The Fields of Experts (FoE) image prior model, a filter-based higher-order Markov Random Fields (MRF) model, has been shown to be effective for many image restoration problems. Motivated by the successes of FoE-based approaches, in this letter, we propose a novel variational model for multiplicative noise reduction based on the FoE image prior model. The resulted model corresponds to a non-convex minimization problem, which can be solved by a recently published non-convex optimization algorithm. Experimental results based on synthetic speckle noise and real synthetic aperture radar (SAR) images suggest that the performance of our proposed method is on par with the best published despeckling algorithm. Besides, our proposed model comes along with an additional advantage, that the inference is extremely efficient. {Our GPU based implementation takes less than 1s to produce state-of-the-art despeckling performance.}
We treat an image restoration problem with a Poisson noise chan- nel using a Bayesian framework. The Poisson randomness might be appeared in observation of low contrast object in the field of imaging. The noise observation is often hard to treat in a theo- retical analysis. In our formulation, we interpret the observation through the Poisson noise channel as a likelihood, and evaluate the bound of it with a Gaussian function using a latent variable method. We then introduce a Gaussian Markov random field (GMRF) as the prior for the Bayesian approach, and derive the posterior as a Gaussian dist…
We propose a Bayesian image super-resolution (SR) method with a causal Gaussian Markov random field (MRF) prior. SR is a technique to estimate a spatially high-resolution image from given multiple low-resolution images. An MRF model with the line process supplies a preferable prior for natural images with edges. We improve the existing image transformation model, the compound MRF model, and its hyperparameter prior model. We also derive the optimal estimator -- not the joint maximum a posteriori (MAP) or marginalized maximum likelihood (ML), but the posterior mean (PM) -- from the objective fu…
Many computer vision problems can be posed as learning a low-dimensional subspace from high dimensional data. The low rank matrix factorization (LRMF) represents a commonly utilized subspace learning strategy. Most of the current LRMF techniques are constructed on the optimization problems using L1-norm and L2-norm losses, which mainly deal with Laplacian and Gaussian noises, respectively. To make LRMF capable of adapting more complex noise, this paper proposes a new LRMF model by assuming noise as Mixture of Exponential Power (MoEP) distributions and proposes a penalized MoEP (PMoEP) model by…
University for Health Sciences, Medical Informatics and Technology (UMIT)（健康科学、医学信息学与技术大学（UMIT））
In this paper, an iterative method for robust deconvolution with positivity constraints is discussed. It is based on the known variational interpretation of the Richardson-Lucy iterative deconvolution as fixed-point iteration for the minimisation of an information divergence functional under a multiplicative perturbation model. The asymmetric penaliser function involved in this functional is then modified into a robust penaliser, and complemented with a regulariser. The resulting functional gives rise to a fixed point iteration that we call robust and regularised Richardson-Lucy deconvolution.…
Variational Deep Unfolding with Mamba-Based Nonlocal Modeling for Underwater Image Enhancement
Institute of Applied Computing and Community Code (IAC3)（应用计算与社区代码研究所 (IAC3)）；Dept. of Mathematics and Computer Science, Universitat de les Illes Balears（巴利阿里群岛大学数学与计算机科学系）
University of Cambridge（剑桥大学）；CNRS（法国国家科学研究中心）；Université Côte d’Azur（蔚蓝海岸大学）；INRIA（法国国家信息与自动化研究所）；Univ. Bordeaux（波尔多大学）；Bordeaux INP（波尔多国立理工学院）；LaBRI（波尔多计算机科学研究所）；IMB（波尔多数学研究所）
We propose a new variational model for non-linear image fusion. Our approach is based on the use of an osmosis energy term related to the one studied in Vogel et al. (2013) and Weickert et al. (2013) The minimization of the proposed non-convex energy realizes visually plausible image data fusion, invariant to multiplicative brightness changes. On the practical side, it requires minimal supervision and parameter tuning and can encode prior information on the structure of the images to be fused. For the numerical solution of the proposed model, we develop a primal-dual algorithm and we apply the…
