Optical sparse aperture imaging is a promising technology to obtain high resolution but with a significant reduction in size and weight by minimizing the total light collection area. However, with the decreasing of collection area, its OTF is also greatly attenuated, and thus the directly imaging quality of sparse aperture system is very poor. In this paper, we focus on the post-processing methods for sparse aperture systems, and propose a non-iterative wavelet-based deconvolution algorithm. The algorithm is performed by adaptively denoising the Fourier-based deconvolution results on the wavelet basis. We set up a Golay-3 sparse-aperture imaging system, where the imaging and deconvolution experiments of the natural scenes are performed. The experiments demonstrate that the proposed method has greatly improved the imaging quality of Golay-3 sparse-aperture system, and produce satisfactory visual quality. Furthermore, our experimental results also indicate that the sparse aperture system has the potential to reach higher resolution with the help of better post-processing deconvolution techniques.