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In this paper, we extend the purely dual formulation that we recently proposed for the three-dimensional assignment problems to solve the more general multidimensional assignment problem. The convex dual representation is derived and its relationship to the Lagrangian relaxation method that is usually used to solve multidimensional assignment problems is investigated. Also, we discuss the condition under which the duality gap is zero. It is also pointed out that the process of Lagrangian relaxation is essentially equivalent to one of relaxing the binary constraint condition, thus necessitating the auction search operation to recover the binary constraint. Furthermore, a numerical algorithm based on the dual formulation along with a local search strategy is presented. The simulation results show that the proposed algorithm outperforms the traditional Lagrangian relaxation approach in terms of both accuracy and computational efficiency.

Aerial images and videos are extensively used for object detection and target tracking. However, due to the presence of thin clouds, haze or smoke from buildings, the processing of aerial data can be challenging. Existing single-image dehazing methods that work on ground-to-ground images, do not perform well on aerial images. Moreover, current dehazing methods are not capable for real-time processing. In this paper, a new end-to-end aerial image dehazing method using a deep convolutional autoencoder is proposed. Using the convolutional autoencoder, the dehazing problem is divided into two parts, namely, encoder, which aims extract important features to dehaze hazy regions and decoder, which aims to reconstruct the dehazed image using the down-sampled image received from the encoder. In this proposed method, we also exploit the superpixels in two different scales to generate synthetic thin cloud data to train our network. Since this network is trained in an end-to-end manner, in the test phase, for each input hazy aerial image, the proposed algorithm outputs a dehazed version without requiring any other information such as transmission map or atmospheric light value. With the proposed method, hazy regions are dehazed and objects within hazy regions become more visible while the contrast of non-hazy regions is increased. Experimental results on synthetic and real hazy aerial images demonstrate the superiority of the proposed method compared to existing dehazing methods in terms of quality and speed.

Temporal registration of sensors is an essential preprocessing step in multisensor target tracking systems. A new approach for multisensor time-offset estimation is proposed in this article. First, the time offset pseudomeasurement equation is derived and calculated in both centralized and decentralized scenarios, where measurements and local tracks are available at the fusion center, respectively. The observability of time offset is analyzed theoretically, which shows that only relative time offsets between sensors are observable. Second, a two-sensor two-stage filtering method is developed with four different formulations corresponding to different time-offset statistical models and target dynamic models to obtain a relative time-offset estimate. A multisensor two-stage filter is also proposed to obtain a minimum-bias time-offset estimate. Furthermore, the interacting multiple model estimator is used to deal with temporal registration in the presence of target maneuvers. Finally, the posterior Cramer–Rao lower bound (PCRLB) is derived for relative time-offset estimation. Simulation results show that the proposed algorithm with two sensors yields an empirically unbiased estimate of the relative time offset, and that the root-mean-square errors (RMSEs) match the corresponding PCRLB. Simulation results for multisensor target tracking are also presented to demonstrate the validity of the proposed algorithms.

In this paper, we propose a novel convex dual approach to the three dimensional assignment problem, which is an NP-hard binary programming problem. It is shown that the proposed dual approach is equivalent to the Lagrangian relaxation method in terms of the best value attainable by the two approaches. However, the pure dual representation is not only more elegant, but also makes the theoretical analysis of the algorithm more tractable. In fact, we obtain a sufficient and necessary condition for the duality gap to be zero, or equivalently, for the Lagrangian relaxation approach to find the optimal solution to the assignment problem with a guarantee. Also, we establish a mild and easy-to-check condition, under which the dual problem is equivalent to the original one. In general cases, the optimal value of the dual problem can provide a satisfactory lower bound on the optimal value of the original assignment problem. Furthermore, the newly proposed approach can be extended to higher dimensional cases and general assignment problems.