Fresnel aperture coding lensless imaging based on second order total generalized variation image denoising algorithm with alternating direction method of multipliers

Conventional lens-based imaging systems modulate incident rays using a set of lenses and focus these rays onto an imaging plane. A lensless imaging system uses a single mask instead of lenses to project incident rays onto the imaging plane. These rays pass through or are blocked off according to the binary mask pattern. These systems are thin, lightweight, and inexpensive. However, they do not converge the rays, causing the local images corresponding to individual light transmission units to heavily overlap in a global scene, requiring a specific algorithm for decoding. Additionally, diffraction is unavoidable when the holes on the mask are extremely small, which can degrade the imaging quality. To address these difficulties, we propose a decoding algorithm called the second-order total generalized variation image denoising algorithm with the alternating direction method of multipliers (TGV-ADMM) to unwrap the overlapped images rapidly. In addition to providing high decoding speed, the proposed technique can suppress the diffraction from the tiny holes, owing to its conjugated structure. Based on this novel decoding algorithm, a lensless imaging system is proposed, which can handle overlapped and diffracted images with a single random mask. The camera can work beyond the theoretical diffraction limit and tremendously enhance the resolution.