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Mapping a truncated optimization method into a deep neural network, deep proximal unrolling network has attracted attention in compressive sensing due to its good interpretability and high performance. Each stage in such networks corresponds to one iteration in optimization. By understanding the network from the perspective of the human brain’s memory processing, we find there exist two categories of memory transmission: intra-stage and inter-stage. For intra-stage, existing methods increase the number of parameters to maximize the information flow. For inter-stage, there are also two methods. One is to transfer the information between adjacent stages, which can be regarded as short-term memory that is usually lost seriously. The other is a mechanism to ensure that the previous stages affect the current stage, which has not been explicitly studied. In this paper, a novel deep proximal unrolling network with …