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

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Convex Non-convex Variational Modelsbtained 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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Fast Iterative Algorithms for Blind Phase Retrieval: A Surveye one has to recover both the sample and the probe (pupil) jointly from phaseless data. This survey first presents the mathematical formula of BPR and related nonlinear optimization problems and then gives a brief review of the recent iterative algorithms. It mainly consists of three types of algori

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Modular ADMM-Based Strategies for Optimized Compression, Restoration, and Distributed Representationr 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

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Connecting Hamilton-Jacobi Partial Differential Equations with Maximum a Posteriori and Posterior Mely consist of minimizing the sum of a data fidelity and regularization terms. In Darbon (SIAM J. Imag. Sci. 8:2268–2293, 2015), Darbon and Meng, (On decomposition models in imaging sciences and multi-time Hamilton-Jacobi partial differential equations, arXiv preprint arXiv:1906.09502, 2019), connect

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Multi-modality Imaging with Structure-Promoting Regularizersy diagnosis of cancer and dementia is PET-MR, a combined positron emission tomography and magnetic resonance imaging scanner which can simultaneously acquire functional and anatomical data. Similarly, in remote sensing, while hyperspectral sensors may allow to characterize and distinguish materials,

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Diffraction Tomography, Fourier Reconstruction, and Full Waveform Inversionial properties of an object by illuminating it with probing waves and recording the scattered waves. Conventional DT relies on the Fourier diffraction theorem, which is applicable under the condition of weak scattering. However, if the object has high contrasts or is too large compared to the wavele

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Models for Multiplicative Noise Removalct recognition, digital entertainment, etc. The digital image can be corrupted with noise during acquisition, storage, and transmission. Noise can be classified as additive noise, multiplicative noise, and non-additive non-multiplicative noise (such as salt and pepper noise, Poisson noise). The main

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