Piecewise Planar Image Restoration via Gradient Graph Laplacian Regularizer

Images in various practical applications often exhibit Piecewise Planar (PWP) characteristics. Common issues such as noise, blur, and distortions arise from sensor limitations, transmission errors, and environmental factors like lighting and sensor quality. Despite advancements in image restoration, significant challenges remain under conditions of poor lighting, camera movement, and occlusions, making PWP image restoration a critical research area. This thesis investigates the restoration of PWP images, focusing on efficiently overcoming these challenges and enhancing image quality in two real-world applications: (i) depth image denoising and (ii) low-light image contrast enhancement. We formulate quadratic objectives regularized by Graph Laplacian Regularizer and Gradient Graph Laplacian Regularizer, tailored for these two applications. These objectives can be efficiently solved in linear time using a conjugate gradient solver and the alternating direction method of multipliers. Experimental results demonstrate that our algorithm achieves competitive image quality while significantly reducing computational complexity.