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294 results on '"Vese, Luminita"'

1. Applications of multiscale hierarchical decomposition to blind deconvolution

Author

Wolf, Tobias, Kindermann, Stefan, Resmerita, Elena, and Vese, Luminita

Subjects
Mathematics - Numerical Analysis
Abstract

The blind image deconvolution is a challenging, highly ill-posed nonlinear inverse problem. We introduce a Multiscale Hierarchical Decomposition Method (MHDM) that is iteratively solving variational problems with adaptive data and regularization parameters, towards obtaining finer and finer details of the unknown kernel and image. We establish convergence of the residual in the noise-free data case, and then in the noisy data case when the algorithm is stopped early by means of a discrepancy principle. Fractional Sobolev norms are employed as regularizers for both kernel and image, with the advantage of computing the minimizers explicitly in a pointwise manner. In order to break the notorious symmetry occurring during each minimization step, we enforce a positivity constraint on the Fourier transform of the kernels. Numerical comparisons with a single-step variational method and a non-blind MHDM show that our approach produces comparable results, while less laborious parameter tuning is necessary at the price of more computations. Additionally, the scale decomposition of both reconstructed kernel and image provides a meaningful interpretation of the involved iteration steps.

Published
2024

2. Multiscale hierarchical decomposition methods for images corrupted by multiplicative noise

Author

Barnett, Joel, Li, Wen, Resmerita, Elena, and Vese, Luminita

Subjects
Mathematics - Numerical Analysis
Abstract

Recovering images corrupted by multiplicative noise is a well known challenging task. Motivated by the success of multiscale hierarchical decomposition methods (MHDM) in image processing, we adapt a variety of both classical and new multiplicative noise removing models to the MHDM form. On the basis of previous work, we further present a tight and a refined version of the corresponding multiplicative MHDM. We discuss existence and uniqueness of solutions for the proposed models, and additionally, provide convergence properties. Moreover, we present a discrepancy principle stopping criterion which prevents recovering excess noise in the multiscale reconstruction. Through comprehensive numerical experiments and comparisons, we qualitatively and quantitatively evaluate the validity of all proposed models for denoising and deblurring images degraded by multiplicative noise. By construction, these multiplicative multiscale hierarchical decomposition methods have the added benefit of recovering many scales of an image, which can provide features of interest beyond image denoising.

Published
2023

5. Multiscale Registration

Author

Debroux, Noémie, Le Guyader, Carole, Vese, Luminita A., Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Woeginger, Gerhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Elmoataz, Abderrahim, editor, Fadili, Jalal, editor, Quéau, Yvain, editor, Rabin, Julien, editor, and Simon, Loïc, editor

Published
2021
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6. Nonlocal Adaptive Biharmonic Regularizer for Image Restoration

Author

Wen, Ying, Vese, Luminita A., Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Woeginger, Gerhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Bebis, George, editor, Yin, Zhaozheng, editor, Kim, Edward, editor, Bender, Jan, editor, Subr, Kartic, editor, Kwon, Bum Chul, editor, Zhao, Jian, editor, Kalkofen, Denis, editor, and Baciu, George, editor

Published
2020
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7. Inverse Problems in Mathematical Imaging with Applications in Multiplicative Noise Removal, Remotely Sensed Atmospheric Wind Velocity Estimation, and Turbulent Fluid Simulation

Author

Barnett, Joel, Bertozzi, Andrea1, Vese, Luminita Aura, Barnett, Joel, Barnett, Joel, Bertozzi, Andrea1, Vese, Luminita Aura, and Barnett, Joel

Abstract

This thesis considers three inverse problems originating in mathematical imaging, remote sensing and simulation. First, it addresses a challenging image processing task: recovering images corrupted by multiplicative noise. Motivated by the success of multiscale hierarchical decomposition methods (MHDM) in image processing, a variety of both classical and new multiplicative noise removing models are adapted to the MHDM form. On the basis of previous work, tight and refined extensions of the multiplicative MHDM process are proposed. Existence and uniqueness of solutions for the proposed models is discussed, in addition to convergence properties. Moreover, the work introduces a discrepancy principle stopping criterion which prevents recovering excess noise in the multiscale reconstruction. The validity of all the proposed models is qualitatively and quantitatively evaluated through comprehensive numerical experiments and comparisons across several images degraded by multiplicative noise. By construction, these multiplicative multiscale hierarchical decomposition methods have the added benefit of recovering many scales of an image, which can provide features of interest beyond image denoising. Second, this work considers an applied mathematical imaging problem in remote sensing. Accurate estimation of atmospheric wind velocity plays an important role in weather forecasting, flight safety assessment and cyclone tracking. Atmospheric data captured by infrared and microwave satellite instruments provide global coverage for weather analysis. Extracting wind velocity fields from such data has traditionally been done through feature tracking, correlation/matching or optical flow means from computer vision. However, these recover either sparse velocity estimates, oversmooth details or are designed for quasi-rigid body motions which over-penalize vorticity and divergence within the often turbulent weather systems. This thesis proposes a texture based optical flow procedure tail

Published
2024

9. Image Processing Variations with Analytic Kernels

Author

Garnett, John B., Le, Triet M., and Vese, Luminita A.

