Imaging through scattering media using semidefinite programming

A clear image of an observed object may deteriorate into unrecognizable speckle when encountering heterogeneous scattering media, thus it is necessary to recover the object image from the speckle. A method combining least square and semidefinite programming is proposed, which can be used for imaging through scattering media. The proposed method consists of two main stages, that is, media scattering characteristics (SCs) estimation and image reconstruction. SCs estimation is accomplished through LS concept after establishing a database of known object-and-speckle pairs. Image reconstruction is realized by solving an SDP problem to obtain the product of the unknown object image and its Hermitian transposition. Finally, the unknown object image can be reconstructed by extracting the largest rank-1 component of the product. Structural similarity (SSIM) index is employed as a performance indicator in speckle prediction and image reconstruction. Numerical simulations and physical experiments are performed to verify the feasibility and practicality of the proposed method. Compared with the existing phase shift interferometry mean square optimization method and the single-shot phase retrieval algorithm, the proposed method is the most precise to obtain the best reconstruction results with highest SSIM index value. The work can be used for exploring the potential applications of scattering media, especially for imaging through turbid media in biomedical, scattering property measurement, and optical image encryption.