To adopt neural networks in safety critical domains, knowing whether we can trust their predictions is crucial. Bayesian neural networks (BNNs) provide uncertainty estimates by averaging predictions with respect to the posterior weight distribution. Variational inference methods for BNNs approximate the intractable weight posterior with a tractable distribution, yet mostly rely on sampling from the variational distribution during training and inference. Recent sampling-free approaches offer an alternative, but incur a significant parameter overhead. We here propose a more efficient parameteriz…
Brown University（布朗大学）；Alpen-Adria Universität Klagenfurt（阿尔卑斯-亚德里亚克拉根福大学）
We consider image denoising problems formulated as variational problems. It is known that Hamilton-Jacobi PDEs govern the solution of such optimization problems when the noise model is additive. In this work, we address certain non-additive noise models and show that they are also related to Hamilton-Jacobi PDEs. These findings allow us to establish new connections between additive and non-additive noise imaging models. Specifically, we study how the solutions to these optimization problems depend on the parameters and the observed images. We show that the optimal values are ruled by some Hami…
Third Military Medical University（第三军医大学）；National University of Defense Technology（国防科学技术大学）
Solving an optimization problem whose objective function is the sum of two convex functions has received considerable interests in the context of image processing recently. In particular, we are interested in the scenario when a non-differentiable convex function such as the total variation (TV) norm is included in the objective function due to many variational models established in image processing have this nature. In this paper, we propose a fast fixed point algorithm based on the quasi-Newton method for solving this class of problem, and apply it in the field of TV-based image deblurring. …
University of Science and Technology Beijing（北京科技大学）；Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；Graz University of Technology（格拉茨工业大学）
Poisson denoising is an essential issue for various imaging applications, such as night vision, medical imaging and microscopy. State-of-the-art approaches are clearly dominated by patch-based non-local methods in recent years. In this paper, we aim to propose a local Poisson denoising model with both structure simplicity and good performance. To this end, we consider a variational modeling to integrate the so-called Fields of Experts (FoE) image prior, that has proven an effective higher-order Markov Random Fields (MRF) model for many classic image restoration problems. We exploit several fea…
Fast Linearized Alternating Direction Minimization Algorithm with Adaptive Parameter Selection for Multiplicative Noise Removal
Department of Mathematics, Third Military Medical University, Chongqing 400038, Chongqing, People's Republic of China（数学系，第三军医大学）；Department of Mathematics and System, School of Sciences, National University of Defense Technology, Changsha 410073, Hunan, People's Republic of China（数学与系统系，国防科技大学）
Additive or multiplicative stationary noise recently became an important issue in applied fields such as microscopy or satellite imaging. Relatively few works address the design of dedicated denoising methods compared to the usual white noise setting. We recently proposed a variational algorithm to tackle this issue. In this paper, we analyze this problem from a statistical point of view and provide deterministic properties of the solutions of the associated variational problems. In the first part of this work, we demonstrate that in many practical problems, the noise can be assimilated to a c…
While 3D reconstruction is a well-established and widely explored research topic, semantic 3D reconstruction has only recently witnessed an increasing share of attention from the Computer Vision community. Semantic annotations allow in fact to enforce strong class-dependent priors, as planarity for ground and walls, which can be exploited to refine the reconstruction often resulting in non-trivial performance improvements. State-of-the art methods propose volumetric approaches to fuse RGB image data with semantic labels; even if successful, they do not scale well and fail to output high resolu…
We introduce a novel geometric approach to the image labeling problem. Abstracting from specific labeling applications, a general objective function is defined on a manifold of stochastic matrices, whose elements assign prior data that are given in any metric space, to observed image measurements. The corresponding Riemannian gradient flow entails a set of replicator equations, one for each data point, that are spatially coupled by geometric averaging on the manifold. Starting from uniform assignments at the barycenter as natural initialization, the flow terminates at some global maximum, each…
