10,852 research outputs found
CLEAR: Covariant LEAst-square Re-fitting with applications to image restoration
In this paper, we propose a new framework to remove parts of the systematic
errors affecting popular restoration algorithms, with a special focus for image
processing tasks. Generalizing ideas that emerged for regularization,
we develop an approach re-fitting the results of standard methods towards the
input data. Total variation regularizations and non-local means are special
cases of interest. We identify important covariant information that should be
preserved by the re-fitting method, and emphasize the importance of preserving
the Jacobian (w.r.t. the observed signal) of the original estimator. Then, we
provide an approach that has a "twicing" flavor and allows re-fitting the
restored signal by adding back a local affine transformation of the residual
term. We illustrate the benefits of our method on numerical simulations for
image restoration tasks
Improving Image Restoration with Soft-Rounding
Several important classes of images such as text, barcode and pattern images
have the property that pixels can only take a distinct subset of values. This
knowledge can benefit the restoration of such images, but it has not been
widely considered in current restoration methods. In this work, we describe an
effective and efficient approach to incorporate the knowledge of distinct pixel
values of the pristine images into the general regularized least squares
restoration framework. We introduce a new regularizer that attains zero at the
designated pixel values and becomes a quadratic penalty function in the
intervals between them. When incorporated into the regularized least squares
restoration framework, this regularizer leads to a simple and efficient step
that resembles and extends the rounding operation, which we term as
soft-rounding. We apply the soft-rounding enhanced solution to the restoration
of binary text/barcode images and pattern images with multiple distinct pixel
values. Experimental results show that soft-rounding enhanced restoration
methods achieve significant improvement in both visual quality and quantitative
measures (PSNR and SSIM). Furthermore, we show that this regularizer can also
benefit the restoration of general natural images.Comment: 9 pages, 6 figure
An optimal subgradient algorithm for large-scale convex optimization in simple domains
This paper shows that the optimal subgradient algorithm, OSGA, proposed in
\cite{NeuO} can be used for solving structured large-scale convex constrained
optimization problems. Only first-order information is required, and the
optimal complexity bounds for both smooth and nonsmooth problems are attained.
More specifically, we consider two classes of problems: (i) a convex objective
with a simple closed convex domain, where the orthogonal projection on this
feasible domain is efficiently available; (ii) a convex objective with a simple
convex functional constraint. If we equip OSGA with an appropriate
prox-function, the OSGA subproblem can be solved either in a closed form or by
a simple iterative scheme, which is especially important for large-scale
problems. We report numerical results for some applications to show the
efficiency of the proposed scheme. A software package implementing OSGA for
above domains is available
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