Regularized deconvolution for structured illumination microscopy via accelerated linearized ADMM

Due to the ill-posedness of the inverse deconvolution for structured illumination microscopy (SIM), the results of Richardson–Lucy algorithm are not ideal in the presence of noise. Here, we propose an accelerated linearized alternating direction method of multipliers (AL-ADMM) method for solving the regularized SIM deconvolution problem. A modification of the generalized inverse is introduced to overcome the large condition number of the convolution operator. This study shows that regularization or priori knowledge can effectively suppress noise and improve the resolution and contrast of the recovered SIM image. Simulations and experiments demonstrate that the proposed algorithm can efficiently extract higher-frequency information beyond the microscope optical transfer function for the corrupted SIM images to achieve computational super-resolution (SR) without hardware modifications.