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The use of mixture of Gaussians (MoGs) for noisy and overcomplete independent component analysis (ICA) when the source distributions are very sparse is explored. The sparsity model can often be justified if an appropriate transform, such as the modified discrete cosine transform, is used. Given the sparsity assumption, a number of simplifying appro...
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Theoretical and practical investigations have shown that some forms of reasoning such as belief revision, non-monotonic reasoning, reasoning about knowledge, and STRIPS-like planning can be formulated by quantified Boolean formulas (QBFs) and can be solved as instances of quantified satisfiability problem (QSAT). Almost all existing QSAT solvers on...
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... In two cases above, ICA is just one of traditional methods. However, ICA cannot be used in UBSS, in which, the number of sensors is less than the source one [6]. In this case, several methods have been developed for source estimation and a method using sparsity of signals is widely used among them [8,11,14,17,18]. ...
In this paper, we propose a noble algorithm for mixing matrix estimation in Underdetermined blind source separation. A concept of confidence measure and that of being able to be single source points at all the points in time frequency plane are introduced in the proposed algorithm. At first, we can detect the single source points from real parts and imaginary parts of time frequency coefficients of mixture signals and calculate principal vectors and its confidence measures through principal component analysis at the single source points using this algorithm. Finally, mixing matrix is obtained by clustering principal vectors according to its confidence measure. Experimental results show that the proposed algorithm is very suitable for actual situation of UBSS.
... A sparse signal is a signal whose most samples are nearly zero (inactive), and just a few ones take significant values (active). This prior information enables us to separate sources with less sensors than sources [10][11][12][13][14]. The mathematical model of the instantaneous underdetermined blind source separation (UBSS) can be expressed as ...
... Using the parameter c in the monotone increasing function is very important because it can take over the effect of the scale parameter b that we can assign the estimate of b as the sample variance. b could be defined as (12). For obtaining the local maximum values of J z ð Þ, the value of c is very important, c can determine the location of peaks in the objective function J z ð Þ. ...
... Using the equation (12) and algorithm 3 to estimate β and γ , respectively. 1 u u = + . ...
This paper proposes a blind recognition algorithm for real orthogonal space–time block code multi-carrier code division multiple access (OSTBC MC-CDMA) underdetermined systems based on Laplacian potential clustering algorithm (LPCA) and sparse component analysis. In our work, the received signal first has been constructed to satisfy the instantaneous underdetermined model, where the mixing matrix (virtual channel matrix) includes the information of space–time block code. The virtual channel matrix is then can be separated by using the LPCA. We show that, for OSTBC, the correlation matrix of virtual channel matrix is a diagonal matrix, while with non-OSTBC (NOSTBC) signal, such correlation matrix of virtual channel matrix was not. According to this property, two characteristic parameters of correlation matrix of virtual channel matrix are extracted, such as sparsity and energy ratio of non-main and main diagonal elements. In recognition process, the energy ratio will be used in pre-decision step, thus it avoids the influence of noise and making sure that the correlation matrix of virtual channel matrix is a diagonal matrix for OSTBC. The last decision will be done through comparing sparsity parameter with the number of transmitted symbols, where the sparsity parameter of OSTBC will be equal the number of transmitted symbols and the such parameter of NOSTBC will not. Simulation results demonstrate the effectiveness of the proposed algorithm.
... The sparse approximation model suggests that a natural signal could be compactly approximated, by only a few atoms out of a properly given dictionary, where the weights associated with the dictionary atoms are called the sparse codes. Proven to be both robust to noise and scalable to high dimensional data, sparse codes are known as powerful features, and benefit a wide range of signal processing applications, such as source coding (Donoho et al. 1998), denoising (Donoho 1995), source separation (Davies and Mitianoudis 2004), pattern classification (Wright et al. 2009), and clustering (Cheng et al. 2010). ...
Despite its nonconvex nature, ℓ0 sparse approximation is desirable in many theoretical and application cases. We study the ℓ0 sparse approximation problem with the tool of deep learning, by proposing Deep ℓ0 Encoders. Two typical forms, the ℓ0 regularized problem and the M-sparse problem, are investigated. Based on solid iterative algorithms, we model them as feed-forward neural networks, through introducing novel neurons and pooling functions. Enforcing such structural priors acts as an effective network regularization. The deep encoders also enjoy faster inference, larger learning capacity, and better scalability compared to conventional sparse coding solutions. Furthermore, under task-driven losses, the models can be conveniently optimized from end to end. Numerical results demonstrate the impressive performances of the proposed encoders.
... The Degenerate Unmixing Estimation Technique (DUET) [1] is a source separation technique used to separate a source with an amplitude and phase difference. In addition, source separation for an underdetermined source using a Gaussian Mixture Model (GMM) [2] or Laplacian Mixture Model (LMM) was proposed [3]. Recently, BSS techniques for a multichannel microphone [4] and Multichannel audio content [5] have also been proposed. ...
