Nonlinear Deblurring for Low-Light Saturated Image

Single image deblurring has achieved significant progress for natural daytime images. Saturation is a common phenomenon in blurry images, due to the low light conditions and long exposure times. However, conventional linear deblurring methods usually deal with natural blurry images well but result in severe ringing artifacts when recovering low-light saturated blurry images. To solve this problem, we formulate the saturation deblurring problem as a nonlinear model, in which all the saturated and unsaturated pixels are modeled adaptively. Specifically, we additionally introduce a nonlinear function to the convolution operator to accommodate the procedure of the saturation in the presence of the blurring. The proposed method has two advantages over previous methods. On the one hand, the proposed method achieves the same high quality of restoring the natural image as seen in conventional deblurring methods, while also reducing the estimation errors in saturated areas and suppressing ringing artifacts. On the other hand, compared with the recent saturated-based deblurring methods, the proposed method captures the formation of unsaturated and saturated degradations straightforwardly rather than with cumbersome and error-prone detection steps. Note that, this nonlinear degradation model can be naturally formulated into a maximum-a posterioriframework, and can be efficiently decoupled into several solvable sub-problems via the alternating direction method of multipliers (ADMM). Experimental results on both synthetic and real-world images demonstrate that the proposed deblurring algorithm outperforms the state-of-the-art low-light saturation-based deblurring methods.