Application of the sequential quadratic programming algorithm for reconstructing the distribution of optical...

Area of Science:

• Optics and Photonics
• Computational Physics
• Biomedical Imaging

Background:

• Accurate optical parameter reconstruction is crucial for applications like biomedical imaging.
• The time-domain radiative transfer equation (TD-RTE) is a fundamental model for light transport.
• Ill-posed inverse problems in optical imaging require robust solution strategies.

Purpose of the Study:

• To develop an efficient and accurate method for reconstructing optical parameters.
• To apply sequential quadratic programming (SQP) for solving inverse problems governed by the TD-RTE.
• To incorporate regularization techniques to handle the ill-posed nature of the problem.

Main Methods:

• Utilized the time-domain radiative transfer equation (TD-RTE) as a forward model.
• Employed sequential quadratic programming (SQP) as the core optimization algorithm.
• Calculated the objective function gradient using an efficient adjoint equation technique.
• Implemented a generalized Gaussian Markov random field (GGMRF) model for regularization.

Main Results:

• The proposed reconstruction scheme demonstrated high computational efficiency.
• Accurate reconstruction of optical parameters was achieved through simulated data.
• The SQP algorithm effectively solved the inverse problem.
• GGMRF regularization successfully addressed the ill-posed nature of the problem.

Conclusions:

• The combined approach of SQP and TD-RTE provides an efficient and accurate method for optical parameter reconstruction.
• Adjoint equation techniques enhance computational performance.
• GGMRF regularization is effective in stabilizing inverse problems in optical imaging.