... However, unlike previous works related to BSS, which cluster signals using the ratio information from two channels [2,3,5], our proposed technique clusters an audio source from a multichannel signal at the same time as the vector concept. In addition, rather than taking inter-channel phase difference (IPD) into consideration such as in [1] and [4] for a multichannel microphone, we focus solely on ILD information since most multichannel movie audio tracks and multichannel music contents are mixed using the interchannel loudness difference (ILD). ...
... To analyze the panning information more properly through a vector representation, we set the axis for each channel with an equal interval angle, as shown in Fig. 2. The center channel is omitted because it typically contains only the speech signal. Like other previous works [1,2,3], the sparsity of the source is assumed, which means there is only one source signal TF (Time-Frequency) bin. Equation (1) describes how an ILVS for one TF bin is plotted on the vector axis. ...
In this paper, a Blind Source Separation (BSS) algorithm for multichannel
audio contents is proposed. Unlike common BSS algorithms targeting stereo audio
contents or microphone array signals, our technique is targeted at multichannel
audio such as 5.1 and 7.1ch audio. Since most multichannel audio object sources
are panned using the Inter-channel Loudness Difference (ILD), we employ the
ILVS (Inter-channel Loudness Vector Sum) concept to cluster common signals
(such as background music) from each channel. After separating the common
signals from each channel, we employ an Expectation Maximization (EM) algorithm
with a von-Mises distribution to successfully classify the clustering of sound
source objects and separate the audio signals from the original mixture. Our
proposed method can therefore separate common audio signals and object source
signals from multiple channels with reasonable quality. Our multichannel audio
content separation technique can be applied to an upmix system or a cinema
audio system requiring multichannel audio source separation.
... The sparse approximation model suggests that a natural signal could be compactly approximated, by only a few atoms out of a properly given dictionary, where the weights associated with the dictionary atoms are called the sparse codes. Proven to be both robust to noise and scalable to high dimensional data, sparse codes are known as powerful features, and benefit a wide range of signal processing applications, such as source coding ( Donoho et al. 1998), denoising (Donoho 1995), source separation ( Davies and Mitianoudis 2004), pattern classification ( Wright et al. 2009), and clustering ( Cheng et al. 2010). ...
Despite its nonconvex, intractable nature, sparse approximation is
desirable in many theoretical and application cases. We study the
sparse approximation problem with the tool of deep learning, by proposing Deep
Encoders. Two typical forms, the regularized problem and the
M-sparse problem, are investigated. Based on solid iterative algorithms, we
model them as feed-forward neural networks, through introducing novel neurons
and pooling functions. The deep encoders enjoy faster inference, larger
learning capacity, and better scalability compared to conventional sparse
coding solutions. Furthermore, when applying them to classification and
clustering, the models can be conveniently optimized from end to end, using
task-driven losses. Numerical results demonstrate the impressive performances
of the proposed encoders.
... For square mixing matrix stable and efficient ICA algorithms exist like FastICA algorithms [25], OBAICA algorithm [16], and Infomax algorithm [26] etc. (b) The number of transmitted signals greater than the number of received signals: This area of research in the ICA literature is called over-complete ICA [17]. ...
Independent component analysis (ICA) is a signal processing technique used for un-mixing of the mixed recorded signals. In wireless communication, ICA is mainly used in multiple input multiple output (MIMO) systems. Most of the existing work regarding the ICA applications in MIMO systems assumed static or quasi static wireless channels. Performance of the ICA algorithms degrades in case of time varying wireless channels and is further degraded if the data block lengths are reduced to get the quasi stationarity. In this paper, we propose an ICA based MIMO transceiver that performs well in time varying wireless channels, even for smaller data blocks. Simulation is performed over quadrature amplitude modulated (QAM) signals. Results show that the proposed transceiver system outperforms the existing MIMO system utilizing the FastICA and the OBAICA algorithms in both the transceiver systems for time varying wireless channels. Performance improvement is observed for different data blocks lengths and signal to noise ratios (SNRs).
... The method does not explicitly rely on identification of the acoustic channel and recovery of the desired source imposes a permutation problem due to mis-alignment of the individual source components (Nesta and Omologo, 2012;Wang et al., 2011). Other extensions of ICA for the underdetermined scenarios consist in integration with sparse masking techniques within a hierarchical separation framework (Araki et al., 2004;Davies and Mitianoudis, 2004). ...
In this paper, the problem of speech source localization and separation from recordings of convolutive underdetermined mixtures is addressed. This problem is cast as recovering the spatio-spectral speech information embedded in a microphone array compressed measurements of the acoustic field. A model-based sparse component analysis framework is formulated for sparse reconstruction of the speech spectra in a reverberant acoustic resulting in joint localization and separation of the individual sources. We compare and contrast the algorithmic approaches to model-based sparse recovery exploiting spatial sparsity as well as spectral structures underlying spectrographic representation of speech signals. In this context, we explore identification of the sparsity structures at the auditory and acoustic representation spaces. The audiory structures are formulated upon the principles of structural grouping based on proximity, autoregressive correlation and harmonicity of the spectral coefficients and they are incoporated for sparse reconstruction. The acoustic structures are formulated upon the image model of multipath propagation and they are exploited to characterize the compressive measurement matrix associated with microphone array recordings.
