Snapshot compressive imaging (SCI) has surged as a crucial tool for data visualization in applications limited to a single-shot. However, most existing methods shortfall in the reiterated use of random coded apertures and the idealization of the shearing function behavior. To overcome these limitations, we develop a new end-to-end convolutional neural network, termed deep high-dimensional adaptive net (D-HAN), that supplies the SCI systems with multifaceted supervision in the encoding operation, the shearing process, and the reconstruction. D-HAN is implemented in a representative SCI system for hyperspectral and ultrahigh-speed imaging.