Adaptive Regularization of Some Inverse Problems in Image Analysis
This work addresses image analysis problems like segmentation and denoising for researchers in computer vision, though it appears incremental as it builds on existing regularization and optimization methods.
The authors tackled inverse problems in image analysis by developing an adaptive regularization scheme that automatically adjusts the trade-off between data fidelity and regularization during optimization, with regularization strongest initially and decreasing as data fit improves. They validated their adaptive Huber-Huber model on synthetic and real images for segmentation, motion estimation, and denoising tasks.
We present an adaptive regularization scheme for optimizing composite energy functionals arising in image analysis problems. The scheme automatically trades off data fidelity and regularization depending on the current data fit during the iterative optimization, so that regularization is strongest initially, and wanes as data fidelity improves, with the weight of the regularizer being minimized at convergence. We also introduce the use of a Huber loss function in both data fidelity and regularization terms, and present an efficient convex optimization algorithm based on the alternating direction method of multipliers (ADMM) using the equivalent relation between the Huber function and the proximal operator of the one-norm. We illustrate and validate our adaptive Huber-Huber model on synthetic and real images in segmentation, motion estimation, and denoising problems.