Compressive spectral imaging (CSI) is an attractive spectral imaging technique since it could acquire a spectral image data cube in a single snapshot. One notable CSI scheme is the spatial spectral compressive spectral imager (SSCSI), which has low complexity and high quality of the recovering spectral image. However, the SSCSI suffers from a small input aperture, which reduces the optical efficiency and signal-to-noise ratio of the system. In this paper, the effect of the input aperture size on the SSCSI system is analyzed. It shows that with the increase of input aperture, the incident light from different spectral bands will overlap with each other on the mask, and the encoding pattern of each spectral band will be ambiguous. Thus, the reconstruction quality of the data cube will highly deteriorate. A new scheme is proposed to deal with this problem. First, the observed image is resampled and recombined into new sub-observed images to improve the frequency response of the encoding pattern. Then each sub-observed image is divided into multiple sub-sets to reduce the coherence of the sensing matrix. Compared to the original reconstruction algorithm for the SSCSI system, the peak signal-to-noise ratio (PSNR) is promoted by more than 3dB, and the spectral reconstruction accuracy and noise suppression capability are also improved.