342 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
Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)
The implicit objective of the biennial "international - Traveling Workshop on
Interactions between Sparse models and Technology" (iTWIST) is to foster
collaboration between international scientific teams by disseminating ideas
through both specific oral/poster presentations and free discussions. For its
second edition, the iTWIST workshop took place in the medieval and picturesque
town of Namur in Belgium, from Wednesday August 27th till Friday August 29th,
2014. The workshop was conveniently located in "The Arsenal" building within
walking distance of both hotels and town center. iTWIST'14 has gathered about
70 international participants and has featured 9 invited talks, 10 oral
presentations, and 14 posters on the following themes, all related to the
theory, application and generalization of the "sparsity paradigm":
Sparsity-driven data sensing and processing; Union of low dimensional
subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph
sensing/processing; Blind inverse problems and dictionary learning; Sparsity
and computational neuroscience; Information theory, geometry and randomness;
Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?;
Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website:
http://sites.google.com/site/itwist1
Sparse and Redundant Representations for Inverse Problems and Recognition
Sparse and redundant representation of data enables the
description of signals as linear combinations of a few atoms from
a dictionary. In this dissertation, we study applications of
sparse and redundant representations in inverse problems and
object recognition. Furthermore, we propose two novel imaging
modalities based on the recently introduced theory of Compressed
Sensing (CS).
This dissertation consists of four major parts. In the first part
of the dissertation, we study a new type of deconvolution
algorithm that is based on estimating the image from a shearlet
decomposition. Shearlets provide a multi-directional and
multi-scale decomposition that has been mathematically shown to
represent distributed discontinuities such as edges better than
traditional wavelets. We develop a deconvolution algorithm that
allows for the approximation inversion operator to be controlled
on a multi-scale and multi-directional basis. Furthermore, we
develop a method for the automatic determination of the threshold
values for the noise shrinkage for each scale and direction
without explicit knowledge of the noise variance using a
generalized cross validation method.
In the second part of the dissertation, we study a reconstruction
method that recovers highly undersampled images assumed to have a
sparse representation in a gradient domain by using partial
measurement samples that are collected in the Fourier domain. Our
method makes use of a robust generalized Poisson solver that
greatly aids in achieving a significantly improved performance
over similar proposed methods. We will demonstrate by experiments
that this new technique is more flexible to work with either
random or restricted sampling scenarios better than its
competitors.
In the third part of the dissertation, we introduce a novel
Synthetic Aperture Radar (SAR) imaging modality which can provide
a high resolution map of the spatial distribution of targets and
terrain using a significantly reduced number of needed transmitted
and/or received electromagnetic waveforms. We demonstrate that
this new imaging scheme, requires no new hardware components and
allows the aperture to be compressed. Also, it
presents many new applications and advantages which include strong
resistance to countermesasures and interception, imaging much
wider swaths and reduced on-board storage requirements.
The last part of the dissertation deals with object recognition
based on learning dictionaries for simultaneous sparse signal
approximations and feature extraction. A dictionary is learned
for each object class based on given training examples which
minimize the representation error with a sparseness constraint. A
novel test image is then projected onto the span of the atoms in
each learned dictionary. The residual vectors along with the
coefficients are then used for recognition. Applications to
illumination robust face recognition and automatic target
recognition are presented
Sparsity in Bayesian Signal Estimation
In this chapter, we describe different methods to estimate an unknown signal from its linear measurements. We focus on the underdetermined case where the number of measurements is less than the dimension of the unknown signal. We introduce the concept of signal sparsity and describe how it could be used as prior information for either regularized least squares or Bayesian signal estimation. We discuss compressed sensing and sparse signal representation as examples where these sparse signal estimation methods could be applied
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Overview of compressed sensing: Sensing model, reconstruction algorithm, and its applications
With the development of intelligent networks such as the Internet of Things, network scales are becoming increasingly larger, and network environments increasingly complex, which brings a great challenge to network communication. The issues of energy-saving, transmission efficiency, and security were gradually highlighted. Compressed sensing (CS) helps to simultaneously solve those three problems in the communication of intelligent networks. In CS, fewer samples are required to reconstruct sparse or compressible signals, which breaks the restrict condition of a traditional Nyquist-Shannon sampling theorem. Here, we give an overview of recent CS studies, along the issues of sensing models, reconstruction algorithms, and their applications. First, we introduce several common sensing methods for CS, like sparse dictionary sensing, block-compressed sensing, and chaotic compressed sensing. We also present several state-of-the-art reconstruction algorithms of CS, including the convex optimization, greedy, and Bayesian algorithms. Lastly, we offer recommendation for broad CS applications, such as data compression, image processing, cryptography, and the reconstruction of complex networks. We discuss works related to CS technology and some CS essentials. © 2020 by the authors
Multi-modal dictionary learning for image separation with application in art investigation
In support of art investigation, we propose a new source separation method
that unmixes a single X-ray scan acquired from double-sided paintings. In this
problem, the X-ray signals to be separated have similar morphological
characteristics, which brings previous source separation methods to their
limits. Our solution is to use photographs taken from the front and back-side
of the panel to drive the separation process. The crux of our approach relies
on the coupling of the two imaging modalities (photographs and X-rays) using a
novel coupled dictionary learning framework able to capture both common and
disparate features across the modalities using parsimonious representations;
the common component models features shared by the multi-modal images, whereas
the innovation component captures modality-specific information. As such, our
model enables the formulation of appropriately regularized convex optimization
procedures that lead to the accurate separation of the X-rays. Our dictionary
learning framework can be tailored both to a single- and a multi-scale
framework, with the latter leading to a significant performance improvement.
