4,736 research outputs found
Exploiting spatial sparsity for multi-wavelength imaging in optical interferometry
Optical interferometers provide multiple wavelength measurements. In order to
fully exploit the spectral and spatial resolution of these instruments, new
algorithms for image reconstruction have to be developed. Early attempts to
deal with multi-chromatic interferometric data have consisted in recovering a
gray image of the object or independent monochromatic images in some spectral
bandwidths. The main challenge is now to recover the full 3-D (spatio-spectral)
brightness distribution of the astronomical target given all the available
data. We describe a new approach to implement multi-wavelength image
reconstruction in the case where the observed scene is a collection of
point-like sources. We show the gain in image quality (both spatially and
spectrally) achieved by globally taking into account all the data instead of
dealing with independent spectral slices. This is achieved thanks to a
regularization which favors spatial sparsity and spectral grouping of the
sources. Since the objective function is not differentiable, we had to develop
a specialized optimization algorithm which also accounts for non-negativity of
the brightness distribution.Comment: This version has been accepted for publication in J. Opt. Soc. Am.
Optimization with Sparsity-Inducing Penalties
Sparse estimation methods are aimed at using or obtaining parsimonious
representations of data or models. They were first dedicated to linear variable
selection but numerous extensions have now emerged such as structured sparsity
or kernel selection. It turns out that many of the related estimation problems
can be cast as convex optimization problems by regularizing the empirical risk
with appropriate non-smooth norms. The goal of this paper is to present from a
general perspective optimization tools and techniques dedicated to such
sparsity-inducing penalties. We cover proximal methods, block-coordinate
descent, reweighted -penalized techniques, working-set and homotopy
methods, as well as non-convex formulations and extensions, and provide an
extensive set of experiments to compare various algorithms from a computational
point of view
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