670 research outputs found
Collaborative sparse regression using spatially correlated supports - Application to hyperspectral unmixing
This paper presents a new Bayesian collaborative sparse regression method for
linear unmixing of hyperspectral images. Our contribution is twofold; first, we
propose a new Bayesian model for structured sparse regression in which the
supports of the sparse abundance vectors are a priori spatially correlated
across pixels (i.e., materials are spatially organised rather than randomly
distributed at a pixel level). This prior information is encoded in the model
through a truncated multivariate Ising Markov random field, which also takes
into consideration the facts that pixels cannot be empty (i.e, there is at
least one material present in each pixel), and that different materials may
exhibit different degrees of spatial regularity. Secondly, we propose an
advanced Markov chain Monte Carlo algorithm to estimate the posterior
probabilities that materials are present or absent in each pixel, and,
conditionally to the maximum marginal a posteriori configuration of the
support, compute the MMSE estimates of the abundance vectors. A remarkable
property of this algorithm is that it self-adjusts the values of the parameters
of the Markov random field, thus relieving practitioners from setting
regularisation parameters by cross-validation. The performance of the proposed
methodology is finally demonstrated through a series of experiments with
synthetic and real data and comparisons with other algorithms from the
literature
A Variable Splitting Augmented Lagrangian Approach to Linear Spectral Unmixing
This paper presents a new linear hyperspectral unmixing method of the minimum
volume class, termed \emph{simplex identification via split augmented
Lagrangian} (SISAL). Following Craig's seminal ideas, hyperspectral linear
unmixing amounts to finding the minimum volume simplex containing the
hyperspectral vectors. This is a nonconvex optimization problem with convex
constraints. In the proposed approach, the positivity constraints, forcing the
spectral vectors to belong to the convex hull of the endmember signatures, are
replaced by soft constraints. The obtained problem is solved by a sequence of
augmented Lagrangian optimizations. The resulting algorithm is very fast and
able so solve problems far beyond the reach of the current state-of-the art
algorithms. The effectiveness of SISAL is illustrated with simulated data.Comment: 4 pages, 2 figures. Submitted to "First IEEE GRSS Workshop on
Hyperspectral Image and Signal Processing, 2009
Robust hyperspectral image classification with rejection fields
In this paper we present a novel method for robust hyperspectral image
classification using context and rejection. Hyperspectral image classification
is generally an ill-posed image problem where pixels may belong to unknown
classes, and obtaining representative and complete training sets is costly.
Furthermore, the need for high classification accuracies is frequently greater
than the need to classify the entire image.
We approach this problem with a robust classification method that combines
classification with context with classification with rejection. A rejection
field that will guide the rejection is derived from the classification with
contextual information obtained by using the SegSALSA algorithm. We validate
our method in real hyperspectral data and show that the performance gains
obtained from the rejection fields are equivalent to an increase the dimension
of the training sets.Comment: This paper was submitted to IEEE WHISPERS 2015: 7th Workshop on
Hyperspectral Image and Signal Processing: Evolution on Remote Sensing. 5
pages, 1 figure, 2 table
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
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