Moreover, to improve further on the visual quality of the separated images, we
propose to train coupled dictionaries that ignore certain parts of the painting
corresponding to craquelure. Experimentation on synthetic and real data - taken
from digital acquisition of the Ghent Altarpiece (1432) - confirms the
superiority of our method against the state-of-the-art morphological component
analysis technique that uses either fixed or trained dictionaries to perform
image separation.Comment: submitted to IEEE Transactions on Images Processin
Compressed sensing and finite rate of innovation for efficient data acquisition of quantitative acoustic microscopy images
La microscopie acoustique quantitative (MAQ) est une modalité d'imagerie bien établie qui donne accès à des cartes paramétriques 2D représentatives des propriétés mécaniques des tissus à une échelle microscopique. Dans la plupart des études sur MAQ, l'échantillons est scanné ligne par ligne (avec un pas de 2µm) à l'aide d'un transducteur à 250 MHz. Ce type d'acquisition permet d'obtenir un cube de données RF 3D, avec deux dimensions spatiales et une dimension temporelle. Chaque signal RF correspondant à une position spatiale dans l'échantillon permet d'estimer des paramètres acoustiques comme par exemple la vitesse du son ou l'impédance. Le temps d'acquisition en MAQ est directement proportionnel à la taille de l'échantillon et peut aller de quelques minutes à quelques dizaines de minutes. Afin d'assurer des conditions d'acquisition stables et étant donnée la sensibilité des échantillons à ces conditions, diminuer le temps d'acquisition est un des grand défis en MAQ. Afin de relever ce défi, ce travail de thèse propose plusieurs solutions basées sur l'échantillonnage compressé (EC) et la théories des signaux ayant un faible nombre de degré de liberté (finite rate of innovation - FRI, en anglais). Le principe de l'EC repose sur la parcimonie des données, sur l'échantillonnage incohérent de celles-ci et sur les algorithmes d'optimisation numérique. Dans cette thèse, les phénomènes physiques derrière la MAQ sont exploités afin de créer des modèles adaptés aux contraintes de l'EC et de la FRI. Plus particulièrement, ce travail propose plusieurs pistes d'application de l'EC en MAQ : un schéma d'acquisition spatiale innovant, un algorithme de reconstruction d'images exploitant les statistiques des coefficients en ondelettes des images paramétriques, un modèle FRI adapté aux signaux RF et un schéma d'acquisition compressée dans le domaine temporel.Quantitative acoustic microscopy (QAM) is a well-accepted modality for forming 2D parameter maps making use of mechanical properties of soft tissues at microscopic scales. In leading edge QAM studies, the sample is raster-scanned (spatial step size of 2µm) using a 250 MHz transducer resulting in a 3D RF data cube, and each RF signal for each spatial location is processed to obtain acoustic parameters, e.g., speed of sound or acoustic impedance. The scanning time directly depends on the sample size and can range from few minutes to tens of minutes. In order to maintain constant experimental conditions for the sensitive thin sectioned samples, the scanning time is an important practical issue. To deal with the current challenge, we propose the novel approach inspired by compressed sensing (CS) and finite rate of innovation (FRI). The success of CS relies on the sparsity of data under consideration, incoherent measurement and optimization technique. On the other hand, the idea behind FRI is supported by a signal model fully characterized as a limited number of parameters. From this perspective, taking into account the physics leading to data acquisition of QAM system, the QAM data can be regarded as an adequate application amenable to the state of the art technologies aforementioned. However, when it comes to the mechanical structure of QAM system which does not support canonical CS measurement manners on the one hand, and the compositions of the RF signal model unsuitable to existing FRI schemes on the other hand, the advanced frameworks are still not perfect methods to resolve the problems that we are facing. In this thesis, to overcome the limitations, a novel sensing framework for CS is presented in spatial domain: a recently proposed approximate message passing (AMP) algorithm is adapted to account for the underlying data statistics of samples sparsely collected by proposed scanning patterns. In time domain, as an approach for achieving an accurate recovery from a small set of samples of QAM RF signals, we employ sum of sincs (SoS) sampling kernel and autoregressive (AR) model estimator. The spiral scanning manner, introduced as an applicable sensing technique to QAM system, contributed to the significant reduction of the number of spatial samples when reconstructing speed of sound images of a human lymph node. Furthermore, the scanning time was also hugely saved due to the merit of the mechanical movement of the proposed sensing pattern. Together with the achievement in spatial domain, the introduction of SoS kernel and AR estimator responsible for an innovation rate sampling and a parameter estimation respectively led to dramatic reduction of the required number of samples per RF signal compared to a conventional approach. Finally, we showed that both data acquisition frameworks based on the CS and FRI can be combined into a single spatio-temporal solution to maximize the benefits stated above
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