With the controllability of the digital micromirror device (DMD), a single-arm ghost imaging experiment platform based on the DMD amplitude modulation is built and DMD amplitude modulation is used to generate prebuilt quasi-Gaussian random measurement matrix with different mean values and standard deviations. The influence of the quasi-Gaussian random measurement matrix with different mean values and standard deviations and the image′s sparsity on the quality of image reconstruction based on ghost imaging via sparsity constraints (GISC) is experimentally analyzed. Both the numerical simulation and experimental results show that: as the mean value u decreases or the standard deviation σ increases (namely as the size of amplitude modulation δ=σ/u of the quasi-Gaussian random measurement matrix A increases), the reconstruction fidelity of GISC is proportion to δ-1/2, and at the same time, it is linearly related to the image′s sparsity β.