Recent years have witnessed a rapid development of network reconstruction approaches, especially for a series of methods based on compressed sensing. Although compressed-sensing based methods require much less data than conventional approaches, the compressed sensing for reconstructing heterogeneous networks has not been fully exploited because of hubs. Hub neighbors require much more data to be inferred than small-degree nodes, inducing a cask effect for the reconstruction of heterogeneous networks. Here, a conflict-based method is proposed to overcome the cast effect to considerably reduce data amounts for achieving accurate reconstruction. Moreover, an element elimination method is presented to use the partially available structural information to reduce data requirements. The integration of both methods can further improve the reconstruction performance than separately using each technique. These methods are validated by exploring two evolutionary games taking place in scale-free networks, where individual information is accessible and an attempt to decode the network structure from measurable data is made. The results demonstrate that for all of the cases, much data are saved compared to that in the absence of these two methods. Due to the prevalence of heterogeneous networks in nature and society and the high cost of data acquisition in large-scale networks, these approaches have wide applications in many fields and are valuable for understanding and controlling the collective dynamics of a variety of heterogeneous networked systems.