Accelerating deep neural network (DNN) inference on resource-limited devices is one of the most important barriers to ensuring a wider and more inclusive adoption. To alleviate this, DNN binary quantization for faster convolution and memory savings is one of the most promising strategies despite its serious drop in accuracy. The present paper therefore proposes a novel binary quantization function based on quantized compressed sensing (QCS). Theoretical arguments conjecture that our proposal preserves the practical benefits of standard methods, while reducing the quantization error and the resulting drop in accuracy.