481 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
Jump-sparse and sparse recovery using Potts functionals
We recover jump-sparse and sparse signals from blurred incomplete data
corrupted by (possibly non-Gaussian) noise using inverse Potts energy
functionals. We obtain analytical results (existence of minimizers, complexity)
on inverse Potts functionals and provide relations to sparsity problems. We
then propose a new optimization method for these functionals which is based on
dynamic programming and the alternating direction method of multipliers (ADMM).
A series of experiments shows that the proposed method yields very satisfactory
jump-sparse and sparse reconstructions, respectively. We highlight the
capability of the method by comparing it with classical and recent approaches
such as TV minimization (jump-sparse signals), orthogonal matching pursuit,
iterative hard thresholding, and iteratively reweighted minimization
(sparse signals)
Sparse Modeling for Image and Vision Processing
In recent years, a large amount of multi-disciplinary research has been
conducted on sparse models and their applications. In statistics and machine
learning, the sparsity principle is used to perform model selection---that is,
automatically selecting a simple model among a large collection of them. In
signal processing, sparse coding consists of representing data with linear
combinations of a few dictionary elements. Subsequently, the corresponding
tools have been widely adopted by several scientific communities such as
neuroscience, bioinformatics, or computer vision. The goal of this monograph is
to offer a self-contained view of sparse modeling for visual recognition and
image processing. More specifically, we focus on applications where the
dictionary is learned and adapted to data, yielding a compact representation
that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics
and Visio
A convex formulation for hyperspectral image superresolution via subspace-based regularization
Hyperspectral remote sensing images (HSIs) usually have high spectral
resolution and low spatial resolution. Conversely, multispectral images (MSIs)
usually have low spectral and high spatial resolutions. The problem of
inferring images which combine the high spectral and high spatial resolutions
of HSIs and MSIs, respectively, is a data fusion problem that has been the
focus of recent active research due to the increasing availability of HSIs and
MSIs retrieved from the same geographical area.
We formulate this problem as the minimization of a convex objective function
containing two quadratic data-fitting terms and an edge-preserving regularizer.
The data-fitting terms account for blur, different resolutions, and additive
noise. The regularizer, a form of vector Total Variation, promotes
piecewise-smooth solutions with discontinuities aligned across the
hyperspectral bands.
The downsampling operator accounting for the different spatial resolutions,
the non-quadratic and non-smooth nature of the regularizer, and the very large
size of the HSI to be estimated lead to a hard optimization problem. We deal
with these difficulties by exploiting the fact that HSIs generally "live" in a
low-dimensional subspace and by tailoring the Split Augmented Lagrangian
Shrinkage Algorithm (SALSA), which is an instance of the Alternating Direction
Method of Multipliers (ADMM), to this optimization problem, by means of a
convenient variable splitting. The spatial blur and the spectral linear
operators linked, respectively, with the HSI and MSI acquisition processes are
also estimated, and we obtain an effective algorithm that outperforms the
state-of-the-art, as illustrated in a series of experiments with simulated and
real-life data.Comment: IEEE Trans. Geosci. Remote Sens., to be publishe
Artifact Removal Methods in EEG Recordings: A Review
To obtain the correct analysis of electroencephalogram (EEG) signals, non-physiological and physiological artifacts should be removed from EEG signals. This study aims to give an overview on the existing methodology for removing physiological artifacts, e.g., ocular, cardiac, and muscle artifacts. The datasets, simulation platforms, and performance measures of artifact removal methods in previous related research are summarized. The advantages and disadvantages of each technique are discussed, including regression method, filtering method, blind source separation (BSS), wavelet transform (WT), empirical mode decomposition (EMD), singular spectrum analysis (SSA), and independent vector analysis (IVA). Also, the applications of hybrid approaches are presented, including discrete wavelet transform - adaptive filtering method (DWT-AFM), DWT-BSS, EMD-BSS, singular spectrum analysis - adaptive noise canceler (SSA-ANC), SSA-BSS, and EMD-IVA. Finally, a comparative analysis for these existing methods is provided based on their performance and merits. The result shows that hybrid methods can remove the artifacts more effectively than individual methods
- …