Abstract
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.
Highlights
The results show that the convergence of the shot phase retrieval (SPR) is almost irrelevant to the object and the SPR can always converge at a high speed
We have demonstrated a method for imaging through scattering media, that is, the least square and semidefinite programming (LSSDP), where the scattering characteristics (SCs) of the scattering media is measured with least square (LS) algorithm and the image reconstruction is accomplished with lift convex optimization by solving an semidefinite programming (SDP) problem
Feasibility and practicality are validated from both simulation and experimentation comparisons with phase-shift interferometry mean square optimization (PSIMSO) and SPR, respectively
Summary
Light suffers from multiple scattering when propagating through heterogeneous media, which is a fundamental problem in practical applications ranging from physics, optics, and biological, to telecommunication and electromagnetism.[1,2,3,4,5,6,7] The presence of scattering media makes the imaging result always a speckle pattern without any recognizable information, rather than the expected object image, limiting the developments of imaging in aforementioned fields. SPR are always lack details, especially the ambiguous profile and low contrast.[14] To address this situation, a method combining least square and semidefinite programming (LSSDP) is proposed for two-dimensional (2-D) imaging through scattering media in this paper. To improve efficiency and quality of image reconstruction when only magnitude of speckle field can be accessible,[18,19,20,21] the SC of media is first estimated through least square (LS) method after establishing a database of known object-and-speckle pairs. Structural similarity (SSIM) index is employed as a performance indicator of the SC estimation and image reconstruction.[19] Simulation and experimentation results validate that the proposed LSSDP outperforms than the PSIMSO and SPR in general.
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