Subjects
Mathematics - Analysis of PDEs
Abstract

Let $f\in L^1(\R^d)$ be real. The Rudin-Osher-Fatemi model is to minimize $\|u\|_{\dot{BV}}+\lambda\|f-u\|_{L^2}^2$, in which one thinks of $f$ as a given image, $\lambda > 0$ as a "tuning parameter", $u$ as an optimal "cartoon" approximation to $f$, and $f-u$ as "noise" or "texture". Here we study variations of the R-O-F model having the form $\inf_u\{\|u\|_{\dot{BV}}+\lambda \|K*(f-u)\|_{L^p}^q\}$ where $K$ is a real analytic kernel such as a Gaussian. For these functionals we characterize the minimizers $u$ and establish several of their properties, including especially their smoothness properties. In particular we prove that on any open set on which $u \in W^{1,1}$ and $\nabla u \neq 0$ almost every level set $\{u =c\}$ is a real analytic surface. We also prove that if $f$ and $K$ are radial functions then every minimizer $u$ is a radial step function., Comment: 18 pages

Published
2012

10. Learning spatial response functions from large multi-sensor AIRS and MODIS datasets

Author

Vese, Luminita, Aumann, Hartmut, Broberg, Steven, Manning, Evan, Pagano, Thomas, and Yanovsky, Igor

Abstract

We use large datasets from the Atmospheric Infrared Sounder (AIRS) and the Moderate Resolution Imaging Spectroradiometer (MODIS) to derive AIRS spatial response functions and study their potential variations over the mission. The new reconstructed spatial response functions can be used to reduce errors in the radiances in non-uniform scenes and improve products generated using both AIRS and MODIS data. AIRS spatial response functions are distinct for each of its 2378 channels and each of its 90 scan angles. We develop the mathematical model and the optimization framework for deriving spatial response functions for two AIRS channels with low water vapor absorption and various scan angles. We quantify uncertainties in the derived reconstructions and study how they differ from pre-flight spatial response functions. We show that our approach generates reconstructions that agree with the data more accurately compared to pre-flight spatial responses. We derive spatial response functions using data collected during successive dates in order to ascertain the repeatability of the reconstructed spatial response functions. We also compare the derived spatial response functions based on data collected in the beginning, the middle, and at the current state of the mission in order to study changes in reconstructions over time.

Published
2021

14. Mathematical Modeling of Textures: Application to Color Image Decomposition with a Projected Gradient Algorithm

Author

Duval, Vincent, Aujol, Jean-François, and Vese, Luminita A.

Subjects
Computer Science, Control , Robotics, Mechatronics, Artificial Intelligence (incl. Robotics), Image Processing and Computer Vision, Computer Imaging, Vision, Pattern Recognition and Graphics, Texture modeling, Color image decomposition, Projected gradient algorithm, Color texture modeling
Abstract

In this paper, we are interested in texture modeling with functional analysis spaces. We focus on the case of color image processing, and in particular color image decomposition. The problem of image decomposition consists in splitting an original image f into two components u and v. u should contain the geometric information of the original image, while v should be made of the oscillating patterns of f, such as textures. We propose here a scheme based on a projected gradient algorithm to compute the solution of various decomposition models for color images or vector-valued images. We provide a direct convergence proof of the scheme, and we give some analysis on color texture modeling.

Published
2010

17. A Technique for Lung Nodule Candidate Detection in CT Using Global Minimization Methods

Author

Duggan, Nóirín, Bae, Egil, Shen, Shiwen, Hsu, William, Bui, Alex, Jones, Edward, Glavin, Martin, Vese, Luminita, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Kobsa, Alfred, Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Tai, Xue-Cheng, editor, Bae, Egil, editor, Chan, Tony F., editor, and Lysaker, Marius, editor

Published
2015
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21. A Variational Model for the Restoration of MR Images Corrupted by Blur and Rician Noise

Author

Getreuer, Pascal, Tong, Melissa, Vese, Luminita A., Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Bebis, George, editor, Boyle, Richard, editor, Parvin, Bahram, editor, Koracin, Darko, editor, Wang, Song, editor, Kyungnam, Kim, editor, Benes, Bedrich, editor, Moreland, Kenneth, editor, Borst, Christoph, editor, DiVerdi, Stephen, editor, Yi-Jen, Chiang, editor, and Ming, Jiang, editor

