  Millimeter-wave (mmWave) and Terahertz (THz)-band communications exploit the
abundant bandwidth to fulfill the increasing data rate demands of 6G wireless
communications. To compensate for the high propagation loss with reduced
hardware costs, ultra-massive multiple-input multiple-output (UM-MIMO) with a
hybrid beamforming structure is a promising technology in the mmWave and THz
bands. However, channel estimation (CE) is challenging for hybrid UM-MIMO
systems, which requires recovering the high-dimensional channels from severely
few channel observations. In this paper, a Pruned Approximate Message Passing
(AMP) Integrated Deep Convolutional-neural-network (DCNN) CE (PRINCE) method is
firstly proposed, which enhances the estimation accuracy of the AMP method by
appending a DCNN network. Moreover, by truncating the insignificant feature
maps in the convolutional layers of the DCNN network, a pruning method
including training with regularization, pruning and refining procedures is
developed to reduce the network scale. Simulation results show that the PRINCE
achieves a good trade-off between the CE accuracy and significantly low
complexity, with normalized-mean-square-error (NMSE) of $-10$ dB at
signal-to-noise-ratio (SNR) as $10$ dB after eliminating $80\%$ feature maps.
