness problem (ETP). Subsequently, an efficient subgradient of relaxation computing constraint (SRCC) algorithm is proposed. The upper and lower bounds of MSTR-TDI are obtained by solving the two subproblems and the dual problem (DP), and the direction of the next iteration is obtained by feedback. Furthermore, arranging the sending sequences of images to improve the quality of the solution. The approximate optimal solution of MSTR-TDI is eventually obtained through repeated iterations. The simulation results verify the superiority of the proposed MDR-TEG model and the effectiveness of the SRCC.