相关论文: RIP-based performance guarantee for low-tubal-rank…

Compressive sensing involves the inversion of a mapping $SD \in \mathbb{R}^{m \times n}$, where $m < n$, $S$ is a sensing matrix, and $D$ is a sparisfying dictionary. The restricted isometry property is a powerful sufficient condition for…

In this paper, we put forth a new joint sparse recovery algorithm called signal space matching pursuit (SSMP). The key idea of the proposed SSMP algorithm is to sequentially investigate the support of jointly sparse vectors to minimize the…

This paper presents an average case denoising performance analysis for the Subspace Pursuit (SP), the CoSaMP and the IHT algorithms. This analysis considers the recovery of a noisy signal, with the assumptions that (i) it is corrupted by an…

Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…

In low-rank tensor completion tasks, due to the underlying multiple large-scale singular value decomposition (SVD) operations and rank selection problem of the traditional methods, they suffer from high computational cost and high…

Compressive sensing (CS) has recently emerged as a powerful framework for acquiring sparse signals. The bulk of the CS literature has focused on the case where the acquired signal has a sparse or compressible representation in an…

Achieving efficient and robust multi-channel data learning is a challenging task in data science. By exploiting low-rankness in the transformed domain, i.e., transformed low-rankness, tensor Singular Value Decomposition (t-SVD) has achieved…

To analyze the abundance of multidimensional data, tensor-based frameworks have been developed. Traditionally, the matrix singular value decomposition (SVD) is used to extract the most dominant features from a matrix containing the…

In this paper, we extend the Discrete Empirical Interpolation Method (DEIM) to the third-order tensor case based on the t-product and use it to select important/ significant lateral and horizontal slices/features. The proposed Tubal DEIM…

We consider the problem of recovering a low-multilinear-rank tensor from a small amount of linear measurements. We show that the Riemannian gradient algorithm initialized by one step of iterative hard thresholding can reconstruct an…

We study extensions of compressive sensing and low rank matrix recovery to the recovery of low rank tensors from incomplete linear information. While the reconstruction of low rank matrices via nuclear norm minimization is rather…

Recently, low-rank matrix recovery theory has been emerging as a significant progress for various image processing problems. Meanwhile, the group sparse coding (GSC) theory has led to great successes in image restoration (IR) problem with…

This paper focuses on recovering a low-rank tensor from its incomplete measurements. We propose a novel algorithm termed the Single Mode Quasi Riemannian Gradient Descent (SM-QRGD). By exploiting the benefits of both fixed-rank matrix…

The massive scale of pretrained models has made efficient compression essential for practical deployment. Low-rank decomposition based on the singular value decomposition (SVD) provides a principled approach for model reduction, but its…

The truncated singular value decomposition (SVD) of the measurement matrix is the optimal solution to the_representation_ problem of how to best approximate a noisy measurement matrix using a low-rank matrix. Here, we consider the…

In this paper we consider the problem of recovering a high dimensional data matrix from a set of incomplete and noisy linear measurements. We introduce a new model that can efficiently restrict the degrees of freedom of the problem and is…

We propose a hybrid stochastic method for the tensor renormalization group (TRG) approach. TRG is known as a powerful tool to study the many-body systems and quantum field theory on the lattice. It is based on a low-rank approximation of…

In the field of compressed sensing, a key problem remains open: to explicitly construct matrices with the restricted isometry property (RIP) whose performance rivals those generated using random matrix theory. In short, RIP involves…

Tensor completion is a fundamental tool for incomplete data analysis, where the goal is to predict missing entries from partial observations. However, existing methods often make the explicit or implicit assumption that the observed entries…

The restricted isometry property (RIP) is a well-known condition that guarantees the absence of spurious local minima in low-rank matrix recovery problems with linear measurements. In this paper, we introduce a novel property named bound…