Lensless imaging eliminates the need for geometric isomorphism between a scene and an image while allowing the construction of compact, lightweight imaging systems. However, a challenging inverse problem remains due to the low reconstructed signal-to-noise ratio. Current implementations require multiple masks or multiple shots to denoise the reconstruction. We propose single-shot lensless imaging with a Fresnel zone aperture and incoherent illumination. By using the Fresnel zone aperture to encode the incoherent rays in wavefront-like form, the captured pattern has the same form as the inline hologram. Since conventional backpropagation reconstruction is troubled by the twin-image problem, we show that the compressive sensing algorithm is effective in removing this twin-image artifact due to the sparsity in natural scenes. The reconstruction with a significantly improved signal-to-noise ratio from a single-shot image promotes a camera architecture that is flat and reliable in its structure and free of the need for strict calibration.