Aiming to address the challenges of lengthy data collection, high memory consumption, elevated transportation costs, and low data utilization in current structural health monitoring, a novel approach for structural damage recognition is proposed by integrating compressive sensing and deep learning networks. Initially, acceleration response signals obtained from finite element simulations are processed using compressive sensing, yielding compressed and reconstructed signals. To address suboptimal reconstruction from conventional methods, an Alternating Direction Method of Multipliers (ADMM) with Total Variation (TV) regularization is introduced to enhance reconstruction performance. The TV-ADMM algorithm demonstrates highly accurate signal reconstruction. Subsequently, a convolutional neural network (CNN) based damage identification model is established, showing excellent accuracy for both original and reconstructed signals, but limited performance for compressed signals. To overcome this, data augmentation and Multi-Head Attention mechanisms are integrated into the model (MHA-CNN), resulting in effective damage recognition using improved compressed signals.