Titlebook: Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging; Mathematical Imaging Ke Chen,Carola-Bibiane Schönlieb,Lauren

Intractable

Convex Non-convex Variational Models,btained by finding a minimizer of an energy function or “model” composed of two terms, the data-fidelity term, and the regularization term. Much research has focused on models where both terms are convex, which leads to convex optimization problems. However, there is evidence that non-convex regular

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Bregman Methods for Large-Scale Optimization with Applications in Imaging,tions. We give an overview on several families of Bregman algorithms and discuss modifications such as accelerated Bregman methods, incremental and stochastic variants, and coordinate descent-type methods. We conclude this chapter with numerical examples in image and video decomposition, image denoi

小丑

吃掉

歌曲

Learned Regularizers for Inverse Problems,ety of approaches have been proposed, showing improvements in reconstruction quality over existing methods. Among those, a class of algorithms builds on the well-established variational framework, training a neural network as a regularization functional. Those approaches come with the advantage of a

Palter

Multiparameter Approaches in Image Processing,dels for image restoration rely on different regularization terms in order to capture the different components of the image in question. While the resulting multipenalty approaches have in principle a greater potential for accurate image reconstructions than single-penalty models, their practical pe

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使纠缠

Modular ADMM-Based Strategies for Optimized Compression, Restoration, and Distributed Representatior computational processes. This approach has been significantly expanded in recent years by iterative designs where explicit solutions of optimization subproblems were replaced by black-box applications of ready-to-use modules for denoising or compression. These modular designs are conceptually simp

cavity

An Overview of SaT Segmentation Methodology and Its Applications in Image Processing,constantly challenging to deliver, particularly, when the given images or data are corrupted by different types of degradations like noise, information loss, and/or blur. In this article, we introduce a segmentation methodology – smoothing and thresholding (SaT) – which can provide a flexible way of

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Data-Informed Regularization for Inverse and Imaging Problems,egularizing the data-informed directions. Our approach is inspired by and has a rigorous root in disintegration theory. We shall, however, present an elementary and constructive path using the classical truncated SVD and Tikhonov regularization methods. Deterministic and statistical properties of th