Optimizing ADMM and Over-Relaxed ADMM Parameters for Linear Quadratic Problems

The Alternating Direction Method of Multipliers (ADMM) has gained significant attention across a broad spectrum of machine learning applications. Incorporating the over-relaxation technique shows potential for enhancing the convergence rate of ADMM. However, determining optimal algorithmic parameters, including both the associated penalty and relaxation parameters, often relies on empirical approaches tailored to specific problem domains and contextual scenarios. Incorrect parameter selection can significantly hinder ADMM's convergence rate. To address this challenge, in this paper we first propose a general approach to optimize the value of penalty parameter, followed by a novel closed-form formula to compute the optimal relaxation parameter in the context of linear quadratic problems (LQPs). We then experimentally validate our parameter selection methods through random instantiations and diverse imaging applications, encompassing diffeomorphic image registration, image deblurring, and MRI reconstruction.

UID2021: An Underwater Image Dataset for Evaluation of No-reference Quality Assessment Metrics

Achieving subjective and objective quality assessment of underwater images is of high significance in underwater visual perception and image/video processing. However, the development of underwater image quality assessment (UIQA) is limited for the lack of comprehensive human subjective user study with publicly available dataset and reliable objective UIQA metric. To address this issue, we establish a large-scale underwater image dataset, dubbed UID2021, for evaluating no-reference UIQA metrics. The constructed dataset contains 60 multiply degraded underwater images collected from various sources, covering six common underwater scenes (i.e. bluish scene, bluish-green scene, greenish scene, hazy scene, low-light scene, and turbid scene), and their corresponding 900 quality improved versions generated by employing fifteen state-of-the-art underwater image enhancement and restoration algorithms. Mean opinion scores (MOS) for UID2021 are also obtained by using the pair comparison sorting method with 52 observers. Both in-air NR-IQA and underwater-specific algorithms are tested on our constructed dataset to fairly compare the performance and analyze their strengths and weaknesses. Our proposed UID2021 dataset enables ones to evaluate NR UIQA algorithms comprehensively and paves the way for further research on UIQA. Our UID2021 will be a free download and utilized for research purposes at: https://github.com/Hou-Guojia/UID2021.

The Chan-Vese Model with Elastica and Landmark Constraints for Image Segmentation

In order to separate completely the objects with larger occluded boundaries in an image, we devise a new variational level set model for image segmentation combing the recently proposed Chan-Vese-Euler model with elastica and landmark constraints. For computational efficiency, we deign its Augmented Lagrangian Method(ALM) or Alternating Direction Method of Multiplier(ADMM) method by introducing some auxiliary variables, Lagrange multipliers and penalty parameters. In each loop of alternating iterative optimization, the sub-problems of minimization can be solved via simple Gauss-Seidel iterative method, or generalized soft thresholding formulas with projection methods respectively. Numerical experiments show that the proposed model not only can recover larger broken boundaries, but also can improve segmentation efficiency, decrease the dependence of segmentation on tuning parameters and initialization.

Tensor Based Second Order Variational Model for Image Reconstruction

Second order total variation (SOTV) models have advantages for image reconstruction over their first order counterparts including their ability to remove the staircase artefact in the reconstructed image, but they tend to blur the reconstructed image. To overcome this drawback, we introduce a new Tensor Weighted Second Order (TWSO) model for image reconstruction. Specifically, we develop a novel regulariser for the SOTV model that uses the Frobenius norm of the product of the SOTV Hessian matrix and the anisotropic tensor. We then adapt the alternating direction method of multipliers (ADMM) to solve the proposed model by breaking down the original problem into several subproblems. All the subproblems have closed-forms and can thus be solved efficiently. The proposed method is compared with a range of state-of-the-art approaches such as tensor-based anisotropic diffusion, total generalised variation, Euler's elastica, etc. Numerical experimental results of the method on both synthetic and real images from the Berkeley database BSDS500 demonstrate that the proposed method eliminates both the staircase and blurring effects and outperforms the existing approaches for image inpainting and denoising applications.