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Terahertz (THz) pulse imaging exhibits a potential application in biomedicine, nondestructive detection and safety inspection. However, the THz time-domain spectroscopy system will affect the THz image quality. To improve the THz image quality, in this article we proposed a novel method by combining the ant colony algorithm with the compressive sensing method. First, the image edge is detected by using the ant colony algorithm. Subsequently, the compressive sensing method based on signal sparse representation and the reconstruction algorithm from partial Fourier is applied on the non-edge image for noise reduction. Finally, the reconstruction result is obtained by combining the noise reduced non-edge image with the edge image. The experimental results on three kinds of images prove that the proposed method can preserve the edge information during noise reduction.