134 research outputs found
Restoration of Poissonian Images Using Alternating Direction Optimization
Much research has been devoted to the problem of restoring Poissonian images,
namely for medical and astronomical applications. However, the restoration of
these images using state-of-the-art regularizers (such as those based on
multiscale representations or total variation) is still an active research
area, since the associated optimization problems are quite challenging. In this
paper, we propose an approach to deconvolving Poissonian images, which is based
on an alternating direction optimization method. The standard regularization
(or maximum a posteriori) restoration criterion, which combines the Poisson
log-likelihood with a (non-smooth) convex regularizer (log-prior), leads to
hard optimization problems: the log-likelihood is non-quadratic and
non-separable, the regularizer is non-smooth, and there is a non-negativity
constraint. Using standard convex analysis tools, we present sufficient
conditions for existence and uniqueness of solutions of these optimization
problems, for several types of regularizers: total-variation, frame-based
analysis, and frame-based synthesis. We attack these problems with an instance
of the alternating direction method of multipliers (ADMM), which belongs to the
family of augmented Lagrangian algorithms. We study sufficient conditions for
convergence and show that these are satisfied, either under total-variation or
frame-based (analysis and synthesis) regularization. The resulting algorithms
are shown to outperform alternative state-of-the-art methods, both in terms of
speed and restoration accuracy.Comment: 12 pages, 12 figures, 2 tables. Submitted to the IEEE Transactions on
Image Processin
Multiplicative Noise Removal Using Variable Splitting and Constrained Optimization
Multiplicative noise (also known as speckle noise) models are central to the
study of coherent imaging systems, such as synthetic aperture radar and sonar,
and ultrasound and laser imaging. These models introduce two additional layers
of difficulties with respect to the standard Gaussian additive noise scenario:
(1) the noise is multiplied by (rather than added to) the original image; (2)
the noise is not Gaussian, with Rayleigh and Gamma being commonly used
densities. These two features of multiplicative noise models preclude the
direct application of most state-of-the-art algorithms, which are designed for
solving unconstrained optimization problems where the objective has two terms:
a quadratic data term (log-likelihood), reflecting the additive and Gaussian
nature of the noise, plus a convex (possibly nonsmooth) regularizer (e.g., a
total variation or wavelet-based regularizer/prior). In this paper, we address
these difficulties by: (1) converting the multiplicative model into an additive
one by taking logarithms, as proposed by some other authors; (2) using variable
splitting to obtain an equivalent constrained problem; and (3) dealing with
this optimization problem using the augmented Lagrangian framework. A set of
experiments shows that the proposed method, which we name MIDAL (multiplicative
image denoising by augmented Lagrangian), yields state-of-the-art results both
in terms of speed and denoising performance.Comment: 11 pages, 7 figures, 2 tables. To appear in the IEEE Transactions on
Image Processing
Learning dependent sources using mixtures of Dirichlet: applications on hyperspectral unmixing
This paper is an elaboration of the DECA algorithm [1] to blindly unmix hyperspectral data. The underlying mixing model is linear, meaning that each pixel is a linear mixture of the endmembers signatures weighted by the correspondent abundance fractions. The proposed method, as DECA, is tailored to highly mixed mixtures in which the geometric based approaches fail to identify the simplex of minimum volume enclosing the observed spectral vectors. We resort then to a statitistical framework, where the abundance fractions are modeled as mixtures of Dirichlet densities, thus enforcing the constraints on abundance fractions imposed by the acquisition process, namely non-negativity and constant sum.
With respect to DECA, we introduce two improvements: 1) the number of Dirichlet modes are inferred based on the minimum description length (MDL) principle; 2) The generalized expectation maximization (GEM) algorithm we adopt to infer the model parameters is improved by using alternating minimization and augmented Lagrangian methods to compute the mixing matrix. The effectiveness of the proposed algorithm is illustrated with simulated and read data
Classificação não-supervisionada de dados hiperespectrais usando análise em componentes independentes
No passado recente foram desenvolvidas v árias t écnicas para classi ca ção de dados hiperspectrais.
Uma abordagem tà pica consiste em considerar que cada pixel e uma mistura linear das reflectancias espectrais dos elementos presentes na c élula de resolu ção, adicionada de ru Ãdo. Para classifi car e estimar os elementos presentes numa imagem hiperespectral, v ários problemas se colocam: Dimensionalidade dos dados, desconhecimento dos elementos presentes e a variabilidade da reflectância destes. Recentemente foi proposta a An álise em Componentes Independentes,para separa ção de misturas lineares. Nesta comunica ção apresenta-se uma metodologia baseada na An álise em Componentes Independentes para detec ção dos elementos presentes em imagens hiperespectrais e estima ção das suas quantidades. Apresentam-se resultados desta metodologia com dados simulados e com dados hiperespectrais reais, ilustrando a potencialidade da t écnica
Estimação do subespaço de sinal em dados hiperespectrais
A redução de dimensionalidade é uma tarefa crucial no processamento e análise de dados hiperespectrais. Esta comunicação propõe um método de estimação do subespaço de sinal baseado no erro quadrático médio. O método consiste em primeiro estimar as matrizes de correlação do sinal e do ruÃdo e em segundo seleccionar o conjunto de vectores próprios que melhor representa o subespaço de sinal. O eficiência deste método é ilustrada em imagens hiperespectrais sintéticas e reais
Scene-adapted plug-and-play algorithm with convergence guarantees
Recent frameworks, such as the so-called plug-and-play, allow us to leverage
the developments in image denoising to tackle other, and more involved,
problems in image processing. As the name suggests, state-of-the-art denoisers
are plugged into an iterative algorithm that alternates between a denoising
step and the inversion of the observation operator. While these tools offer
flexibility, the convergence of the resulting algorithm may be difficult to
analyse. In this paper, we plug a state-of-the-art denoiser, based on a
Gaussian mixture model, in the iterations of an alternating direction method of
multipliers and prove the algorithm is guaranteed to converge. Moreover, we
build upon the concept of scene-adapted priors where we learn a model targeted
to a specific scene being imaged, and apply the proposed method to address the
hyperspectral sharpening problem
Fast Image Recovery Using Variable Splitting and Constrained Optimization
We propose a new fast algorithm for solving one of the standard formulations
of image restoration and reconstruction which consists of an unconstrained
optimization problem where the objective includes an data-fidelity
term and a non-smooth regularizer. This formulation allows both wavelet-based
(with orthogonal or frame-based representations) regularization or
total-variation regularization. Our approach is based on a variable splitting
to obtain an equivalent constrained optimization formulation, which is then
addressed with an augmented Lagrangian method. The proposed algorithm is an
instance of the so-called "alternating direction method of multipliers", for
which convergence has been proved. Experiments on a set of image restoration
and reconstruction benchmark problems show that the proposed algorithm is
faster than the current state of the art methods.Comment: Submitted; 11 pages, 7 figures, 6 table
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