575 research outputs found
A new steplength selection for scaled gradient methods with application to image deblurring
Gradient methods are frequently used in large scale image deblurring problems
since they avoid the onerous computation of the Hessian matrix of the objective
function. Second order information is typically sought by a clever choice of
the steplength parameter defining the descent direction, as in the case of the
well-known Barzilai and Borwein rules. In a recent paper, a strategy for the
steplength selection approximating the inverse of some eigenvalues of the
Hessian matrix has been proposed for gradient methods applied to unconstrained
minimization problems. In the quadratic case, this approach is based on a
Lanczos process applied every m iterations to the matrix of the most recent m
back gradients but the idea can be extended to a general objective function. In
this paper we extend this rule to the case of scaled gradient projection
methods applied to non-negatively constrained minimization problems, and we
test the effectiveness of the proposed strategy in image deblurring problems in
both the presence and the absence of an explicit edge-preserving regularization
term
A Tensor-Based Dictionary Learning Approach to Tomographic Image Reconstruction
We consider tomographic reconstruction using priors in the form of a
dictionary learned from training images. The reconstruction has two stages:
first we construct a tensor dictionary prior from our training data, and then
we pose the reconstruction problem in terms of recovering the expansion
coefficients in that dictionary. Our approach differs from past approaches in
that a) we use a third-order tensor representation for our images and b) we
recast the reconstruction problem using the tensor formulation. The dictionary
learning problem is presented as a non-negative tensor factorization problem
with sparsity constraints. The reconstruction problem is formulated in a convex
optimization framework by looking for a solution with a sparse representation
in the tensor dictionary. Numerical results show that our tensor formulation
leads to very sparse representations of both the training images and the
reconstructions due to the ability of representing repeated features compactly
in the dictionary.Comment: 29 page
Large Scale 3D Image Reconstruction in Optical Interferometry
Astronomical optical interferometers (OI) sample the Fourier transform of the
intensity distribution of a source at the observation wavelength. Because of
rapid atmospheric perturbations, the phases of the complex Fourier samples
(visibilities) cannot be directly exploited , and instead linear relationships
between the phases are used (phase closures and differential phases).
Consequently, specific image reconstruction methods have been devised in the
last few decades. Modern polychromatic OI instruments are now paving the way to
multiwavelength imaging. This paper presents the derivation of a
spatio-spectral ("3D") image reconstruction algorithm called PAINTER
(Polychromatic opticAl INTErferometric Reconstruction software). The algorithm
is able to solve large scale problems. It relies on an iterative process, which
alternates estimation of polychromatic images and of complex visibilities. The
complex visibilities are not only estimated from squared moduli and closure
phases, but also from differential phases, which help to better constrain the
polychromatic reconstruction. Simulations on synthetic data illustrate the
efficiency of the algorithm.Comment: EUSIPCO, Aug 2015, NICE, Franc
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