Hidden Markov models for wavelet-based blind source separation

Shuffle GAN With Autoencoder: A Deep Learning Approach to Separate Moving and Stationary Targets in SAR Imagery

Synthetic aperture radar (SAR) has been widely applied in both civilian and military fields because it provides high-resolution images of the ground target regardless of weather conditions, day or night. In SAR imaging, the separation of moving and stationary targets is of great significance as it is capable of removing the ambiguity stemming from inevitable moving targets in stationary scene imaging and suppressing clutter in moving target imaging. The newly emerged generative adversarial networks (GANs) have great performance in many other signal processing areas; however, they have not been introduced to radar imaging tasks. In this work, we propose a novel shuffle GAN with autoencoder separation method to separate the moving and stationary targets in SAR imagery. The proposed algorithm is based on the independence of well-focused stationary targets and blurred moving targets for creating adversarial constraints. Note that the algorithm operates in a totally unsupervised fashion without requiring a sample set that contains mixed and separated SAR images. Experiments are carried out on synthetic and real SAR data to validate the effectiveness of the proposed method.

Frame-Based Variational Bayesian Learning for Independent or Dependent Source Separation

Variational Bayesian (VB) learning has been successfully applied to instantaneous blind source separation. However, the traditional VB learning is restricted to the separation of independent source signals. Moreover, it has the difficulty to recover source signals with a sizable number of samples because of its rapidly increasing computational requirement. To overcome such shortcomings, frame-based VB (FVB) learning is proposed to address both independent and dependent source separation with a large number of samples in this paper. Specifically, a Gaussian process (GP) is employed to model independent or dependent source signals. To our knowledge, GP has been only used to model each of independent source signals. For dependent source signals, this paper proposes a novel modeling process: initial source signals are zigzag concatenated into a long serial and GP is then used to model it. In order to obtain a reliable covariance function for GP, first, we apply singular value decomposition to give initial estimated source signals and then we select an appropriate covariance function with which GP can perfectly fit them. In order to alleviate the computational burden of VB learning, we split observed signals into frames, and then model and infer source signals for each frame. Compared with the state-of-the-art algorithms, the experimental results show that the FVB learning has potential to provide improvement in separation performance not only for independent source signals but also for dependent ones, especially for long data records.

Nonstationary source separation using sequential and variational Bayesian learning

Independent component analysis (ICA) is a popular approach for blind source separation where the mixing process is assumed to be unchanged with a fixed set of stationary source signals. However, the mixing system and source signals are nonstationary in real-world applications, e.g., the source signals may abruptly appear or disappear, the sources may be replaced by new ones or even moving by time. This paper presents an online learning algorithm for the Gaussian process (GP) and establishes a separation procedure in the presence of nonstationary and temporally correlated mixing coefficients and source signals. In this procedure, we capture the evolved statistics from sequential signals according to online Bayesian learning. The activity of nonstationary sources is reflected by an automatic relevance determination, which is incrementally estimated at each frame and continuously propagated to the next frame. We employ the GP to characterize the temporal structures of time-varying mixing coefficients and source signals. A variational Bayesian inference is developed to approximate the true posterior for estimating the nonstationary ICA parameters and for characterizing the activity of latent sources. The differences between this ICA method and the sequential Monte Carlo ICA are illustrated. In the experiments, the proposed algorithm outperforms the other ICA methods for the separation of audio signals in the presence of different nonstationary scenarios.

Blind separation of image sources via adaptive dictionary learning

Sparsity has been shown to be very useful in source separation of multichannel observations. However, in most cases, the sources of interest are not sparse in their current domain and one needs to sparsify them using a known transform or dictionary. If such a priori about the underlying sparse domain of the sources is not available, then the current algorithms will fail to successfully recover the sources. In this paper, we address this problem and attempt to give a solution via fusing the dictionary learning into the source separation. We first define a cost function based on this idea and propose an extension of the denoising method in the work of Elad and Aharon to minimize it. Due to impracticality of such direct extension, we then propose a feasible approach. In the proposed hierarchical method, a local dictionary is adaptively learned for each source along with separation. This process improves the quality of source separation even in noisy situations. In another part of this paper, we explore the possibility of adding global priors to the proposed method. The results of our experiments are promising and confirm the strength of the proposed approach.

Time-frequency approach to underdetermined blind source separation

This paper presents a new time-frequency (TF) underdetermined blind source separation approach based on Wigner-Ville distribution (WVD) and Khatri-Rao product to separate N non-stationary sources from M(M <; N) mixtures. First, an improved method is proposed for estimating the mixing matrix, where the negative value of the auto WVD of the sources is fully considered. Then after extracting all the auto-term TF points, the auto WVD value of the sources at every auto-term TF point can be found out exactly with the proposed approach no matter how many active sources there are as long as N ≤ 2M-1. Further discussion about the extraction of auto-term TF points is made and finally the numerical simulation results are presented to show the superiority of the proposed algorithm by comparing it with the existing ones.

Estimation of sparse nonnegative sources from noisy overcomplete mixtures using MAP

In this letter, we propose a new algorithm for estimating sparse nonnegative sources from a set of noisy linear mixtures. In particular, we consider difficult situations with high noise levels and more sources than sensors (underdetermined case). We show that when sources are very sparse in time and overlapped at some locations, they can be recovered even with very low signal-to-noise ratio, and by using many fewer sensors than sources. A theoretical analysis based on Bayesian estimation tools is included showing strong connections with algorithms in related areas of research such as ICA, NMF, FOCUSS, and sparse representation of data with overcomplete dictionaries. Our algorithm uses a Bayesian approach by modeling sparse signals through mixed-state random variables. This new model for priors imposes l(0) norm-based sparsity. We start our analysis for the case of nonoverlapped sources (1-sparse), which allows us to simplify the search of the posterior maximum avoiding a combinatorial search. General algorithms for overlapped cases, such as 2-sparse and k-sparse sources, are derived by using the algorithm for 1-sparse signals recursively. Additionally, a combination of our MAP algorithm with the NN-KSVD algorithm is proposed for estimating the mixing matrix and the sources simultaneously in a real blind fashion. A complete set of simulation results is included showing the performance of our algorithm.