We address the unified near-field and far-field time-difference-of-arrival source localization problem, in which the signal propagation speed is unknown, and the prior knowledge that whether the source is in the near-field or far-field is unavailable. Using the unified near-field and far-field model obtained by expressing the source position in the modified polar representation (MPR), two different methods, the semidefinite relaxation (SDR) method that achieves noise resilience and the two-step closed-from solution method that accomplishes low complexity, are proposed to jointly estimate the MPR coordinates and the propagation speed. For the SDR method, we express the propagation speed as the sum of a pre-selected constant and the residual to form a non-convex constrained weighted least squares problem, which is then relaxed into a convex semidefinite program by applying SDR. The two-step method obtains a coarse estimate in Step 1 by solving the quadratic programming problem without considering the relations among the variables, and then refines the coarse estimate in Step 2 by estimating the correction to compensate the error resulting from ignoring the relations. Theoretical mean square error analysis confirms that the proposed methods can reach the Cramer-Rao Lower Bound performance, which is also validated by using both simulated and real data.

Multi-Task Learning (MTL) has attracted increasing attention in recommender systems. A crucial challenge in MTL is to learn suitable shared parameters among tasks and to avoid negative transfer of information. The most recent sparse sharing models use independent parameter masks, which only activate useful parameters for a task, to choose the useful subnet for each task. However, as all the subnets are optimized in parallel for each task independently, it is faced with the problem of conflict between parameter gradient updates (i.e, parameter conflict problem). To address this challenge, we propose a novel Contrastive Sharing Recommendation model in MTL learning (CSRec). Each task in CSRec learns from the subnet by the independent parameter mask as in sparse sharing models, but a contrastive mask is carefully designed to evaluate the contribution of the parameter to a specific task. The conflict parameter will be optimized relying more on the task which is more impacted by the parameter. Besides, we adopt an alternating training strategy in CSRec, making it possible to self-adaptively update the conflict parameters by fair competitions. We conduct extensive experiments on three real-world large scale datasets, i.e., Tencent Kandian, Ali-CCP and Census-income, showing better effectiveness of our model over state-of-the-art methods for both offline and online MTL recommendation scenarios.

This paper addresses automatic inpainting of a specific but common kind of videos captured by imaging a far or planar scene with a moving camera. The projective model tells that the frames of such videos can be approximately aligned by linear mappings except for some to-be-inpainted small regions. Mathematically, we treat inpainting as a global optimization with a linear system incorporating both the temporal consistency and the priors of the inpainting regions: (i) temporally registered frames form a low rank matrix; (ii) the pixels in the given inpainting regions destroy the low rank-ness with gross sparse errors. Besides, we also use a soft mask to ensure consistent global brightness before and after inpainting. Further, we propose a numerical solution to above optimization based on Augmented Lagrangian Method. The experiment results demonstrated our advantageous in both preserving thin scene structures and the details prone to be smoothed out by previous methods.