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Weight and activation binarization can efficiently compress deep neural networks and accelerate model inference, but cause severe accuracy degradation. Existing optimization methods for binary neural networks (BNNs) focus on fitting full-precision networks to reduce quantization errors, and suffer from the trade-off between accuracy and computational complexity. In contrast, considering the limited learning ability and information loss caused by the limited representational capability of BNNs, we propose IR$^2$Net to stimulate the potential of BNNs and improve the network accuracy by restricting the input information and recovering the feature information, including: 1) information restriction: for a BNN, by evaluating the learning ability on the input information, discarding some of the information it cannot focus on, and limiting the amount of input information to match its learning ability; 2) information recovery: due to the information loss in forward propagation, the output feature information of the network is not enough to support accurate classification. By selecting some shallow feature maps with richer information, and fusing them with the final feature maps to recover the feature information. In addition, the computational cost is reduced by streamlining the information recovery method to strike a better trade-off between accuracy and efficiency. Experimental results demonstrate that our approach still achieves comparable accuracy even with $ \sim $10x floating-point operations (FLOPs) reduction for ResNet-18. The models and code are available at https://github.com/pingxue-hfut/IR2Net.