... Although the traditional ICA algorithms do not consider the sparsity of sources, there are some ICA algorithms that explicitly model source distributions. Both mixture of Gaussian (Attias, 1999;Davies and Mitianoudis, 2004;Todros and Tabrikian, 2007;Welling and Weber, 2001) and Laplacian distribution (Allassonniere and Younes, 2012;Bermond and Cardoso, 1999;Højen-Sørensen et al., 2002) were used as the probability density functions (pdf) of sources in these ICA algorithms. The sparseness-inducing nature of the Laplacian prior is well-known and has been exploited in many areas (Kotz et al., 2001). ...
Independent component analysis (ICA) has been widely applied to functional magnetic resonance imaging (fMRI) data analysis. Although ICA assumes that the sources underlying data are statistically independent, it usually ignores sources' additional properties, such as sparsity. In this study, we propose a two-step super-GaussianICA (2SGICA) method that incorporates the sparse prior of the sources into the ICA model. 2SGICA uses the super-Gaussian ICA (SGICA) algorithm that is based on a simplified Lewicki-Sejnowski's model to obtain the initial source estimate in the first step. Using a kernel estimator technique, the source density is acquired and fitted to the Laplacian function based on the initial source estimates. The fitted Laplacian prior is used for each source at the second SGICA step. Moreover, the automatic target generation process for initial value generation is used in 2SGICA to guarantee the stability of the algorithm. An adaptive step size selection criterion is also implemented in the proposed algorithm. We performed experimental tests on both simulated data and real fMRI data to investigate the feasibility and robustness of 2SGICA and made a performance comparison between InfomaxICA, FastICA, mean field ICA (MFICA) with Laplacian prior, sparse online dictionary learning (ODL), SGICA and 2SGICA. Both simulated and real fMRI experiments showed that the 2SGICA was most robust to noises, and had the best spatial detection power and the time course estimation among the six methods.
Copyright © 2015. Published by Elsevier Inc.
... In addition, it imposes a permutation problem due to misalignment of the individual source components [3,4,5]. To further extend this framework to non-invertible matrices, additional prior on sparse representation of the sources can be incorporated [6,7]. ...
... This formulation indicates a parametric approach to sourcesensor localization and signal reconstruction by minimizing the objective function stated in (7). It defines the locations as continuous random vectors in space and results in a non-linear objective which is difficult to optimize. ...
We propose a sparse coding approach to address the problem of source-sensor localization and speech reconstruction. This approach relies on designing a dictionary of spatialized signals by projecting the microphone array recordings into the array manifolds characterized for different locations in a reverberant enclosure using the image model. Sparse representation over this dictionary enables identifying the subspace of the actual recordings and its correspondence to the source and sensor locations. The speech signal is reconstructed by inverse filtering the acoustic channels associated to the array manifolds. We provide rigorous analysis on the optimality of speech reconstruction by elucidating the links between inverse filtering and source separation followed by deconvolution. This procedure is evaluated for localization, reconstruction and recognition of simultaneous speech sources using real data recordings. The results demonstrate the effectiveness of the proposed approach and compare favorably against beamforming and independent component analysis techniques.
... A sparse signal is a signal whose most samples are nearly zero (say they are "inactive"), and just a few percents takes significant values (say they are "active"). This prior information enables us to separate sources with less sensors than sources [2][3][4][5][6][7][8][9]. The mathematical model of instantaneous underdetermined Blind Source Separation (BSS) in the noisy case is: ...
... Therefore, similar to [7] and [21], we approximate the likelihood as: ...
... In the first experiment, to validate our approximations, the FIM matrix is calculated and compared with the approximated FIM (diagonal matrix) in the case of totally distinct angles. In the second experiment, the results of four different methods of estimating the mixing matrix are compared with each other and also with the CRB in (7). It shows a gap between the results of empirical methods and the CRB. ...
In this paper, we address theoretical limitations in estimating the mixing matrix in noisy Sparse Component Analysis (SCA) in the two-sensor case. We obtain the Cramér–Rao Bound (CRB) error estimation of the mixing matrix based on the observation vector x=(x1,x2)Tx=(x1,x2)T. Using the Bernoulli–Gaussian (BG) sparse distribution for sources, and some reasonable approximations, the Fisher Information Matrix (FIM) is approximated by a diagonal matrix. Then, the effect of off-diagonal terms in computing the CRB is investigated. Moreover, we compute an oracle CRB versus the blind uniform CRB and show that this is only 3 dB better than the blind uniform CRB. Finally, the CRB, the approximated CRB, the uniform CRB and the oracle CRB are compared to each other and to some of the main mixing matrix estimation methods in the literature. Simulation results show that the approximated CRB is close to the CRB for high SNRʼs. They also show that the approximated CRB is approximately equal to the oracle CRB.
