Usually the test detector of a standard ghost imaging scheme is a bucket detector; here the test detector in the scheme of multiple-input ghost imaging via sparsity constraints (MI-GISC) we proposed is characterized by some sparse-array single-pixel detectors, and the propagation process between the object plane and the test detection plane is also considered. Combining ghost imaging with the target's sparsity constraints, the theory and reconstruction of MI-GISC are investigated. The property and differences between MI-GISC and compressive ghost imaging (CGI) are studied theoretically and backed up by numerical simulations. MI-GISC can be applied in a remote imaging system with a small receiving numerical aperture, improving the reconstruction's quality of the target.