This article analyzes the composition and characteristics of echo signals in a pseudo-random-coded ground -penetrating radar (GPR). Based on these characteristics, an innovative low-rank sparse matrix decomposition (LRSD) method is developed using equivalent matrix gamma norm (EMGN) and equivalent minimax-concave penalty (EMCP) to suppress clutter in the echo signals. The proposed method employs non-convex alternatives to the matrix rank and sparsity functions. Therefore, it can alleviate biased estimates of the matrix rank and sparsity of the pseudo-random-coded radar’s received signals. The proposed method is verified by simulations and experiments on a real dataset. The results demonstrate that the proposed method can achieve better performance in terms of signal-to-clutter ratio (SCR) than the robust nonnegative matrix factorization (RNMF), and robust principal component analysis (RPCA) methods.

As a new imaging framework, the rotating synthetic aperture radar (ROSAR) derives a synthetic aperture through antenna rotation instead of traditional linear platform motion. The rotational synthetic aperture is sensitive to high-frequency vibrations aboard helicopters. The vibration causes severe phase error in signal echoes and imaging degradation. Unlike traditional synthetic aperture radar (SAR) imaging where range-Doppler algorithm (RDA) maybe applied for autofocus to improve the imaging performance, vibration phase errors cannot be estimated via conventional imaging algorithms due to severe range and azimuth couplings. A new ROSAR imaging procedure is proposed to compensate the phase error resulting from high-frequency vibrations of helicopters. A vibration model of ROSAR signal echo is established. The double Doppler keystone transform (DDKT) is adopted to correct the range cell migration (RCM) induced by slant range history and vibration errors. Analytical echo expression with range-independent vibration phase error is also derived in greater details. The focused image can then be obtained via classical autofocus algorithms. The effectiveness of the proposed technique is sufficiently demonstrated through simulation studies.

Sparse signal recoveries from multiple measurement vectors (MMV) with joint sparsity property have many applications in signal, image, and video processing. The problem becomes much more involved when snapshots of the signal matrix are temporally correlated. With signal's temporal correlation in mind, we provide a framework of iterative MMV algorithms based on thresholding, functional feedback and null space tuning. Convergence analysis for exact recovery is established. Unlike most of iterative greedy algorithms that select indices in a measurement/solution space, we determine indices based on an orthogonal subspace spanned by the iterative sequence. In addition, a functional feedback that controls the amount of energy relocation from the “tails” is implemented and analyzed. It is seen that the principle of functional feedback is capable to lower the number of iteration and speed up the convergence of the algorithm. Numerical experiments demonstrate that the proposed algorithm has a clearly advantageous balance of efficiency, adaptivity and accuracy compared with other state-of-the-art algorithms.

The rank of the sparse signals brought by multiple measurement vectors (MMV) augments the performance of joint sparse recovery. In general, suppose the sparsity level k is less than or equal to [rank(X)+spark(A)-1]/2, the sparsest solution of the MMV problem is unique and recoverable via various methods. It is shown in this letter that the unique solution of the sparsity level k up to spark(A)-1 actually exists in a measure theoretical point of view. More specifically, even when [rank(X)+spark(A)-1]/2 ≤ kA), the sparsest solution toAX=Yis still unique with full Lebesgue measure in every k-sparse coordinate space. This phenomenon is fully confirmed by the MMV tail-l2,1minimization technique. Furthermore, the phenomenon that the traditionall2,1minimization actually fails to recoverXwith k ≥ [spark(A)-1]/2 is investigated from the same perspective of measure theory. Extensive numerical tests conducted by the MMV tail-l2,1minimization andl2,1minimization are demonstrated to confirm the findings. The tail minimization procedure exhibits the most prominent effectiveness for the larger sparsity levels among all known techniques.

Summary In unmanned aerial vehicles navigation, path planning is aimed at obtaining the optimal safety path between start and destination locations. The efficiency and optimality criterion depend on the environment and planning method adopted. In this paper, a general fast path planning framework is proposed for unmanned aerial vehicles navigation. Standard A* search is performed online on the roadmap, which consists of path segments that are pre‐computed offline with the aid of a multi‐resolution grid and terminate at somewhere along the boundary between adjacent cells. Fast marching method (FMM) was employed for two aspects of the roadmap pre‐computation: the location of segment termination points is determined by FMM propagation from the center of a given cell at the highest resolution grid, and the actual segments are computed using FMM between all pairs of nodes belonging to a given cell at all resolutions. Environment dynamics are taken into account by replanning from scratch after modifying the costs associated with the path segments that intersect ‘threat’ or ‘no‐fly’ zones. The altitude along the planned path is determined in a post‐processing step by inspecting the elevation profile along the path and using Sparse A*searching method. The experimental results show that planning speed can be improved significantly with the proposed method, especially, fast online path planning can be achieved to adapt to environmental changes. Copyright © 2014 John Wiley & Sons, Ltd.

