A novel matrix completion ESPRIT (MC-ESPRIT) algorithm is proposed to estimate the direction of arrival (DOA) with nonuniform linear arrays (NLA). By exploiting the matrix completion theory and the characters of Hankel matrix, the received data matrix of an NLA is tranformed into a two-fold Hankel matrix, which is a treatable for matrix completion. Then the decision variable can be reconstructed by the inexact augmented Lagrange multiplier method. This approach yields a completed data matrix, which is the same as the data matrix of uniform linear array (ULA). Thus the ESPRIT-type algorithm can be used to estimate the DOA. The MC-ESPRIT could resolve more signals than the MUSIC-type algorithms with NLA. Furthermore, the proposed algorithm does not need to divide the field of view of the array compared to the existing virtual interpolated array ESPRIT (VIA-ESPRIT). Simulation results confirm the effectiveness of MC-ESPRIT.

The conventional bilateral motion estimation (BME) for motion-compensated frame rate up-conversion (MC-FRUC) can avoid the problem of overlapped areas and holes but usually results in lots of inaccurate motion vectors (MVs) since 1) the MV of an object between the previous and following frames is more likely to have no temporal symmetry with respect to the target block of the interpolated frame and 2) the repetitive patterns existing in video frame lead to the problem of mismatch due to the lack of the interpolated block. In this paper, a new BME algorithm with a low computational complexity is proposed to resolve the above problems. The proposed algorithm incorporates multi-resolution search into BME, since it can easily utilize the MV consistency between two adjacent pyramid levels and spatial neighboring MVs to correct the inaccurate MVs resulting from no temporal symmetry while guaranteeing low computational cost. Besides, the multi-resolution search uses the fast wavelet transform to construct the wavelet pyramid, which not only can guarantee low computational complexity but also can reserve the high-frequency components of image at each level while sub-sampling. The high-frequency components are used to regularize the traditional block matching criterion for reducing the probability of mismatch in BME. Experiments show that the proposed algorithm can significantly improve both the objective and subjective quality of the interpolated frame with low computational complexity, and provide the better performance than the existing BME algorithms.