In this letter, we propose an extended nested array (ENA) strategy, which relaxes the constraints on the two-side subarrays of the augmented nested array and allows the sensors further placed from the sparse uniform linear array. To guarantee the continuity of the difference co-array (DCA), several conditions are provided for specific design. Based on these rules, two ENAs, referred to as one-side extended nested array (OS-ENA) and two-side extended nested array (TS-ENA), are developed. The DCAs of both the OS-ENA and TS-ENA are hole-free and possess more consecutive lags than the existing nested-like arrays. Simulations verify the superiorities of the proposed ENAs with the spacial smoothing MUSIC algorithm used.

Recently, sparse arrays such as nested array and coprime array have attracted much attention in the field of array signal processing. In this letter, we develop a symmetric coprime array (SCA) whose sensor locations satisfy the nesting property, so it can be used as a dense subarray of nested array. Based on this observation, we propose a new sparse array named coprime nested array, which can achieve the same number of uniform degrees of freedom (uDOFs) as the prototype nested array, while the mutual coupling effect is at the same level as the coprime arrays. Moreover, an improved coprime nested array (ICNA) is proposed by rearranging some sensors in SCA to the right side of the sparse subarray. ICNA possesses more uDOFs than the existing nested arrays with further reduced mutual coupling effect. Numerical simulations verify the effectiveness of the proposed configurations.

In this paper, we propose a vectorized noncircular MUSIC (VNCM) algorithm based on the concept of the coarray, which can construct the difference and sum (diff–sum) coarray, for direction finding of the noncircular (NC) quasi-stationary sources. Utilizing both the NC property and the concept of the Khatri–Rao product, the proposed method can be applied to not only the ULA but also sparse arrays. In addition, we utilize the quasi-stationary characteristic instead of the spatial smoothing method to solve the coherent issue generated by the Khatri–Rao product operation so that the available degree of freedom (DOF) of the constructed virtual array will not be reduced by half. Compared with the traditional NC virtual array obtained in the NC MUSIC method, the diff–sum coarray achieves a higher number of DOFs as it comprises both the difference set and the sum set. Due to the complementarity between the difference set and the sum set for the coprime array, we choose the coprime array with multiperiod subarrays (CAMpS) as the array model and summarize the properties of the corresponding diff–sum coarray. Furthermore, we develop a diff–sum coprime array with multiperiod subarrays (DsCAMpS) whose diff–sum coarray has a higher DOF. Simulation results validate the effectiveness of the proposed method and the high DOF of the diff–sum coarray.

The thyroid nodule segmentation of ultrasound images is a critical step for the early diagnosis of thyroid cancers in clinics. Due to the weak edge of ultrasound images and the complexity of thyroid tissue structure, it is still challenging to accurately segment the delicate contour of thyroid nodules. A local and context-attention adaptive network (LCA-Net) for thyroid nodule segmentation is proposed to address these shortcomings, which leverages both local feature information from convolution neural networks and global context information from transformers. Firstly, since most existing thyroid nodule segmentation models are skilled at local detail features and lose some context information, we propose a transformers-based context-attention module to capture more global associative information for the network and perceive the edge information of the nodule contour. Secondly, a backbone module with $7\times 1$, $1\times 7$ convolutions and the activation function Mish is designed, which enlarges the receptive field and extracts more feature details. Furthermore, a nodule adaptive convolution (NAC) module is introduced to adaptively deal with thyroid nodules of different sizes and positions, thereby improving the generalization performance of the model. Simultaneously, an optimized loss function is proposed to solve the pixels class imbalance problem in segmentation. The proposed LCA-Net, validated on the public TN-SCUI2020 and TN3K datasets, achieves Dice scores of 90.26% and 82.08% and PA scores of 98.87% and 96.97%, respectively, which outperforms other state-of-the-art thyroid nodule segmentation models. This paper demonstrates the superiority of the proposed LCA-Net for thyroid nodule segmentation, which possesses strong generalization performance and promising segmentation accuracy. Consequently, the proposed model has wide application prospects for thyroid nodule diagnosis in clinics.

Multiple Signal Classification (MUSIC) is a high-performance Direction of Arrival (DOA) estimation algorithm, which has been widely used. The algorithm needs to calculate the covariance matrix, eigenvalue decomposition and spectral peak search. In the paper, the hardware structure of the existing Jacobi algorithm for Hermitian matrices is proposed. On this basis, a novel hardware acceleration of the MUSIC algorithm for sparse arrays and uniform linear arrays is proposed, and the sparse array is a nested array. There are two designs, Design 1 supports 1~10 nested array elements or 1~32 uniform linear array elements, distinguishes 1~32 sources, configures snapshots 1~2048, and the maximum number of iterations and iteration accuracy of the complex Jacobi algorithm. Design 2 only needs $101.8~\mu $ s to complete a DOA estimation when the number of array elements is 8, the number of sources is 1, and the snapshots is 128. In more detail, the Root Mean Squared Error (RMSE) of both can reach 0.03°. The logic resources on the Zynq-7000 development board are 14,761 and 28,305 Look-Up Tables (LUTs), respectively.