A Fresnel Zone Aperture (FZA) mask for a lensless camera, an ultra-thin and functional computational imaging system, is beneficial because the FZA pattern makes it easy to model the imaging process and reconstruct captured images through a simple and fast deconvolution. However, diffraction causes a mismatch between the forward model used in the reconstruction and the actual imaging process, which affects the recovered image's resolution. This work theoretically analyzes the wave-optics imaging model of an FZA lensless camera and focuses on the zero points caused by diffraction in the frequency response. We propose a novel idea of image synthesis to compensate for the zero points through two different realizations based on the linear least-mean-square-error (LMSE) estimation. Results from computer simulation and optical experiments verify a nearly two-fold improvement in spatial resolution from the proposed methods compared with the conventional geometrical-optics-based method.