1,155 research outputs found
Underdetermined source separation using a sparse STFT framework and weighted laplacian directional modelling
The instantaneous underdetermined audio source separation problem of
K-sensors, L-sources mixing scenario (where K < L) has been addressed by many
different approaches, provided the sources remain quite distinct in the virtual
positioning space spanned by the sensors. This problem can be tackled as a
directional clustering problem along the source position angles in the mixture.
The use of Generalised Directional Laplacian Densities (DLD) in the MDCT domain
for underdetermined source separation has been proposed before. Here, we derive
weighted mixtures of DLDs in a sparser representation of the data in the STFT
domain to perform separation. The proposed approach yields improved results
compared to our previous offering and compares favourably with the
state-of-the-art.Comment: EUSIPCO 2016, Budapest, Hungar
Blind Source Separation: the Sparsity Revolution
International audienceOver the last few years, the development of multi-channel sensors motivated interest in methods for the coherent processing of multivariate data. Some specific issues have already been addressed as testified by the wide literature on the so-called blind source separation (BSS) problem. In this context, as clearly emphasized by previous work, it is fundamental that the sources to be retrieved present some quantitatively measurable diversity. Recently, sparsity and morphological diversity have emerged as a novel and effective source of diversity for BSS. We give here some essential insights into the use of sparsity in source separation and we outline the essential role of morphological diversity as being a source of diversity or contrast between the sources. This paper overviews a sparsity-based BSS method coined Generalized Morphological Component Analysis (GMCA) that takes advantages of both morphological diversity and sparsity, using recent sparse overcomplete or redundant signal representations. GMCA is a fast and efficient blind source separation method. In remote sensing applications, the specificity of hyperspectral data should be accounted for. We extend the proposed GMCA framework to deal with hyperspectral data. In a general framework, GMCA provides a basis for multivariate data analysis in the scope of a wide range of classical multivariate data restorate. Numerical results are given in color image denoising and inpainting. Finally, GMCA is applied to the simulated ESA/Planck data. It is shown to give effective astrophysical component separation
Blind Curvelet based Denoising of Seismic Surveys in Coherent and Incoherent Noise Environments
The localized nature of curvelet functions, together with their frequency and
dip characteristics, makes the curvelet transform an excellent choice for
processing seismic data. In this work, a denoising method is proposed based on
a combination of the curvelet transform and a whitening filter along with
procedure for noise variance estimation. The whitening filter is added to get
the best performance of the curvelet transform under coherent and incoherent
correlated noise cases, and furthermore, it simplifies the noise estimation
method and makes it easy to use the standard threshold methodology without
digging into the curvelet domain. The proposed method is tested on
pseudo-synthetic data by adding noise to real noise-less data set of the
Netherlands offshore F3 block and on the field data set from east Texas, USA,
containing ground roll noise. Our experimental results show that the proposed
algorithm can achieve the best results under all types of noises (incoherent or
uncorrelated or random, and coherent noise)
A New Basis for Sparse PCA
The statistical and computational performance of sparse principal component
analysis (PCA) can be dramatically improved when the principal components are
allowed to be sparse in a rotated eigenbasis. For this, we propose a new method
for sparse PCA. In the simplest version of the algorithm, the component scores
and loadings are initialized with a low-rank singular value decomposition.
Then, the singular vectors are rotated with orthogonal rotations to make them
approximately sparse. Finally, soft-thresholding is applied to the rotated
singular vectors. This approach differs from prior approaches because it uses
an orthogonal rotation to approximate a sparse basis. Our sparse PCA framework
is versatile; for example, it extends naturally to the two-way analysis of a
data matrix for simultaneous dimensionality reduction of rows and columns. We
identify the close relationship between sparse PCA and independent component
analysis for separating sparse signals. We provide empirical evidence showing
that for the same level of sparsity, the proposed sparse PCA method is more
stable and can explain more variance compared to alternative methods. Through
three applications---sparse coding of images, analysis of transcriptome
sequencing data, and large-scale clustering of Twitter accounts, we demonstrate
the usefulness of sparse PCA in exploring modern multivariate data.Comment: 33 pages, 8 figure
Robust Algorithms for Low-Rank and Sparse Matrix Models
Data in statistical signal processing problems is often inherently matrix-valued, and a natural first step in working with such data is to impose a model with structure that captures the distinctive features of the underlying data. Under the right model, one can design algorithms that can reliably tease weak signals out of highly corrupted data. In this thesis, we study two important classes of matrix structure: low-rankness and sparsity. In particular, we focus on robust principal component analysis (PCA) models that decompose data into the sum of low-rank and sparse (in an appropriate sense) components. Robust PCA models are popular because they are useful models for data in practice and because efficient algorithms exist for solving them.
This thesis focuses on developing new robust PCA algorithms that advance the state-of-the-art in several key respects. First, we develop a theoretical understanding of the effect of outliers on PCA and the extent to which one can reliably reject outliers from corrupted data using thresholding schemes. We apply these insights and other recent results from low-rank matrix estimation to design robust PCA algorithms with improved low-rank models that are well-suited for processing highly corrupted data. On the sparse modeling front, we use sparse signal models like spatial continuity and dictionary learning to develop new methods with important adaptive representational capabilities. We also propose efficient algorithms for implementing our methods, including an extension of our dictionary learning algorithms to the online or sequential data setting. The underlying theme of our work is to combine ideas from low-rank and sparse modeling in novel ways to design robust algorithms that produce accurate reconstructions from highly undersampled or corrupted data. We consider a variety of application domains for our methods, including foreground-background separation, photometric stereo, and inverse problems such as video inpainting and dynamic magnetic resonance imaging.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/143925/1/brimoor_1.pd
- …