The traditional 2D MUSIC algorithm fixes the azimuth or the elevation, and searches for the other without considering the directions of sources. A spectrum peak diffusion effect phenomenon is observed and may be utilized to detect the approximate directions of sources. Accordingly, a fast 2D MUSIC algorithm, which performs azimuth and elevation simultaneous searches (henceforth referred to as AESS) based on only three rounds of search is proposed. Firstly, AESS searches along a circle to detect the approximate source directions. Then, a subsequent search is launched along several straight lines based on these approximate directions. Finally, the 2D Direction of Arrival (DOA) of each source is derived by searching on several small concentric circles. Unlike the 2D MUSIC algorithm, AESS does not fix any azimuth and elevation parameters. Instead, the adjacent point of each search possesses different azimuth and elevation, i.e., azimuth and elevation are simultaneously searched to ensure that the search path is minimized, and hence the total spectral search over the angular field of view is avoided. Simulation results demonstrate the performance characters of the proposed AESS over some existing algorithms.

An efficient ratio-based edge detector (RBED) is proposed for synthetic aperture radar (SAR) images to decrease the false positive detection rate. Low false rate is achieved by taking full advantage of the integrative information associated with multiple adjacent edge-pixels. The RBED introduces a novel 2D separable filter. The 2D filter is represented as the direct product between a 1D vertical filter and a 1D parallel filter. The vertical filter is heuristically designed as the product of a power function and a Gaussian function, simply called the power-modulated-Gaussian function with a weaker tail. Under the non-ideal edge model, this power-modulated-Gaussian vertical filter keeps the false positive rate low and provides a good localization precision. The parallel filter is set as a flat bell-shaped function that is designed by taking a good trade-off between the Gaussian function and the gate function. Such a flat bell-shaped parallel filter with two flexible parameters can be properly adjusted so that the false positive rate can further be decreased. The constant false alarm rate and localization bias of the RBED are analysed theoretically. A set of objective and subjective experiments demonstrate that the RBED can markedly decrease the false positive rate and obtain closed skeleton edges.

In this paper, a fast approximate inverse-power (AIP) iteration is applied to compute recursively the total least squares (TLS) solution for unbiased equation-error adaptive infinite impulse response (IIR) filtering, which is established by approximating the well-known inverse-power iteration with Galerkin method. The AIP algorithm is based on an interesting modification of the inverse-power iteration in which the first entry of the parameter vector is constrained to the negative one. The distinctive feature of the proposed algorithm lies in its high computational efficiency, which is characterized by efficient computation of the fast gain vector (FGV), adaptation of the interesting modification of the inverse-power iteration, and rank-one update of the augmented correlation matrix. The shift structure of the input data vector is exploited to develop a fast algorithm for computing the gain vector. This FGV algorithm can be implemented at a numerical cost lower than the well-known fast Kalman algorithm. Since the first entry of the parameter vector has been fixed as the negative one and the weight vector is updated along the input data vector, a very efficient AIP algorithm is obtained by using the FGV algorithm. The proposed AIP algorithm is of computational complexity O(L) per iteration. Moreover, with no need to use the well-known matrix-inversion lemma, the AIP algorithm has another attractive feature of numerical stability. The proposed algorithm is shown to have global convergence. Simulation examples are included to demonstrate the effectiveness of the proposed AIP algorithm.

We propose an adaptive improved natural gradient algorithm for blind separation of independent sources. First, inspired by the well-known backpropagation algorithm, we incorporate a momentum term into the natural gradient learning process to accelerate the convergence rate and improve the stability. Then an estimation function for the adaptation of the separation model is obtained to adaptively control a step-size parameter and a momentum factor. The proposed natural gradient algorithm with variable step-size parameter and variable momentum factor is therefore particularly well suited to blind source separation in a time-varying environment, such as an abruptly changing mixing matrix or signal power. The expected improvement in the convergence speed, stability, and tracking ability of the proposed algorithm is demonstrated by extensive simulation results in both time-invariant and time-varying environments. The ability of the proposed algorithm to separate extremely weak or badly scaled sources is also verified. In addition, simulation results show that the proposed algorithm is suitable for separating mixtures of many sources (e.g., the number of sources is 10) in the complete case.