89 research outputs found

    Variational models for multiplicative noise removal

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    학위논문 (박사)-- 서울대학교 대학원 자연과학대학 수리과학부, 2017. 8. 강명주.This dissertation discusses a variational partial differential equation (PDE) models for restoration of images corrupted by multiplicative Gamma noise. The two proposed models are suitable for heavy multiplicative noise which is often seen in applications. First, we propose a total variation (TV) based model with local constraints. The local constraint involves multiple local windows which is related a spatially adaptive regularization parameter (SARP). In addition, convergence analysis such as the existence and uniqueness of a solution is also provided. Second model is an extension of the first one using nonconvex version of the total generalized variation (TGV). The nonconvex TGV regularization enables to efficiently denoise smooth regions, without staircasing artifacts that appear on total variation regularization based models, and to conserve edges and details.1. Introduction 1 2. Previous works 6 2.1 Variational models for image denoising 6 2.2.1 Convex and nonconvex regularizers 6 2.2.2 Variational models for multiplicative noise removal 8 2.2 Proximal linearized alternating direction method of multipliers 10 3. Proposed models 13 3.1 Proposed model 1 :exp TV model with SARP 13 3.1.1 Derivation of our model 13 3.1.2 Proposed TV model with local constraints 16 3.1.3 A SARP algorithm for solving model (3.1.16) 27 3.1.4 Numerical results 32 3.2 Proposed model 2 :exp NTGV model with SARP 51 3.2.1 Proposed NTGV model 51 3.2.2 Updating rule for λ(x)\lambda(x) in (3.2.1) 52 3.2.3 Algorithm for solving the proposed model (3.2.1) 55 3.2.4 Numerical results 62 3.2.5 Selection of parameters 63 3.2.6 Image denoising 65 4. Conclusion 79Docto

    Diffusion-Steered Super-Resolution Image Reconstruction

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    For decades, super-resolution has been a widely applied technique to improve the spatial resolution of an image without hardware modification. Despite the advantages, super-resolution suffers from ill-posedness, a problem that makes the technique susceptible to multiple solutions. Therefore, scholars have proposed regularization approaches as attempts to address the challenge. The present work introduces a parameterized diffusion-steered regularization framework that integrates total variation (TV) and Perona-Malik (PM) smoothing functionals into the classical super-resolution model. The goal is to establish an automatic interplay between TV and PM regularizers such that only their critical useful properties are extracted to well pose the super-resolution problem, and hence, to generate reliable and appreciable results. Extensive analysis of the proposed resolution-enhancement model shows that it can respond well on different image regions. Experimental results provide further evidence that the proposed model outperforms

    A Novel Fractional-Order Variational Approach for Image Restoration Based on Fuzzy Membership Degrees

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    We propose a new fractional-order (space and time) total variation regularized model for multiplicative noise removal in this research article. We use the regularly varying fuzzy membership degrees to characterize the likelihood of a pixel related to edges, texture regions, and flat regions to improve model efficiency. This approach is capable of maintaining edges, textures, and other image information while significantly reducing the blocky effect. We opt for the option of local actions. In order to efficiently find the minimizer of the prescribed energy function, the semi-implicit gradient descent approach is used (which derives the corresponding fractional-order Euler-Lagrange equations). The existence and uniqueness of a solution to the suggested variational model are proved. Experimental results show the efficiency of the suggested model in visual enhancement, preserving details and reducing the blocky effect while extracting noise as well as an increase in the PSNR (dB), SSIM, relative error, and less CPU time(s) comparing to other schemes

    Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches

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    Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher spectral resolution enables material identification via spectroscopic analysis, which facilitates countless applications that require identifying materials in scenarios unsuitable for classical spectroscopic analysis. Due to low spatial resolution of HSCs, microscopic material mixing, and multiple scattering, spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus, accurate estimation requires unmixing. Pixels are assumed to be mixtures of a few materials, called endmembers. Unmixing involves estimating all or some of: the number of endmembers, their spectral signatures, and their abundances at each pixel. Unmixing is a challenging, ill-posed inverse problem because of model inaccuracies, observation noise, environmental conditions, endmember variability, and data set size. Researchers have devised and investigated many models searching for robust, stable, tractable, and accurate unmixing algorithms. This paper presents an overview of unmixing methods from the time of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models are first discussed. Signal-subspace, geometrical, statistical, sparsity-based, and spatial-contextual unmixing algorithms are described. Mathematical problems and potential solutions are described. Algorithm characteristics are illustrated experimentally.Comment: This work has been accepted for publication in IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensin

    Interpretable Hyperspectral AI: When Non-Convex Modeling meets Hyperspectral Remote Sensing

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    Hyperspectral imaging, also known as image spectrometry, is a landmark technique in geoscience and remote sensing (RS). In the past decade, enormous efforts have been made to process and analyze these hyperspectral (HS) products mainly by means of seasoned experts. However, with the ever-growing volume of data, the bulk of costs in manpower and material resources poses new challenges on reducing the burden of manual labor and improving efficiency. For this reason, it is, therefore, urgent to develop more intelligent and automatic approaches for various HS RS applications. Machine learning (ML) tools with convex optimization have successfully undertaken the tasks of numerous artificial intelligence (AI)-related applications. However, their ability in handling complex practical problems remains limited, particularly for HS data, due to the effects of various spectral variabilities in the process of HS imaging and the complexity and redundancy of higher dimensional HS signals. Compared to the convex models, non-convex modeling, which is capable of characterizing more complex real scenes and providing the model interpretability technically and theoretically, has been proven to be a feasible solution to reduce the gap between challenging HS vision tasks and currently advanced intelligent data processing models
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