It was previously shown that sparse representations can improve and simplify the estimation of an unknown mixing matrix of a set of images and thereby improve the quality of separation of source images. Here we propose a multiscale approach to the problem of blind separation of images from a set of their mixtures. We take advantage of the properties of multiscale transforms such as wavelet packets and decompose signals and images according to sets of local features. The resulting partial representations on a tree of data structure depict various degrees of sparsity. We show how the separation error is affected by the sparsity of the decomposition coefficients, and by the misfit between the prior, formulated in accordance with the probabilistic model of the coefficients' distribution, and the actual distribution of the coefficients. Our error estimator, based on the Taylor expansion of the quasi Log-Likelihood function, is used in selection of the best subsets of coefficients, utilized in turn for further separation. The performance of the proposed method is assessed by separation of noise-free and noisy data. Experiments with simulated and real signals and images demonstrate significant improvement of separation quality over previously reported results.
It was previously shown that sparse representations can improve and simplify the estimation of an unknown mixing matrix of a set of images and thereby improve the quality of separation of source images. Here we propose a multiscale approach to the problem of blind separation of images from a set of their mixtures. We take advantage of the properties of multiscale transforms such as wavelet packets and decompose signals and images according to sets of local features. The resulting partial representations on a tree of data structure depict various degrees of sparsity. We show how the separation error is affected by the sparsity of the decomposition coefficients, and by the misfit between the prior, formulated in accordance with the probabilistic model of the coefficients' distribution, and the
actual distribution of the coefficients. Our error estimator, based on the Taylor expansion of the quasi Log-Likelihood function, is used in selection of the best subsets of coefficients, utilized in turn for further separation. The performance of the proposed method is assessed by separation of noise-free and noisy data. Experiments with simulated and real signals and images demonstrate significant improvement of separation quality over previously reported results.
The concern of the blind source separation problem is to extract the underlying source signals from a set of their linear mixtures, where the mixing matrix is unknown. It was discovered recently, that use of sparsity of source representation in some signal dictionary dramatically improves the quality of separation. In this work we use the property of multiscale transforms, such as wavelet or wavelet packets, to decompose signals into sets of local features with various degrees of sparsity. We use this intrinsic property for selecting the best (most sparse) subsets of features for further separation. Experiments with simulated signals, musical sounds and images demonstrate significant improvement of separation quality.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.