A second look at the toric h-polynomial of a cubical complex

We provide an explicit formula for the toric $h$-contribution of each cubical shelling component, and a new combinatorial model to prove Clara Chan's result on the non-negativity of these contributions. Our model allows for a variant of the Gessel-Shapiro result on the $g$-polynomial of the cubical lattice, this variant may be shown by simple inclusion-exclusion. We establish an isomorphism between our model and Chan's model and provide a reinterpretation in terms of noncrossing partitions. By discovering another variant of the Gessel-Shapiro result in the work of Denise and Simion, we find evidence that the toric $h$-polynomials of cubes are related to the Morgan-Voyce polynomials via Viennot's combinatorial theory of orthogonal polynomials.Comment: Minor correction

Mixed rectilinear sources localization under unknown mutual coupling

In this paper, a novel rectilinearity-based localization method for mixed near-field (NF) and far-field (FF) sources is proposed under unknown mutual coupling. The multiple parameters including direction of arrival (DOA), range and mutual coupling coefficient (MCC) are decoupled, thus only three one-dimensional (1-D) spectral searches are required to estimate the parameters of mixed rectilinear signals successively. Furthermore, the closed-form deterministic Cramer–Rao bound (CRB) of the concerned problem is also derived. Simulation results are provided to demonstrate the effectiveness of the proposed method for the classification and localization of mixed rectilinear sources

Efficient Two-Dimensional Direction-of-Arrival Estimation for a Mixture of Circular and Noncircular Sources

In this paper, the two-dimensional (2-D) direction-of-arrival (DOA) estimation problem for a mixture of circular and noncircular sources is considered. In particular, we focus on a 2-D array structure consisting of two parallel uniform linear arrays and build a general array model with mixed circular and noncircular sources. The received array data and its conjugate counterparts are combined together to form a new data vector, based on which a series of 2-D DOA estimators is derived. Compared with existing methods, the proposed one has three main advantages. First, it can give a more accurate estimation in situations, where the number of sources is within the traditional limit of high-resolution methods. Second, it can still work effectively when the number of mixed signals is larger than that of the array elements. Finally, the paired 2-D DOAs of the proposed method can be obtained automatically without the complicated 2-D spectrum peak search and, therefore, has a much lower computational complexity

Compnet: A New Scheme for Single Image Super Resolution Based on Deep Convolutional Neural Network

The features produced by the layers of a neural network become increasingly more sparse as the network gets deeper and consequently, the learning capability of the network is not further enhanced as the number of layers is increased. In this paper, a novel residual deep network, called CompNet, is proposed for the single image super resolution problem without an excessive increase in the network complexity. The idea behind the proposed network is to compose the residual signal that is more representative of the features produced by the different layers of the network and it is not as sparse. The proposed network is experimented on different benchmark datasets and is shown to outperform the state-of-the-art schemes designed to solve the super resolution problem

Visual tracking using structural local DCT sparse appearance model with occlusion detection

In this paper, a structural local DCT sparse appearance model with occlusion detection is proposed for visual tracking in a particle filter framework. The energy compaction property of the 2D-DCT is exploited to reduce the size of the dictionary as well as that of the candidate samples so that the computational cost of l1-minimization can be lowered. Further, a holistic image reconstruction procedure is proposed for robust occlusion detection and used for appearance model update, thus avoiding the degradation of the appearance model in the presence of occlusion/outliers. Also, a patch occlusion ratio is introduced in the confidence score computation to enhance the tracking performance. Quantitative and qualitative performance evaluations on two popular benchmark datasets demonstrate that the proposed tracking algorithm generally outperforms several state-of-the-art methods

Visual Tracking Based on Correlation Filter and Robust Coding in Bilateral 2DPCA Subspace

The success of correlation filters in visual tracking has attracted much attention in computer vision due to their high efficiency and performance. However, they are not equipped with a mechanism to cope with challenging situations like scale variations, out-of-view, and camera motion. With the aim of dealing with such situations, a collaborative scheme of tracking based on the discriminative and generative models is proposed. Instead of finding all the affine motion parameters of the target by the combined likelihood of these models, the correlation filters, based on discriminative model, are used to find the position of the target, whereas 2D robust coding in a bilateral 2DPCA subspace, based on generative model, is used to find the other affine motion parameters of the target. Further, a 2D robust coding distance is proposed to differentiate the candidate samples from the subspace and used to compute the observation likelihood in the generative model. In addition, it is proposed to generate a robust occlusion map from the weights obtained during the residual minimization and a novel update mechanism of the appearance model for both the correlation filters and bilateral 2DPCA subspace is proposed. The proposed method is evaluated on the challenging image sequences available in the OTB-50, VOT2016, and UAV20L benchmark datasets, and its performance is compared with that of the state-of-the-art tracking algorithms. In contrast to OTB-50 and VOT2016, the dataset UAV20L contains long duration sequences with additional challenges introduced by both the camera motion and the view points in three dimensions. Quantitative and qualitative performance evaluations on three benchmark datasets demonstrate that the proposed tracking algorithm outperforms the state-of-the-art methods

RARE-based localization for mixed near-field and far-field rectilinear sources

In this paper, a novel localization method for mixed near-field (NF) and far-field (FF) rectilinear or strictly noncircular sources is proposed using the noncircular information for a symmetric uniform linear array (ULA). For FF case, we adopt the NC-MUSIC method to achieve the DOA parameter, for NF case, by exploiting the center symmetrical characteristic of the ULA, we decouple the array steering vectors into two new vectors: one related only to the DOA parameter, and the other dependent on both DOA and range parameters. Based on the principle of rank reduction (RARE), three MUSIC-like estimators are formed to estimate the direction of arrival (DOA) and the range of mixed NF and FF rectilinear sources successively. Meanwhile, distinguishing the types of sources is also solved. The deterministic Cramer–Rao bound (CRB) of the mixed rectilinear signals is derived by the Slepian–Bangs formulation. Simulation results are provided, showing that the proposed method yields a performance better than existing ones