6,335 research outputs found
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
A Primal-Dual Proximal Algorithm for Sparse Template-Based Adaptive Filtering: Application to Seismic Multiple Removal
Unveiling meaningful geophysical information from seismic data requires to
deal with both random and structured "noises". As their amplitude may be
greater than signals of interest (primaries), additional prior information is
especially important in performing efficient signal separation. We address here
the problem of multiple reflections, caused by wave-field bouncing between
layers. Since only approximate models of these phenomena are available, we
propose a flexible framework for time-varying adaptive filtering of seismic
signals, using sparse representations, based on inaccurate templates. We recast
the joint estimation of adaptive filters and primaries in a new convex
variational formulation. This approach allows us to incorporate plausible
knowledge about noise statistics, data sparsity and slow filter variation in
parsimony-promoting wavelet frames. The designed primal-dual algorithm solves a
constrained minimization problem that alleviates standard regularization issues
in finding hyperparameters. The approach demonstrates significantly good
performance in low signal-to-noise ratio conditions, both for simulated and
real field seismic data
Multiuser MIMO-OFDM for Next-Generation Wireless Systems
This overview portrays the 40-year evolution of orthogonal frequency division multiplexing (OFDM) research. The amelioration of powerful multicarrier OFDM arrangements with multiple-input multiple-output (MIMO) systems has numerous benefits, which are detailed in this treatise. We continue by highlighting the limitations of conventional detection and channel estimation techniques designed for multiuser MIMO OFDM systems in the so-called rank-deficient scenarios, where the number of users supported or the number of transmit antennas employed exceeds the number of receiver antennas. This is often encountered in practice, unless we limit the number of users granted access in the base station’s or radio port’s coverage area. Following a historical perspective on the associated design problems and their state-of-the-art solutions, the second half of this treatise details a range of classic multiuser detectors (MUDs) designed for MIMO-OFDM systems and characterizes their achievable performance. A further section aims for identifying novel cutting-edge genetic algorithm (GA)-aided detector solutions, which have found numerous applications in wireless communications in recent years. In an effort to stimulate the cross pollination of ideas across the machine learning, optimization, signal processing, and wireless communications research communities, we will review the broadly applicable principles of various GA-assisted optimization techniques, which were recently proposed also for employment inmultiuser MIMO OFDM. In order to stimulate new research, we demonstrate that the family of GA-aided MUDs is capable of achieving a near-optimum performance at the cost of a significantly lower computational complexity than that imposed by their optimum maximum-likelihood (ML) MUD aided counterparts. The paper is concluded by outlining a range of future research options that may find their way into next-generation wireless systems
Algorithms for nonnegative matrix factorization with the beta-divergence
This paper describes algorithms for nonnegative matrix factorization (NMF)
with the beta-divergence (beta-NMF). The beta-divergence is a family of cost
functions parametrized by a single shape parameter beta that takes the
Euclidean distance, the Kullback-Leibler divergence and the Itakura-Saito
divergence as special cases (beta = 2,1,0, respectively). The proposed
algorithms are based on a surrogate auxiliary function (a local majorization of
the criterion function). We first describe a majorization-minimization (MM)
algorithm that leads to multiplicative updates, which differ from standard
heuristic multiplicative updates by a beta-dependent power exponent. The
monotonicity of the heuristic algorithm can however be proven for beta in (0,1)
using the proposed auxiliary function. Then we introduce the concept of
majorization-equalization (ME) algorithm which produces updates that move along
constant level sets of the auxiliary function and lead to larger steps than MM.
Simulations on synthetic and real data illustrate the faster convergence of the
ME approach. The paper also describes how the proposed algorithms can be
adapted to two common variants of NMF : penalized NMF (i.e., when a penalty
function of the factors is added to the criterion function) and convex-NMF
(when the dictionary is assumed to belong to a known subspace).Comment: \`a para\^itre dans Neural Computatio
Learning the Morphological Diversity
International audienceThis article proposes a new method for image separation into a linear combination of morphological components. Sparsity in global dictionaries is used to extract the cartoon and oscillating content of the image. Complicated texture patterns are extracted by learning adapted local dictionaries that sparsify patches in the image. These global and local sparsity priors together with the data fidelity define a non-convex energy and the separation is obtained as a stationary point of this energy. This variational optimization is extended to solve more general inverse problems such as inpainting. A new adaptive morphological component analysis algorithm is derived to find a stationary point of the energy. Using adapted dictionaries learned from data allows to circumvent some difficulties faced by fixed dictionaries. Numerical results demonstrate that this adaptivity is indeed crucial to capture complex texture patterns
Tensor Decompositions for Signal Processing Applications From Two-way to Multiway Component Analysis
The widespread use of multi-sensor technology and the emergence of big
datasets has highlighted the limitations of standard flat-view matrix models
and the necessity to move towards more versatile data analysis tools. We show
that higher-order tensors (i.e., multiway arrays) enable such a fundamental
paradigm shift towards models that are essentially polynomial and whose
uniqueness, unlike the matrix methods, is guaranteed under verymild and natural
conditions. Benefiting fromthe power ofmultilinear algebra as theirmathematical
backbone, data analysis techniques using tensor decompositions are shown to
have great flexibility in the choice of constraints that match data properties,
and to find more general latent components in the data than matrix-based
methods. A comprehensive introduction to tensor decompositions is provided from
a signal processing perspective, starting from the algebraic foundations, via
basic Canonical Polyadic and Tucker models, through to advanced cause-effect
and multi-view data analysis schemes. We show that tensor decompositions enable
natural generalizations of some commonly used signal processing paradigms, such
as canonical correlation and subspace techniques, signal separation, linear
regression, feature extraction and classification. We also cover computational
aspects, and point out how ideas from compressed sensing and scientific
computing may be used for addressing the otherwise unmanageable storage and
manipulation problems associated with big datasets. The concepts are supported
by illustrative real world case studies illuminating the benefits of the tensor
framework, as efficient and promising tools for modern signal processing, data
analysis and machine learning applications; these benefits also extend to
vector/matrix data through tensorization. Keywords: ICA, NMF, CPD, Tucker
decomposition, HOSVD, tensor networks, Tensor Train
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