GPU-optimized matrix method for phase retrieval with the transport of intensity equation

The transport of intensity equation (TIE) facilitates quantitative and deterministic retrieval of the optical phase and has been established as a non-interferometric approach for quantitative phase imaging. However, state-of-the-art methods face limitations in terms of the trade-off between accuracy and execution time. In this work, we propose a GPU-optimized iterative phase retrieval method based on the TIE, called the matrix solution to the TIE (MS-TIE). The MS-TIE employs a matrix formulation in the Fourier domain at each iteration, enabling parallelization of the solution and minimizing the number of operations required. The MS-TIE exhibits improved performance in terms of both accuracy and execution time, particularly demonstrating significant advancements in balancing these aspects in comparison to state-of-the-art methods. Simulations with arbitrary phase and intensity patterns as well as experiments with biological samples, verify the effectiveness of the proposed method.