Published
2011
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22. Registration for 3D Morphological Comparison of Brain Aneurysm Growth

Author

Lederman, Carl, Vese, Luminita, Chien, Aichi, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Bebis, George, editor, Boyle, Richard, editor, Parvin, Bahram, editor, Koracin, Darko, editor, Wang, Song, editor, Kyungnam, Kim, editor, Benes, Bedrich, editor, Moreland, Kenneth, editor, Borst, Christoph, editor, DiVerdi, Stephen, editor, Yi-Jen, Chiang, editor, and Ming, Jiang, editor

Published
2011
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23. EM+TV Based Reconstruction for Cone-Beam CT with Reduced Radiation

Author

Yan, Ming, Chen, Jianwen, Vese, Luminita A., Villasenor, John, Bui, Alex, Cong, Jason, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Bebis, George, editor, Boyle, Richard, editor, Parvin, Bahram, editor, Koracin, Darko, editor, Wang, Song, editor, Kyungnam, Kim, editor, Benes, Bedrich, editor, Moreland, Kenneth, editor, Borst, Christoph, editor, DiVerdi, Stephen, editor, Yi-Jen, Chiang, editor, and Ming, Jiang, editor

Published
2011
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25. An Iterative Method with General Convex Fidelity Term for Image Restoration

Author

Jung, Miyoun, Resmerita, Elena, Vese, Luminita, Hutchison, David, Kanade, Takeo, Kittler, Josef, Kleinberg, Jon M., Mattern, Friedemann, Mitchell, John C., Naor, Moni, Nierstrasz, Oscar, Pandu Rangan, C., Steffen, Bernhard, Sudan, Madhu, Terzopoulos, Demetri, Tygar, Doug, Vardi, Moshe Y., Weikum, Gerhard, Daniilidis, Kostas, editor, Maragos, Petros, editor, and Paragios, Nikos, editor

Published
2010
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26. Nonlinear Elasticity Registration and Sobolev Gradients

Author

Lin, Tungyou, Dinov, Ivo, Toga, Arthur, Vese, Luminita, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Fischer, Bernd, editor, Dawant, Benoît M., editor, and Lorenz, Cristian, editor

Published
2010
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28. Color Image Restoration Using Nonlocal Mumford-Shah Regularizers

Author

Jung, Miyoun, Bresson, Xavier, Chan, Tony F., Vese, Luminita A., Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Cremers, Daniel, editor, Boykov, Yuri, editor, Blake, Andrew, editor, and Schmidt, Frank R., editor

Published
2009
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29. HARDI Denoising: Variational Regularization of the Spherical Apparent Diffusion Coefficient sADC

Author

Kim, Yunho, Thompson, Paul M., Toga, Arthur W., Vese, Luminita, Zhan, Liang, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Prince, Jerry L., editor, Pham, Dzung L., editor, and Myers, Kyle J., editor

Published
2009
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30. A Combined Segmentation and Registration Framework with a Nonlinear Elasticity Smoother

Author

Le Guyader, Carole, Vese, Luminita A., Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Tai, Xue-Cheng, editor, Mørken, Knut, editor, Lysaker, Marius, editor, and Lie, Knut-Andreas, editor

Published
2009
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31. Nonlocal Variational Image Deblurring Models in the Presence of Gaussian or Impulse Noise

Author

Jung, Miyoun, Vese, Luminita A., Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Tai, Xue-Cheng, editor, Mørken, Knut, editor, Lysaker, Marius, editor, and Lie, Knut-Andreas, editor

Published
2009
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32. Projected Gradient Based Color Image Decomposition

Author

Duval, Vincent, Aujol, Jean-François, Vese, Luminita, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Tai, Xue-Cheng, editor, Mørken, Knut, editor, Lysaker, Marius, editor, and Lie, Knut-Andreas, editor

Published
2009
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34. Energy Minimization Based Segmentation and Denoising Using a Multilayer Level Set Approach

Author

Chung, Ginmo, Vese, Luminita A., Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Dough, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Rangarajan, Anand, editor, Vemuri, Baba, editor, and Yuille, Alan L., editor

Published
2005
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38. An Active Contour Model without Edges

Author

Chan, Tony, Vese, Luminita, Goos, Gerhard, editor, Hartmanis, Juris, editor, van Leeuwen, Jan, editor, Nielsen, Mads, editor, Johansen, Peter, editor, Olsen, Ole Fogh, editor, and Weickert, Joachim, editor

Published
1999
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47. Some variational problems from image processing

Author

Garnett, John B., Le, Triet M., Vese, Luminita A., and Universitat Autònoma de Barcelona. Centre de Recerca Matemàtica

Subjects
Variables (Matemàtica), Imatges Processament
Abstract

"Vegeu el resum a l'inici del document del fitxer adjunt".

Published
2021

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