Robust image dehazing based on low-rank and sparse decomposition of the degree of polarization

Low signal-to-noise ratio and sparse anomalous interference under non-ideal imaging conditions often lead to inaccurate degree of polarization (DoP) calculations, severely limiting the final performance of polarization dehazing. To address this, this paper proposes a robust image dehazing method based on low-rank sparse decomposition of DoP, achieving high-precision image restoration while controlling the algorithm’s time complexity at the O ( N ) level. First, a low-rank sparse decomposition model incorporating a spectral diagnostic mechanism is constructed. This model dynamically senses local noise patterns using the singular value ratio (SVR) and adaptively switches between truncated singular value decomposition (TSVD) and robust principal component analysis (RPCA) to efficiently remove interference and reconstruct high-fidelity low-rank degree of polarization (LRDoP). Second, a transmittance optimization framework based on both statistical and structural constraints is proposed. This framework collaboratively suppresses distant noise through global gamma mapping and introduces an element-wise maximum fusion mechanism to inject near-field textures, achieving an effective balance between noise reduction and edge preservation. Finally, a two-stage polarization screening mechanism based on LRDoP is designed as an independent physical prior to remove high-brightness interference and accurately locate atmospheric light anchor points. Extensive experimental comparisons with existing state-of-the-art methods show that this method significantly improves dehazing quality, color fidelity, and detail recovery in complex scenes.