The quantitative phase imaging technique based on the Kramers–Kronig relation is an innovative computational imaging method that does not require iteration and only needs four low-resolution images to achieve a large spatial bandwidth–time product, optimizing imaging performance. Based on this, the method employs polarization-multiplexed LED illumination, with three LED components each covered by 0°/45°/135° polarization filters, providing numerically aperture-matched illumination for the sample. Using Malus's law, the three polarized light fields recorded by the polarization camera are decoupled, allowing us to obtain intensity images of LED illumination from three different angles in a single measurement. The intensity images for each polarization channel are separated and processed, and the spectral subregions of different channels are rotated and shifted to reconstruct the spectrum. Compared to traditional Fourier ptychography and rapid quantitative phase imaging techniques based on the spatial-domain Kramers–Kronig relation, this technology uses single-frame capture to successfully deduce the quantitative phase distribution of samples from intensity information, significantly increasing the frame rate of acquisition and reducing the overall acquisition time. It is highly suitable for dynamic imaging, such as live cell observation, and minimizing the impact of motion artifacts. Because it can provide higher resolution and a broader range of applications, this technology is expected to become an important tool in the fields of biomedical and surface inspection.