19 research outputs found
Image Restoration for Remote Sensing: Overview and Toolbox
Remote sensing provides valuable information about objects or areas from a
distance in either active (e.g., RADAR and LiDAR) or passive (e.g.,
multispectral and hyperspectral) modes. The quality of data acquired by
remotely sensed imaging sensors (both active and passive) is often degraded by
a variety of noise types and artifacts. Image restoration, which is a vibrant
field of research in the remote sensing community, is the task of recovering
the true unknown image from the degraded observed image. Each imaging sensor
induces unique noise types and artifacts into the observed image. This fact has
led to the expansion of restoration techniques in different paths according to
each sensor type. This review paper brings together the advances of image
restoration techniques with particular focuses on synthetic aperture radar and
hyperspectral images as the most active sub-fields of image restoration in the
remote sensing community. We, therefore, provide a comprehensive,
discipline-specific starting point for researchers at different levels (i.e.,
students, researchers, and senior researchers) willing to investigate the
vibrant topic of data restoration by supplying sufficient detail and
references. Additionally, this review paper accompanies a toolbox to provide a
platform to encourage interested students and researchers in the field to
further explore the restoration techniques and fast-forward the community. The
toolboxes are provided in https://github.com/ImageRestorationToolbox.Comment: This paper is under review in GRS
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ìŁŒ.Image restoration has been an active research area in image processing and computer vision during the past several decades. We explore variational partial
differential equations (PDE) models in image restoration problem. We start our discussion by reviewing classical models, by which the works of this dissertation are highly motivated. The content of the dissertation is divided
into two main subjects. First topic is on image denoising, where we propose non-convex hybrid total variation model, and then we apply iterative reweighted algorithm to solve the proposed model. Second topic is on image
decomposition, in which we separate an image into structural component and oscillatory component using local gradient constraint.Abstract i
1 Introduction 1
1.1 Image restoration 2
1.2 Brief overview of the dissertation 3
2 Previous works 4
2.1 Image denoising 4
2.1.1 Fundamental model 4
2.1.2 Higher order model 7
2.1.3 Hybrid model 9
2.1.4 Non-convex model 12
2.2 Image decomposition 22
2.2.1 Meyers model 23
2.2.2 Nonlinear filter 24
3 Non-convex hybrid TV for image denoising 28
3.1 Variational model with non-convex hybrid TV 29
3.1.1 Non-convex TV model and non-convex HOTV model 29
3.1.2 The Proposed model: Non-convex hybrid TV model 31
3.2 Iterative reweighted hybrid Total Variation algorithm 33
3.3 Numerical experiments 35
3.3.1 Parameter values 37
3.3.2 Comparison between the non-convex TV model and
the non-convex HOTV model 38
3.3.3 Comparison with other non-convex higher order regularizers 40
3.3.4 Comparison between two non-convex hybrid TV models 42
3.3.5 Comparison with Krishnan et al. [39] 43
3.3.6 Comparison with state-of-the-art 44
4 Image decomposition 59
4.1 Local gradient constraint 61
4.1.1 Texture estimator 62
4.2 The proposed model 65
4.2.1 Algorithm : Anisotropic TV-L2 67
4.2.2 Algorithm : Isotropic TV-L2 69
4.2.3 Algorithm : Isotropic TV-L1 71
4.3 Numerical experiments and discussion 72
5 Conclusion and future works 80
Abstract (in Korean) 92Docto
Détection de changement par fusion d'images de télédétection de résolutions et modalités différentes
La dĂ©tection de changements dans une scĂšne est lâun des problĂšmes les plus complexes en tĂ©lĂ©dĂ©tection. Il sâagit de dĂ©tecter des modifications survenues dans une zone gĂ©ographique donnĂ©e par comparaison dâimages de cette zone acquises Ă diffĂ©rents instants. La comparaison est facilitĂ©e lorsque les images sont issues du mĂȘme type de capteur câest-Ă -dire correspondent Ă la mĂȘme modalitĂ© (le plus souvent optique multi-bandes) et possĂšdent des rĂ©solutions spatiales et spectrales identiques. Les techniques de dĂ©tection de changements non supervisĂ©es sont, pour la plupart, conçues spĂ©cifiquement pour ce scĂ©nario. Il est, dans ce cas, possible de comparer directement les images en calculant la diffĂ©rence de pixels homologues, câest-Ă -dire correspondant au mĂȘme emplacement au sol. Cependant, dans certains cas spĂ©cifiques tels que les situations dâurgence, les missions ponctuelles, la dĂ©fense et la sĂ©curitĂ©, il peut sâavĂ©rer nĂ©cessaire dâexploiter des images de modalitĂ©s et de rĂ©solutions diffĂ©rentes. Cette hĂ©tĂ©rogĂ©nĂ©itĂ© dans les images traitĂ©es introduit des problĂšmes supplĂ©mentaires pour