3D Tomographic Phase Microscopy Image Reconstruction With Total Variation Regularization Constraint

Optical microscopy plays an essential role in the microcosmic study. Tomographic phase microscopy (TPM) is a novel optical measuring method which allows the 3D determination of refractive index quantitatively with measurement of projections of refractive index in multiple directions by a phase-shifting heterodyne interferometer, in analogy to computed X-ray tomography. Numerous biological samples, including live cells, are quite transparent under visible-light illumination and behave essentially as phase objects. So they are difficult to be imaged by measuring absorption properties in traditional optical microscopy. The refractive index distribution among organelles reveals unique morphological characteristics of cells, which has potential to serve as intrinsic contrast. The phase delay of the measuring light caused by the index distribution is used in the reconstruction in TPM, which improve the resolution of the reconstruction. TPM is also a Contrast-agent-free microscopy.The traditional reconstruction methods fall into two main categories. One is the filtered back-projection (FBP) algorithm which regards the phase of the transmitted field as the line integral of refractive index. The other takes the diffraction into account and adopts Born or Rytov approximation to make the relation linear between the refractive index of sample and the measured field in frequency domain, known as Fourier diffraction theorem and then the direct fourier (DF) algorithm is adopted in the reconstruction. There are some disadvantages in the traditional methods. Firstly, these algorithms are too sensitive to noises in the measurements. Secondly, previous methods often produce reconstructed images that have blurry edges. Thirdly, the number of total illumination angles should be large enough for optimum image quality.To overcome the backwards of the traditional reconstruction methods, a novel total variation (TV) based reconstruction method is proposed. TV is widely used in the image reconstruction, which performed successfully in smoothing away noisy textures while preserving edges and images reconstruction from sparse datum. Experimental results on synthetic and real measurements provide insights into the superior ability and performance of this strategy.The main contribution of this paper is:(1) A reconstruction model of TV-L2 is used in the tomographic reconstruction by incorporating total variation into the direct fourier (DF) algorithm.(2) To simplify the minimization scheme, alternating direction method of multipliers (ADMM) is utilized and the Barzilai—Borwein stepsize selection method is also adopted in the algorithm for much faster convergence.(3) Experiments on synthetic and real datum demonstrated the superior ability of the proposed method.