The incident light will be scattered away because of the inhomogeneity of refractive index in random scattering media, so the image target cannot be observed directly through random scattering media, and we can only observe the speckle patterns formed by multiply scattering. As a consequence, achieving image reconstruction for speckles through random scattering media is a key issue, where speckle patterns reconstruction method based on the random scattering media transmission matrix is one of the most important methods. However, general reconstruction methods is exceedingly time consuming, because it must obtain the speckle field data before reconstructing, which is a complex process and needs large amount of data. Considering the above problems, an image reconstruction algorithm based on compressed sensing theory is presented. Firstly, according to the nature that the transfer matrix in accordance with the random Gaussian distribution, we regard the transfer matrix of random scattering medium as measurement matrix in compressive sensing. Secondly, the image reconstruction with the speckle pattern can be achieved, which has less related data, in accordance with the compressed sensing (CS) theory. Comparing the reconstruction results based on the whole speckle field and the CS theory found that the novel method can ensure the quality of reconstruction and the same time decrease the reconstruction time and computational complexity. In addition, in the speckle field reconstruction based on compressive sensing theory, three kinds of sparse method are selected, which contain Fourier transform (FT), discrete cosine transform (DCT) and discrete wavelet transform (WT). The results show that wavelet transform has obvious advantages in the random scattering medium imaging based on compressive sensing.

© 2014 Optical Society of America

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