Traditional underwater polarization imaging methods can only provide clear degree of polarization (DOP) and intensity images of the object but cannot provide images of the polarization state of the object. This paper proposes a method to extract clear object information from turbid water in all four Stokes parameter (I, Q, U, and V) channels by using the full Stokes camera, enabling clear polarization state image reconstruction. The method utilizes multiple images from different angles to construct a low-rank and sparse matrix. Then, by decomposing this matrix into sparse and low-rank components, clear Q, U, and V images (i.e., the full polarization state) can be obtained. Unlike traditional methods that assume the circularly polarized component (V component) to be zero, this method retains V channel information, allowing for circular polarization component measurement. The study successfully reconstructed clear underwater images of samples with inhomogeneous DOP distribution and obtained the clear polarization states of polarizers and fish in the turbid water. The results show that the proposed method can visualize and analyze the object's polarization state quantitatively with high accuracy in turbid water for the first time, potentially extending the applicability of polarization underwater imaging in ocean exploration.