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Block sparsity is an important parameter in many algorithms to successfully recover block-sparse signals under the framework of compressive sensing. However, it is often unknown and needs to be estimated. Recently there emerges a few research work about how to estimate block sparsity of real-valued signals, while there is, to the best of our knowledge, no research that has been done for complex-valued signals. In this study, we propose a method to estimate the block sparsity of complex-valued signal. Its statistical properties are obtained and verified by simulations. In addition, we demonstrate the importance of accurately estimating the block sparsity through a sensitivity analysis.

There are three equivalent ways of representing two jointly observed real-valued signals: as a bivariate vector signal, as a single complex-valued signal, or as two analytic signals known as the rotary components. Each representation has unique advantages depending on the system of interest and the application goals. In this paper, we provide a joint framework for all three representations in the context of frequency-domain stochastic modeling. This framework allows us to extend many established statistical procedures for bivariate vector time series to complex-valued and rotary representations. These include procedures for parametrically modeling signal coherence, estimating model parameters using the Whittle likelihood, performing semiparametric modeling, and choosing between classes of nested models using model choice. We also provide a new method of testing for impropriety in complex-valued signals, which tests for noncircular or anisotropic second-order statistical structure when the signal is represented in the complex plane. Finally, we demonstrate the usefulness of our methodology in capturing the anisotropic structure of signals observed from fluid dynamic simulations of turbulence.

This paper proposes a novel method based on first-order statistics, aims to solve the problem of the independent component extraction of complex valued signals in instantaneous linear mixtures. Single-step and iterative algorithms are proposed and discussed under the engineering practice. Theoretical performance analysis about asymptotic interference-to-signal ratio (ISR) and probability of correct support estimation (PCE) are accomplished. Simulation examples validate the theoretic analysis, and demonstrate that the single-step algorithm is extremely effective. Moreover, the iterative algorithm is more efficient than complex FastICA under certain circumstances.

This paper proposes a novel method based on first-order statistics, aims to solve the problem of the independent component extraction of complex valued signals in instantaneous linear mixtures. Single-step and iterative algorithms are proposed and discussed under the engineering practice. Theoretical performance analysis about asymptotic interference-to-signal ratio (ISR) and probability of correct support estimation (PCE) are accomplished. Simulation examples validate the theoretic analysis, and demonstrate that the single-step algorithm is extremely effective. Moreover, the iterative algorithm is more efficient than complex FastICA under certain circumstances.

This paper proposes a novel method based on first-order statistics, aims to solve the problem of the independent component extraction of complex valued signals in instantaneous linear mixtures. Single-step and iterative algorithms are proposed and discussed under the engineering practice. Theoretical performance analysis about asymptotic interference-to-signal ratio (ISR) and probability of correct support estimation (PCE) are accomplished. Simulation examples validate the theoretic analysis, and demonstrate that the single-step algorithm is extremely effective. Moreover, the iterative algorithm is more efficient than complex FastICA under certain circumstances.

In this paper, we present a compressed sensing method for complex-valued signals based on multiple measurement vector compressed sensing model. The proposed method constrains the real and imaginary parts of the recovered signal to have the same sparsity profile. It is applied to a compressed sensing through-the-wall radar imaging problem. Experiments based on synthetic data shows that the proposed method achieves lower reconstruction error than the existing CS method.