Regularized deconvolution for structured illumination microscopy via accelerated linearized ADMM

• Published in: Optics and laser technology 2024-02, Vol.169, p.110119, Article 110119
• Main Authors: Xu, Yueshu, Sun, Yile, Wu, Hanmeng, Cao, Wen, Bai, Ling, Tao, Siwei, Tian, Zonghan, Cui, Yudong, Hao, Xiang, Kuang, Cuifang, Liu, Xu
• Format: Article
• Language: English
• Subjects: Accelerated linearized alternating direction method of multipliers; Deconvolution; Regularization; Richardson-Lucy algorithm; Structured illumination microscopy
• ISSN: 0030-3992; 1879-2545
• DOI: 10.1016/j.optlastec.2023.110119

•To overcome the ill-posedness of the inverse deconvolution for SIM, 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 can effectively suppress noise and improve the resolution and contrast of the recovered SIM image. AL-ADMM can efficiently extract higher-frequency information beyond the microscope optical transfer function for the corrupted SIM images.•For imaging condition with high-level noises, AL-ADMM could still achieve an 49% resolution improvement on the basis of SIM deconvolved by Wiener filter, which is significantly superior to RL deconvolution (∼23%). Further, remarkable enhancement has also been made in image contrast, SNR and artifact elimination.•As a computational deconvolution method, AL-ADMM could be extended to more imaging systems, such as the classic confocal microscopy, Airyscan microscopy, STED and light-sheet microscopy. Additionally, by introducing deep-learning strategy to AL-ADMM, higher resolution and image SNR could be accessible without any hardware modification in near future. 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.