Image Reconstruction Using Variable Exponential Function Regularization for Wide-Field Polarization Modulation Imaging

Polarization modulation imaging technology plays an important role in microscopic super-resolution imaging. However, the specimen medium contains retardancy, while charge-coupled devices may provide discrete under-sampling, and the coupled wavefronts consisting of the polarization state of the light and the anisotropic distribution of the specimen can lead to vectorial phase fitting degradation. Considering that the point spread function (PSF) of the main degradation parts can be regarded as an asymmetric generalized Gaussian distribution with uncertain parameters, an adaptive image reconstruction method is proposed based on variable exponential function regularization. The proposed method concentrates on the diversity of the PSF and uses a variable exponent regularization to improve flexibility of the kernel. Moreover, it can balance image edge preservation and provide staircase artifact suppression, which reduces the over- and under-reconstruction of the microscopic images effectively. By optimizing the Split–Bregman algorithm, we create an efficient method that minimizes the iterative loss function under the premise of achieving high estimation accuracy. Compared with other methods, the experimental results reveal better effectiveness and robustness of the proposed method, with improvements of 18% in the peak signal-to-noise ratio, 21% in the structural similarity index measurement, and 337% in the mean structural similarity index measurement.