36 research outputs found
A convex formulation for hyperspectral image superresolution via subspace-based regularization
Hyperspectral remote sensing images (HSIs) usually have high spectral
resolution and low spatial resolution. Conversely, multispectral images (MSIs)
usually have low spectral and high spatial resolutions. The problem of
inferring images which combine the high spectral and high spatial resolutions
of HSIs and MSIs, respectively, is a data fusion problem that has been the
focus of recent active research due to the increasing availability of HSIs and
MSIs retrieved from the same geographical area.
We formulate this problem as the minimization of a convex objective function
containing two quadratic data-fitting terms and an edge-preserving regularizer.
The data-fitting terms account for blur, different resolutions, and additive
noise. The regularizer, a form of vector Total Variation, promotes
piecewise-smooth solutions with discontinuities aligned across the
hyperspectral bands.
The downsampling operator accounting for the different spatial resolutions,
the non-quadratic and non-smooth nature of the regularizer, and the very large
size of the HSI to be estimated lead to a hard optimization problem. We deal
with these difficulties by exploiting the fact that HSIs generally "live" in a
low-dimensional subspace and by tailoring the Split Augmented Lagrangian
Shrinkage Algorithm (SALSA), which is an instance of the Alternating Direction
Method of Multipliers (ADMM), to this optimization problem, by means of a
convenient variable splitting. The spatial blur and the spectral linear
operators linked, respectively, with the HSI and MSI acquisition processes are
also estimated, and we obtain an effective algorithm that outperforms the
state-of-the-art, as illustrated in a series of experiments with simulated and
real-life data.Comment: IEEE Trans. Geosci. Remote Sens., to be publishe
영상 복원 문제의 변분법적 접근
학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2013. 2. 강명주.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
First order algorithms in variational image processing
Variational methods in imaging are nowadays developing towards a quite
universal and flexible tool, allowing for highly successful approaches on tasks
like denoising, deblurring, inpainting, segmentation, super-resolution,
disparity, and optical flow estimation. The overall structure of such
approaches is of the form ; where the functional is a data fidelity term also
depending on some input data and measuring the deviation of from such
and is a regularization functional. Moreover is a (often linear)
forward operator modeling the dependence of data on an underlying image, and
is a positive regularization parameter. While is often
smooth and (strictly) convex, the current practice almost exclusively uses
nonsmooth regularization functionals. The majority of successful techniques is
using nonsmooth and convex functionals like the total variation and
generalizations thereof or -norms of coefficients arising from scalar
products with some frame system. The efficient solution of such variational
problems in imaging demands for appropriate algorithms. Taking into account the
specific structure as a sum of two very different terms to be minimized,
splitting algorithms are a quite canonical choice. Consequently this field has
revived the interest in techniques like operator splittings or augmented
Lagrangians. Here we shall provide an overview of methods currently developed
and recent results as well as some computational studies providing a comparison
of different methods and also illustrating their success in applications.Comment: 60 pages, 33 figure
A Convex Optimization Model and Algorithm for Retinex
Retinex is a theory on simulating and explaining how human visual system perceives colors under different illumination conditions. The main contribution of this paper is to put forward a new convex optimization model for Retinex. Different from existing methods, the main idea is to rewrite a multiplicative form such that the illumination variable and the reflection variable are decoupled in spatial domain. The resulting objective function involves three terms including the Tikhonov regularization of the illumination component, the total variation regularization of the reciprocal of the reflection component, and the data-fitting term among the input image, the illumination component, and the reciprocal of the reflection component. We develop an alternating direction method of multipliers (ADMM) to solve the convex optimization model. Numerical experiments demonstrate the advantages of the proposed model which can decompose an image into the illumination and the reflection components