Signals with sparse representations in frames comprise a much more realistic model of nature, it is therefore highly desirable to extend the compressed sensing methodology to redundant dictionaries (or frames) as opposed to orthonormal bases only. In the generalized setting, the standard approach to recover the signal is known as ℓ1-synthesis (or Basis Pursuit). In this paper, we present the performance analysis of this approach in which the dictionary may be highly - and even perfectly - correlated. Our results do not depend on an accurate recovery of the coefficients. We demonstrate the validity of the results via several experiments.

A sparse-dual-frame based ℓ1-analysis approach for compressed sensing (CS) is proposed. The sparse dual frame is a notion of optimal dual frames of a non-exact frame. It is motivated in the study of compressed sensing problems where signals are sparse with respect to redundant dictionaries (frames). An alternating iterative algorithm is proposed. An error bound ensuring the correct signal recovery is obtained. Empirical studies over generally difficult CS problems demonstrate that the new sparse-dual-based approach provides satisfactory solutions, whereas other existing means may not.

Frame and fusion frame high-resolution image fusion formulations are presented. These techniques use the physical point spread function (PSF) of cameras as the building block of the mathematical frames in the fusion process. Cameras producing the low-resolution images are allowed to be different, and thereby possess different PSFs. Fused image reconstructions are carried out by a dimension invariance principle and by a set of iterative reconstruction algorithms. These frame fundamental approaches are also seen to be robust to realistic fusion problems from inhomogeneous image measurements (taken at different space or time or by different cameras), which is one of the main focuses of this paper. The effectiveness of this approach is demonstrated through both simulated and realistic examples. The results are quite encouraging.

Compressed sensing with sparse frame representations is seen to have much greater range of practical applications than that with orthonormal bases. In such settings, one approach to recover the signal is known as ℓ1-analysis. We expand in this paper the performance analysis of this approach by providing a weaker recovery condition than existing results in the literature. Our analysis is also broadly based on general frames and alter native dual frames (as analysis operators). As one application to such a general-dual-based approach and performance analysis, an optimal-dual-based technique is proposed to demonstrate the effectiveness of using alternative dual frames as ℓ1-analysis operators. An iterative algorithm is outlined for solving the optimal-dual-based -analysis problem. The effectiveness of the proposed method and algorithm is demonstrated through several experiments.

A discrete multi-Gabor expansion (DMGE) is developed to meet the requirements of localized and refined time-frequency (TF) representation of signals. The DMGE uses multiple windows and their translations and complex modulations as synthesis (or analysis) waveforms. It includes and generalizes the metaplectic (translation, modulation, and dilation) representations which are useful in signal analysis. Uniform, nonuniform, and proportional time sampling schemes are analyzed. The fundamental features and the importance of the DMGE are discussed. We focus on the construction of DMGE and deriving fast algorithms for the computation of related multi-analysis sequences. With matrix algebra, the algorithms derived apply to both multi-Gabor expansions and uni-(window) Gabor expansions. Another useful feature of the DMGE lies in the fact that the multi-Gabor transform can be realized in a parallel FFT-based implementation structure. Examples of DMGE and their applications to TF analysis are also discussed.

In the previous discrete Gabor expansion (DGE) presented by Wexler and Raz (1990), the ratio of the signal length L to the number of frequency channels N is restricted to be an integer. If L is a power of 2, then the oversampling rate is limited to 1, 2, 4, 8, etc. We derive a complementary condition to the derivation of the discrete Gabor expansion of Wexler et. al. and give a general pointwise biorthogonal relationship that relaxes the constraint on N. Consequently, the resulting Gabor expansion applies for integer as well as rational oversampling rates.>

We present a theory of generalized non-separable two dimensional (2-D) discrete Gabor expansions (DGE). We show that a DGE is essentially a general frame decomposition. Using this theory, we show that a non-separable 2-D analysis sequence can also be the translation and modulation of a single 2-D function /spl gamma/. A novel algorithm for computing all possible nonseparable 2-D /spl gamma/ is also derived. The non-separable 2-D DGE scheme is useful, e.g., in applications where the orientation of the 2-D Gabor analysis window is important.>

A backpropagation learning algorithm is presented. The algorithm is a combination of the conventional backpropagation and an objective of minimizing the norm of weights. It is optimal in the sense that it can learn to achieve a set of minimum norm weights while still possessing the best error performance. Fast learning is proven in the algorithm. Simulation results strongly prove its good prospects. The uniqueness of the norm of weights is also demonstrated in the simulation. This algorithm is actually an example of a class of optimized back-propagation learning. The generalization for some problems is straightforward