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Register a new userNon-Convex Tensor Low-Rank Approximation for Infrared Small Target Detection
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Yingqian Wang
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Infrared small target detection plays an important role in many infrared systems. Recently, many infrared small target detection methods have been proposed, in which the lowrank model has been used as a powerful tool. However, most low-rank-based methods assign the same weights for different singular values, which will lead to inaccurate background estimation. Considering that different singular values have different importance and should be treated discriminatively, in this paper, we propose a non-convex tensor low-rank approximation (NTLA) method for infrared small target detection. In our method, NTLA adaptively assigns different weights to different singular values for accurate background estimation. Based on the proposed NTLA, we use the asymmetric spatial-temporal total variation (ASTTV) to thoroughly describe background feature, which can achieve good background estimation and detection in complex scenes. Compared with the traditional total variation approach, ASTTV exploits different smoothness strength for spatial and temporal regularization. We develop an efficient algorithm to find the optimal solution of the proposed model. Compared with some state-of-the-art methods, the proposed method achieve an improvement in different evaluation metrics. Extensive experiments on both synthetic and real data demonstrate the proposed method provide a more robust detection in complex situations with low false rates.
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Higher-order low-rank tensor arises in many data processing applications and has attracted great interests. Inspired by low-rank approximation theory, researchers have proposed a series of effective tensor completion methods. However, most of these methods directly consider the global low-rankness of underlying tensors, which is not sufficient for a low sampling rate; in addition, the single nuclear norm or its relaxation is usually adopted to approximate the rank function, which would lead to suboptimal solution deviated from the original one. To alleviate the above problems, in this paper, we propose a novel low-rank approximation of tensor multi-modes (LRATM), in which a double nonconvex $L_{gamma}$ norm is designed to represent the underlying joint-manifold drawn from the modal factorization factors of the underlying tensor. A block successive upper-bound minimization method-based algorithm is designed to efficiently solve the proposed model, and it can be demonstrated that our numerical scheme converges to the coordinatewise minimizers. Numerical results on three types of public multi-dimensional datasets have tested and shown that our algorithm can recover a variety of low-rank tensors with significantly fewer samples than the compared methods.
Single-frame infrared small target (SIRST) detection aims at separating small targets from clutter backgrounds. With the advances of deep learning, CNN-based methods have yielded promising results in generic object detection due to their powerful modeling capability. However, existing CNN-based methods cannot be directly applied for infrared small targets since pooling layers in their networks could lead to the loss of targets in deep layers. To handle this problem, we propose a dense nested attention network (DNANet) in this paper. Specifically, we design a dense nested interactive module (DNIM) to achieve progressive interaction among high-level and low-level features. With the repeated interaction in DNIM, infrared small targets in deep layers can be maintained. Based on DNIM, we further propose a cascaded channel and spatial attention module (CSAM) to adaptively enhance multi-level features. With our DNANet, contextual information of small targets can be well incorporated and fully exploited by repeated fusion and enhancement. Moreover, we develop an infrared small target dataset (namely, NUDT-SIRST) and propose a set of evaluation metrics to conduct comprehensive performance evaluation. Experiments on both public and our self-developed datasets demonstrate the effectiveness of our method. Compared to other state-of-the-art methods, our method achieves better performance in terms of probability of detection (Pd), false-alarm rate (Fa), and intersection of union (IoU).
The goal of this work is to fill a gap in [Yang, SIAM J. Matrix Anal. Appl, 41 (2020), 1797--1825]. In that work, an approximation procedure was proposed for orthogonal low-rank tensor approximation; however, the approximation lower bound was only established when the number of orthonormal factors is one. To this end, by further exploring the multilinearity and orthogonality of the problem, we introduce a modified approximation algorithm. Approximation lower bound is established, either in deterministic or expected sense, no matter how many orthonormal factors there are. In addition, a major feature of the new algorithm is its flexibility to allow either deterministic or randomized procedures to solve a key step of each latent orthonormal factor involved in the algorithm. This feature can reduce the computation of large SVDs, making the algorithm more efficient. Some numerical studies are provided to validate the usefulness of the proposed algorithm.
Context information plays an indispensable role in the success of semantic segmentation. Recently, non-local self-attention based methods are proved to be effective for context information collection. Since the desired context consists of spatial-wise and channel-wise attentions, 3D representation is an appropriate formulation. However, these non-local methods describe 3D context information based on a 2D similarity matrix, where space compression may lead to channel-wise attention missing. An alternative is to model the contextual information directly without compression. However, this effort confronts a fundamental difficulty, namely the high-rank property of context information. In this paper, we propose a new approach to model the 3D context representations, which not only avoids the space compression but also tackles the high-rank difficulty. Here, inspired by tensor canonical-polyadic decomposition theory (i.e, a high-rank tensor can be expressed as a combination of rank-1 tensors.), we design a low-rank-to-high-rank context reconstruction framework (i.e, RecoNet). Specifically, we first introduce the tensor generation module (TGM), which generates a number of rank-1 tensors to capture fragments of context feature. Then we use these rank-1 tensors to recover the high-rank context features through our proposed tensor reconstruction module (TRM). Extensive experiments show that our method achieves state-of-the-art on various public datasets. Additionally, our proposed method has more than 100 times less computational cost compared with conventional non-local-based methods.
This paper considers the completion problem for a tensor (also referred to as a multidimensional array) from limited sampling. Our greedy method is based on extending the low-rank approximation pursuit (LRAP) method for matrix completions to tensor completions. The method performs a tensor factorization using the tensor singular value decomposition (t-SVD) which extends the standard matrix SVD to tensors. The t-SVD leads to a notion of rank, called tubal-rank here. We want to recreate the data in tensors from low resolution samples as best we can here. To complete a low resolution tensor successfully we assume that the given tensor data has low tubal-rank. For tensors of low tubal-rank, we establish convergence results for our method that are based on the tensor restricted isometry property (TRIP). Our result with the TRIP condition for tensors is similar to low-rank matrix completions under the RIP condition. The TRIP condition uses the t-SVD for low tubal-rank tensors, while RIP uses the SVD for matrices. We show that a subgaussian measurement map satisfies the TRIP condition with high probability and gives an almost optimal bound on the number of required measurements. We compare the numerical performance of the proposed algorithm with those for state-of-the-art approaches on video recovery and color image recovery.
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