相关论文: RIP-based performance guarantee for low-tubal-rank…
Low-rank tensor recovery problems have been widely studied in many applications of signal processing and machine learning. Tucker decomposition is known as one of the most popular decompositions in the tensor framework. In recent years,…
Higher-order tensors can represent scores in a rating system, frames in a video, and images of the same subject. In practice, the measurements are often highly quantized due to the sampling strategies or the quality of devices. Existing…
Iterative hard thresholding (IHT) and compressive sampling matching pursuit (CoSaMP) are two types of mainstream compressed sensing algorithms using hard thresholding operators for signal recovery and approximation. The guaranteed…
The most frequently used condition for sampling matrices employed in compressive sampling is the restricted isometry (RIP) property of the matrix when restricted to sparse signals. At the same time, imposing this condition makes it…
The nuclear norm is widely used as a convex surrogate of the rank function in compressive sensing for low rank matrix recovery with its applications in image recovery and signal processing. However, solving the nuclear norm based relaxed…
Tensor numerical methods, based on the rank-structured tensor representation of $d$-variate functions and operators, are designed to provide $O(dn)$ complexity of numerical calculations on $n^{\otimes d }$ grids contrary to $O(n^d)$ scaling…
While it is well known that the restricted isometry property (RIP) guarantees uniform sparse recovery from noisy linear measurements, uniform recovery of structured signals from nonlinear observations remains much less understood. This…
Sparse and low rank tensor recovery has emerged as a significant area of research with applications in many fields such as computer vision. However, minimizing the $\ell_0$-norm of a vector or the rank of a matrix is NP-hard. Instead, their…
Recovery of the sparsity pattern (or support) of an unknown sparse vector from a limited number of noisy linear measurements is an important problem in compressed sensing. In the high-dimensional setting, it is known that recovery with a…
Tensors with unit Frobenius norm are fundamental objects in many fields, including scientific computing and quantum physics, which are able to represent normalized eigenvectors and pure quantum states. While the tensor train decomposition…
In this paper a new Riemannian rank adaptive method (RRAM) is proposed for the low-rank tensor completion problem (LRTCP) formulated as a least-squares optimization problem on the algebraic variety of tensors of bounded tensor-train (TT)…
An optimization-based approach for the Tucker tensor approximation of parameter-dependent data tensors and solutions of tensor differential equations with low Tucker rank is presented. The problem of updating the tensor decomposition is…
From linear classifiers to neural networks, image classification has been a widely explored topic in mathematics, and many algorithms have proven to be effective classifiers. However, the most accurate classifiers typically have…
We address some theoretical guarantees for Schatten-$p$ quasi-norm minimization ($p \in (0,1]$) in recovering low-rank matrices from compressed linear measurements. Firstly, using null space properties of the measurement operator, we…
Low-rank tensor models have been applied in accelerating dynamic magnetic resonance imaging (dMRI). Recently, a new tensor nuclear norm based on t-SVD has been proposed and applied to tensor completion. Inspired by the different properties…
We introduce and analyze the new range-separated (RS) canonical/Tucker tensor format which aims for numerical modeling of the 3D long-range interaction potentials in multi-particle systems. The main idea of the RS tensor format is the…
In this paper, we study joint network coding and distributed source coding of inter-node dependent messages, with the perspective of compressed sensing. Specifically, the theoretical guarantees for robust $\ell_1$-min recovery of an…
We propose a loop optimization algorithm based on nuclear norm regularization for tensor network. The key ingredient of this scheme is to introduce a rank penalty term proposed in the context of data processing. Compared to standard…
We propose a new algorithm for the computation of a singular value decomposition (SVD) low-rank approximation of a matrix in the Matrix Product Operator (MPO) format, also called the Tensor Train Matrix format. Our tensor network randomized…
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…