la mise en Ćuvre de la dĂ©tection de changements. Ces problĂšmes ne sont pas traitĂ©s par la plupart des mĂ©thodes de lâĂ©tat de lâart. Lorsque la modalitĂ© est identique mais les rĂ©solutions diffĂ©rentes, il est possible de se ramener au scĂ©nario favorable en appliquant des prĂ©traitements tels que des opĂ©rations de rĂ©Ă©chantillonnage destinĂ©es Ă atteindre les mĂȘmes rĂ©solutions spatiales et spectrales. NĂ©anmoins, ces prĂ©traitements peuvent conduire Ă une perte dâinformations pertinentes pour la dĂ©tection de changements. En particulier, ils sont appliquĂ©s indĂ©pendamment sur les deux images et donc ne tiennent pas compte des relations fortes existant entre les deux images. Lâobjectif de cette thĂšse est de dĂ©velopper des mĂ©thodes de dĂ©tection de changements qui exploitent au mieux lâinformation contenue dans une paire dâimages observĂ©es, sans condition sur leur modalitĂ© et leurs rĂ©solutions spatiale et spectrale. Les restrictions classiquement imposĂ©es dans lâĂ©tat de lâart sont levĂ©es grĂące Ă une approche utilisant la fusion des deux images observĂ©es. La premiĂšre stratĂ©gie proposĂ©e sâapplique au cas dâimages de modalitĂ©s identiques mais de rĂ©solutions diffĂ©rentes. Elle se dĂ©compose en trois Ă©tapes. La premiĂšre Ă©tape consiste Ă fusionner les deux images observĂ©es ce qui conduit Ă une image de la scĂšne Ă haute rĂ©solution portant lâinformation des changements Ă©ventuels. La deuxiĂšme Ă©tape rĂ©alise la prĂ©diction de deux images non observĂ©es possĂ©dant des rĂ©solutions identiques Ă celles des images observĂ©es par dĂ©gradation spatiale et spectrale de lâimage fusionnĂ©e. Enfin, la troisiĂšme Ă©tape consiste en une dĂ©tection de changements classique entre images observĂ©es et prĂ©dites de mĂȘmes rĂ©solutions. Une deuxiĂšme stratĂ©gie modĂ©lise les images observĂ©es comme des versions dĂ©gradĂ©es de deux images non observĂ©es caractĂ©risĂ©es par des rĂ©solutions spectrales et spatiales identiques et Ă©levĂ©es. Elle met en Ćuvre une Ă©tape de fusion robuste qui exploite un a priori de parcimonie des changements observĂ©s. Enfin, le principe de la fusion est Ă©tendu Ă des images de modalitĂ©s diffĂ©rentes. Dans ce cas oĂč les pixels ne sont pas directement comparables, car correspondant Ă des grandeurs physiques diffĂ©rentes, la comparaison est rĂ©alisĂ©e dans un domaine transformĂ©. Les deux images sont reprĂ©sentĂ©es par des combinaisons linĂ©aires parcimonieuses des Ă©lĂ©ments de deux dictionnaires couplĂ©s, appris Ă partir des donnĂ©es. La dĂ©tection de changements est rĂ©alisĂ©e Ă partir de lâestimation dâun code couplĂ© sous condition de parcimonie spatiale de la diffĂ©rence des codes estimĂ©s pour chaque image. LâexpĂ©rimentation de ces diffĂ©rentes mĂ©thodes, conduite sur des changements simulĂ©s de maniĂšre rĂ©aliste ou sur des changements rĂ©els, dĂ©montre les avantages des mĂ©thodes dĂ©veloppĂ©es et plus gĂ©nĂ©ralement de lâapport de la fusion pour la dĂ©tection de changement
Provably robust estimation of modulo 1 samples of a smooth function with applications to phase unwrapping
Consider an unknown smooth function , and
say we are given noisy mod 1 samples of , i.e., , for , where denotes the noise. Given
the samples , our goal is to recover smooth, robust
estimates of the clean samples . We formulate a natural
approach for solving this problem, which works with angular embeddings of the
noisy mod 1 samples over the unit circle, inspired by the angular
synchronization framework. This amounts to solving a smoothness regularized
least-squares problem -- a quadratically constrained quadratic program (QCQP)
-- where the variables are constrained to lie on the unit circle. Our approach
is based on solving its relaxation, which is a trust-region sub-problem and
hence solvable efficiently. We provide theoretical guarantees demonstrating its
robustness to noise for adversarial, and random Gaussian and Bernoulli noise
models. To the best of our knowledge, these are the first such theoretical
results for this problem. We demonstrate the robustness and efficiency of our
approach via extensive numerical simulations on synthetic data, along with a
simple least-squares solution for the unwrapping stage, that recovers the
original samples of (up to a global shift). It is shown to perform well at
high levels of noise, when taking as input the denoised modulo samples.
Finally, we also consider two other approaches for denoising the modulo 1
samples that leverage tools from Riemannian optimization on manifolds,
including a Burer-Monteiro approach for a semidefinite programming relaxation
of our formulation. For the two-dimensional version of the problem, which has
applications in radar interferometry, we are able to solve instances of
real-world data with a million sample points in under 10 seconds, on a personal
laptop.Comment: 68 pages, 32 figures. arXiv admin note: text overlap with
arXiv:1710.1021