Related papers: Sparse tensor recovery via N-mode FISTA with suppo…

Low-rank tensor completion problem aims to recover a tensor from limited observations, which has many real-world applications. Due to the easy optimization, the convex overlapping nuclear norm has been popularly used for tensor completion.…

The convergence rate is analyzed for the SpaSRA algorithm (Sparse Reconstruction by Separable Approximation) for minimizing a sum $f (\m{x}) + \psi (\m{x})$ where $f$ is smooth and $\psi$ is convex, but possibly nonsmooth. It is shown that…

We consider the problem of high-dimensional misspecified phase retrieval. This is where we have an $s$-sparse signal vector $\mathbf{x}_*$ in $\mathbb{R}^n$, which we wish to recover using sampling vectors…

Conventional sparse phase retrieval schemes can recover sparse signals from the magnitude of linear measurements only up to a global phase ambiguity. This work proposes a novel approach that instead utilizes the magnitude of affine…

We present an algorithm for low rank decomposition of tensors of any symmetry type, from fully asymmetric to fully symmetric. It recovers the decomposition one summand at a time via the higher-order power method. This approach is known to…

This paper presents a multilevel framework for inertial and inexact proximal algorithms, that encompasses multilevel versions of classical algorithms such as forward-backward and FISTA. The methods are supported by strong theoretical…

Sparse phase retrieval plays an important role in many fields of applied science and thus attracts lots of attention. In this paper, we propose a \underline{sto}chastic alte\underline{r}nating \underline{m}inimizing method for…

Network pruning reduces the computational requirements of large neural networks, with N:M sparsity -- retaining only N out of every M consecutive weights -- offering a compelling balance between compressed model quality and hardware…

Existing tensor completion formulation mostly relies on partial observations from a single tensor. However, tensors extracted from real-world data are often more complex due to: (i) Partial observation: Only a small subset (e.g., 5%) of…

We study the problem of sparse tensor principal component analysis: given a tensor $\pmb Y = \pmb W + \lambda x^{\otimes p}$ with $\pmb W \in \otimes^p\mathbb{R}^n$ having i.i.d. Gaussian entries, the goal is to recover the $k$-sparse unit…

We study the sparse phase retrieval problem, which seeks to recover a sparse signal from a limited set of magnitude-only measurements. In contrast to prevalent sparse phase retrieval algorithms that primarily use first-order methods, we…

In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…

We study the problem of low-rank tensor factorization in the presence of missing data. We ask the following question: how many sampled entries do we need, to efficiently and exactly reconstruct a tensor with a low-rank orthogonal…

Two-dimensional terahertz spectroscopy (2DTS) is a low-frequency analogue of two-dimensional optical spectroscopy that is rapidly maturing as a probe of a wide variety of condensed matter systems. However, a persistent problem of 2DTS is…

Tensor decomposition is one of the well-known approaches to reduce the latency time and number of parameters of a pre-trained model. However, in this paper, we propose an approach to use tensor decomposition to reduce training time of…

In sparse coding, we attempt to extract features of input vectors, assuming that the data is inherently structured as a sparse superposition of basic building blocks. Similarly, neural networks perform a given task by learning features of…

We develop and analyze stochastic variants of ISTA and a full backtracking FISTA algorithms [Beck and Teboulle, 2009, Scheinberg et al., 2014] for composite optimization without the assumption that stochastic gradient is an unbiased…

Low-rank tensor completion recovers missing entries based on different tensor decompositions. Due to its outstanding performance in exploiting some higher-order data structure, low rank tensor ring has been applied in tensor completion. To…

The attention mechanism has been proven to be an effective way to improve spiking neural network (SNN). However, based on the fact that the current SNN input data flow is split into tensors to process on GPUs, none of the previous works…

As low-rank modeling has achieved great success in tensor recovery, many research efforts devote to defining the tensor rank. Among them, the recent popular tensor tubal rank, defined based on the tensor singular value decomposition…