622 research outputs found
Variational Texture Synthesis with Sparsity and Spectrum Constraints
International audienceThis paper introduces a new approach for texture synthesis. We propose a unified framework that both imposes first order statistical constraints on the use of atoms from an adaptive dictionary, as well as second order constraints on pixel values. This is achieved thanks to a variational approach, the minimization of which yields local extrema, each one being a possible texture synthesis. On the one hand, the adaptive dictionary is created using a sparse image representation rationale, and a global constraint is imposed on the maximal number of use of each atom from this dictionary. On the other hand, a constraint on second order pixel statistics is achieved through the power spectrum of images. An advantage of the proposed method is its ability to truly synthesize textures, without verbatim copy of small pieces from the exemplar. In an extensive experimental section, we show that the resulting synthesis achieves state of the art results, both for structured and small scale textures
Texture Synthesis Through Convolutional Neural Networks and Spectrum Constraints
This paper presents a significant improvement for the synthesis of texture
images using convolutional neural networks (CNNs), making use of constraints on
the Fourier spectrum of the results. More precisely, the texture synthesis is
regarded as a constrained optimization problem, with constraints conditioning
both the Fourier spectrum and statistical features learned by CNNs. In contrast
with existing methods, the presented method inherits from previous CNN
approaches the ability to depict local structures and fine scale details, and
at the same time yields coherent large scale structures, even in the case of
quasi-periodic images. This is done at no extra computational cost. Synthesis
experiments on various images show a clear improvement compared to a recent
state-of-the art method relying on CNN constraints only
Image Decomposition and Separation Using Sparse Representations: An Overview
This paper gives essential insights into the use of sparsity and morphological diversity in image decomposition and source separation by reviewing our recent work in this field. The idea to morphologically decompose a signal into its building blocks is an important problem in signal processing and has far-reaching applications in science and technology. Starck , proposed a novel decomposition method—morphological component analysis (MCA)—based on sparse representation of signals. MCA assumes that each (monochannel) signal is the linear mixture of several layers, the so-called morphological components, that are morphologically distinct, e.g., sines and bumps. The success of this method relies on two tenets: sparsity and morphological diversity. That is, each morphological component is sparsely represented in a specific transform domain, and the latter is highly inefficient in representing the other content in the mixture. Once such transforms are identified, MCA is an iterative thresholding algorithm that is capable of decoupling the signal content. Sparsity and morphological diversity have also been used as a novel and effective source of diversity for blind source separation (BSS), hence extending the MCA to multichannel data. Building on these ingredients, we will provide an overview the generalized MCA introduced by the authors in and as a fast and efficient BSS method. We will illustrate the application of these algorithms on several real examples. We conclude our tour by briefly describing our software toolboxes made available for download on the Internet for sparse signal and image decomposition and separation
Data augmentation for galaxy density map reconstruction
The matter density is an important knowledge for today cosmology as many
phenomena are linked to matter fluctuations. However, this density is not
directly available, but estimated through lensing maps or galaxy surveys. In
this article, we focus on galaxy surveys which are incomplete and noisy
observations of the galaxy density. Incomplete, as part of the sky is
unobserved or unreliable. Noisy as they are count maps degraded by Poisson
noise. Using a data augmentation method, we propose a two-step method for
recovering the density map, one step for inferring missing data and one for
estimating of the density. The results show that the missing areas are
efficiently inferred and the statistical properties of the maps are very well
preserved
Low Complexity Regularization of Linear Inverse Problems
Inverse problems and regularization theory is a central theme in contemporary
signal processing, where the goal is to reconstruct an unknown signal from
partial indirect, and possibly noisy, measurements of it. A now standard method
for recovering the unknown signal is to solve a convex optimization problem
that enforces some prior knowledge about its structure. This has proved
efficient in many problems routinely encountered in imaging sciences,
statistics and machine learning. This chapter delivers a review of recent
advances in the field where the regularization prior promotes solutions
conforming to some notion of simplicity/low-complexity. These priors encompass
as popular examples sparsity and group sparsity (to capture the compressibility
of natural signals and images), total variation and analysis sparsity (to
promote piecewise regularity), and low-rank (as natural extension of sparsity
to matrix-valued data). Our aim is to provide a unified treatment of all these
regularizations under a single umbrella, namely the theory of partial
smoothness. This framework is very general and accommodates all low-complexity
regularizers just mentioned, as well as many others. Partial smoothness turns
out to be the canonical way to encode low-dimensional models that can be linear
spaces or more general smooth manifolds. This review is intended to serve as a
one stop shop toward the understanding of the theoretical properties of the
so-regularized solutions. It covers a large spectrum including: (i) recovery
guarantees and stability to noise, both in terms of -stability and
model (manifold) identification; (ii) sensitivity analysis to perturbations of
the parameters involved (in particular the observations), with applications to
unbiased risk estimation ; (iii) convergence properties of the forward-backward
proximal splitting scheme, that is particularly well suited to solve the
corresponding large-scale regularized optimization problem
Combining local regularity estimation and total variation optimization for scale-free texture segmentation
Texture segmentation constitutes a standard image processing task, crucial to
many applications. The present contribution focuses on the particular subset of
scale-free textures and its originality resides in the combination of three key
ingredients: First, texture characterization relies on the concept of local
regularity ; Second, estimation of local regularity is based on new multiscale
quantities referred to as wavelet leaders ; Third, segmentation from local
regularity faces a fundamental bias variance trade-off: In nature, local
regularity estimation shows high variability that impairs the detection of
changes, while a posteriori smoothing of regularity estimates precludes from
locating correctly changes. Instead, the present contribution proposes several
variational problem formulations based on total variation and proximal
resolutions that effectively circumvent this trade-off. Estimation and
segmentation performance for the proposed procedures are quantified and
compared on synthetic as well as on real-world textures
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