6,386 research outputs found
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
Autofocus for digital Fresnel holograms by use of a Fresnelet-sparsity criterion
We propose a robust autofocus method for reconstructing digital Fresnel holograms. The numerical reconstruction
involves simulating the propagation of a complex wave front to the appropriate distance. Since the latter value is difficult to determine manually, it is desirable to rely on an automatic procedure for finding the optimal distance to achieve high-quality reconstructions. Our algorithm maximizes a sharpness metric related to the sparsity of the signal’s expansion in distance-dependent waveletlike Fresnelet bases. We show results from simulations and experimental situations that confirm its applicability
Structured Sparsity: Discrete and Convex approaches
Compressive sensing (CS) exploits sparsity to recover sparse or compressible
signals from dimensionality reducing, non-adaptive sensing mechanisms. Sparsity
is also used to enhance interpretability in machine learning and statistics
applications: While the ambient dimension is vast in modern data analysis
problems, the relevant information therein typically resides in a much lower
dimensional space. However, many solutions proposed nowadays do not leverage
the true underlying structure. Recent results in CS extend the simple sparsity
idea to more sophisticated {\em structured} sparsity models, which describe the
interdependency between the nonzero components of a signal, allowing to
increase the interpretability of the results and lead to better recovery
performance. In order to better understand the impact of structured sparsity,
in this chapter we analyze the connections between the discrete models and
their convex relaxations, highlighting their relative advantages. We start with
the general group sparse model and then elaborate on two important special
cases: the dispersive and the hierarchical models. For each, we present the
models in their discrete nature, discuss how to solve the ensuing discrete
problems and then describe convex relaxations. We also consider more general
structures as defined by set functions and present their convex proxies.
Further, we discuss efficient optimization solutions for structured sparsity
problems and illustrate structured sparsity in action via three applications.Comment: 30 pages, 18 figure
Automated analysis of quantitative image data using isomorphic functional mixed models, with application to proteomics data
Image data are increasingly encountered and are of growing importance in many
areas of science. Much of these data are quantitative image data, which are
characterized by intensities that represent some measurement of interest in the
scanned images. The data typically consist of multiple images on the same
domain and the goal of the research is to combine the quantitative information
across images to make inference about populations or interventions. In this
paper we present a unified analysis framework for the analysis of quantitative
image data using a Bayesian functional mixed model approach. This framework is
flexible enough to handle complex, irregular images with many local features,
and can model the simultaneous effects of multiple factors on the image
intensities and account for the correlation between images induced by the
design. We introduce a general isomorphic modeling approach to fitting the
functional mixed model, of which the wavelet-based functional mixed model is
one special case. With suitable modeling choices, this approach leads to
efficient calculations and can result in flexible modeling and adaptive
smoothing of the salient features in the data. The proposed method has the
following advantages: it can be run automatically, it produces inferential
plots indicating which regions of the image are associated with each factor, it
simultaneously considers the practical and statistical significance of
findings, and it controls the false discovery rate.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS407 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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