A New Criterion for Bounded Component Analysis

<div>In this paper we present a new criterion for bounded component analysis, a quite new approach for the Blind Source Separation problem. For the determined case, we show that the `1-norm of the estimated sources can be used as a contrast for the problem. We present a blind algorithm for the source separation of independents sources or mixtures of correlated sources by only a rotation matrix. We also present a variety of simulations assessing the performance of the proposed approach.</div>

A New Criterion for Bounded Component Analysis

<div>In this paper we present a new criterion for bounded component analysis, a quite new approach for the Blind Source Separation problem. For the determined case, we show that the `1-norm of the estimated sources can be used as a contrast for the problem. We present a blind algorithm for the source separation of independents sources or mixtures of correlated sources by only a rotation matrix. We also present a variety of simulations assessing the performance of the proposed approach.</div>

Antisparsity as a Prior in Blind Separation of Correlated Sources

<div>This letter introduces the concept of antisparse Blind Source Separation (BSS), proposing a suitable criterion based on the $\ell_\infty$ norm to explore the antisparsity feature. </div><div>The effectiveness of the criterion is theoretically demonstrated and it is also evaluated by computational simulations, which consider up to ten distinct sources with different correlation levels. Moreover, we simulated a scenario in wireless communication with binary sources, comparing our approach to the Constant Modulus algorithm. Both the theoretical and the simulation results highlight the potentiality of using antisparsity as a prior in BSS.</div>

Antisparsity as a Prior in Blind Separation of Correlated Sources

<div>This letter introduces the concept of antisparse Blind Source Separation (BSS), proposing a suitable criterion based on the $\ell_\infty$ norm to explore the antisparsity feature. </div><div>The effectiveness of the criterion is theoretically demonstrated and it is also evaluated by computational simulations, which consider up to ten distinct sources with different correlation levels. Moreover, we simulated a scenario in wireless communication with binary sources, comparing our approach to the Constant Modulus algorithm. Both the theoretical and the simulation results highlight the potentiality of using antisparsity as a prior in BSS.</div>

Subspace based Multiple Constrained Minimum Variance (SMCMV) Beamformers

In MEG and EEG brain imaging research two popular approaches are often used for spatial localization of focal task- or stimuli-related brain activations. One is a so called MUSIC approach applied in the form of RAP or TRAP MUSIC algorithms. Another one is the beamformer approach, specifically multiple constrained minimum variance (MCMV) beamformer when dealing with significantly correlated activations. Either method is using its own source localizer functions. Considering simplicity, accuracy and computational efficiency both approaches have their advantages and disadvantages. In this study we introduce a novel set of so called Subspace MCMV (or SMCMV) beamformers whose localizer functions combine MUSIC and MCMV localizers. We show that in ideal situations where forward modeling, data recording and noise measurements are error-free, SMCMV localizers allow precise identification of n arbitrarily correlated sources irrespective to their strength in just n scans of the brain volume using RAP MUSIC type algorithm. We also demonstrate by extensive computer simulations that with respect to source localization errors and the total number of identified sources SMCMV outperforms both the TRAP MUSIC and MIA MCMV (which is the most accurate MCMV algorithm to our knowledge) in non-ideal practical situations, specifically when the noise covariance cannot be estimated precisely, signal to noise ratios are small, source correlations are significant and larger numbers of sources are involved.

Hybrid Reweighted Optimization Method for Gridless Direction of Arrival Estimation in Heteroscedastic Noise Environment

In this paper, we present a hybrid optimization framework for gridless sparse Direction of Arrival (DoA) estimation under the consideration of heteroscedastic noise scenarios. The key idea of the proposed framework is to combine global and local minima search techniques that offer a sparser optimizer with boosted immunity to noise variation. In particular, we enforce sparsity by means of reformulating the Atomic Norm Minimization (ANM) problem through applying the nonconvex Schatten-p quasi-norm (0<p<1) relaxation. In addition, to enhance the adaptability of the relaxed ANM in more practical noise scenarios, it is combined with a covariance fitting (CF) criterion resulting in a locally convergent reweighted iterative approach. This combination forms a hybrid optimization framework and offers the advantages of both optimization approaches while balancing their drawbacks. Numerical simulations are performed taking into account the configuration of co-prime array (CPA). The simulations have demonstrated that the proposed method can maintain a high estimation resolution even in heteroscedastic noise environments, a low number of snapshots, and correlated sources.