A new tensor-based approach, which is capable of significantly increasing the degrees of freedom (DOF) of an L-shaped array consisting of two orthogonal uniform linear arrays (ULAs), is proposed. By dividing each ULA into some overlapping subarrays and then combining their received signals into a data tensor, a new cross-correlation tensor between the two data tensors from the two ULAs is built. Analyses show that such a cross-correlation tensor can be transformed into an equivalent received data matrix of a virtual rectangular array (URA). Under the constraint of a fixed actual number of physical sensors, the optimal number of the subarrays is found by maximizing the DOF of the URA. It is shown that a virtual URA with approximately $0.34{{(M+1)}^{2}}$ DOF can be obtained from an L-shaped array with $2M$ physical sensors. To exploit the increased DOF for the 2-D DOA estimation without the multidimensional search, a parallel factor (PARAFAC) model of the URA is provided so that the PARAFAC decomposition can be used to do the 2-D DOA estimation effectively. Simulation results show that the proposed method can yield a better estimation performance and resolve more sources than the computationally efficient methods reported in literature.

A new mathematical tool, the geometric algebra of Euclidean 3-space (G3), is introduced for electromagnetic vector-sensor array processing herein. This paper focuses on modeling the six-component outputs of a vector-sensor holistically by an entry called as a multivector in G3. A compact polarized model for the array, termed as a geometric algebra model (G-MODEL), is then presented. Using the G-MODEL, a novel data covariance matrix model is defined by the geometric products in G3 and then analyzed. The analytical results show that the six-component measurement noise of a vector-sensor can naturally be whitened if the noise cross-correlations between the different axial electric and magnetic components are equal to one another. Compared with the known best quad-quaternion model, the new covariance matrix model results in a reduction of half memory requirements while the amount of divisions is reduced to 1/2, multiplications and additions reduced to almost 1/7.

In human vision, it has been well understood that the RGB (red, green, and blue) trichromatic system, whose colors can be well expressed by an RGB hue ring with complementary color relations, is the most accessible and extensible color representation. However, such color relations rarely play a role in color image/video processing tools such as wavelets. In this paper, the gap between wavelets and complementary color relations is filled by designing a novel color image/video processing tool called the Complementary Color Wavelet Transform (CCWT). Our novel wavelets consist of a family of well-designed 2D complex wavelets with 2π/3 phase differences copied from the R, G, and B angle relations on the RGB hue ring. Analyses show that our new wavelets can not only utilize the complementary color relations but also inherit and improve upon the advantages of classical complex wavelets such as their multi-resolution, directional selectivity, and shift-invariance properties. By the newly designed wavelets and by properly adding and/or subtracting the wavelet coefficients of a color image/video, some color-related image/video processing applications that are typically seen as infeasible or difficult to achieve by traditional methods, for instance, capturing and classifying local color changes, statistical modeling of the wavelet coefficients among the color channels, and multi-resolution directional color filtering, can be performed very easily. The cost for this is simply a transform redundancy increase (2.25 times that of classical complex wavelets). We provide three application examples of our method: color filtering, texture retrieval, and video quality assessment (VQA). The results show that our new wavelet tool greatly outperforms traditional methods.

In this paper, a new approach to guided wave ray tomography for temperature-robust damage detection with time-of-flight (TOF) temperature compensation is developed. Based on the linear relationship between the TOF of a guided wave and temperature, analyses show that the TOF of the baseline signal can be compensated by the temperature measurement of the inspected materials without estimating the temperature compensation parameters. The inversion is based on the optimization of the TOF misfit function between the inspected and compensated baseline TOFs of the guided waves, and is applied by the elastic net penalty approach to perform thickness change mapping in a structural health monitoring (SHM) application. Experiments that are conducted in isotropic plates by piezoelectric sensors demonstrate the effectiveness of the proposed method. According to the results, our approach not only eliminates the artefacts that are caused by a temperature variation from 25 °C to 70 °C but also provides more accurate and clearer imaging of damage than conventional ray tomography methods.

In designing the Hilbert transform pairs of orthonormal wavelet bases, several authors have shown that the requirements of the equal magnitude responses and the half-sample phase offset are the necessary and sufficient conditions on the scaling filters of conjugate quadrature filter (CQF) banks. In this paper, we first show that the scaling filters of CQF banks with equal magnitude responses cannot approach the half-sample phase offset in the high-frequency range properly. Then, a new design scheme, making a tradeoff between the requirements of the equal magnitude responses and the half-sample phase offset, is presented. The design scheme can make the scaling filter pairs approximately satisfy the requirement of the half-sample phase offset over the full frequency range while the magnitude responses of each pair remain nearly equal. As a result, the corresponding orthonormal wavelet bases can approximate to Hilbert transform pairs better. Some orthogonal wavelet bases we designed demonstrate the superiority of our scheme.

In this paper, a novel parallel factor (PARAFAC) model for processing the nested vector-sensor array is proposed. It is first shown that a nested vector-sensor array can be divided into multiple nested scalar-sensor subarrays. By means of the autocorrelation matrices of the measurements of these subarrays and the cross-correlation matrices among them, it is then demonstrated that these subarrays can be transformed into virtual scalar-sensor uniform linear arrays (ULAs). When the measurement matrices of these scalar-sensor ULAs are combined to form a third-order tensor, a novel PARAFAC model is obtained, which corresponds to a longer vector-sensor ULA and includes all of the measurements of the difference co-array constructed from the original nested vector-sensor array. Analyses show that the proposed PARAFAC model can fully use all of the measurements of the difference co-array, instead of its partial measurements as the reported models do in literature. It implies that all of the measurements of the difference co-array can be fully exploited to do the 2-D direction of arrival (DOA) and polarization parameter estimation effectively by a PARAFAC decomposition method so that both the better estimation performance and slightly improved identifiability are achieved. Simulation results confirm the efficiency of the proposed model.