相关论文: Matrix Completion from One-Bit Dither Samples
Sparse signal recoveries from multiple measurement vectors (MMV) with joint sparsity property have many applications in signal, image, and video processing. The problem becomes much more involved when snapshots of the signal matrix are…
We consider the problem of recovering an $n_1 \times n_2$ low-rank matrix with $k$-sparse singular vectors from a small number of linear measurements (sketch). We propose a sketching scheme and an algorithm that can recover the singular…
In 1-bit compressive sensing, each measurement is quantized to a single bit, namely the sign of a linear function of an unknown vector, and the goal is to accurately recover the vector. While it is most popular to assume a standard Gaussian…
Given a matrix $M\in \mathbb{R}^{m\times n}$, the low rank matrix completion problem asks us to find a rank-$k$ approximation of $M$ as $UV^\top$ for $U\in \mathbb{R}^{m\times k}$ and $V\in \mathbb{R}^{n\times k}$ by only observing a few…
In this paper, we present and analyze a new set of low-rank recovery algorithms for linear inverse problems within the class of hard thresholding methods. We provide strategies on how to set up these algorithms via basic ingredients for…
Estimating singular subspaces from noisy matrices is a fundamental problem with wide-ranging applications across various fields. Driven by the challenges of data integration and multi-view analysis, this study focuses on estimating shared…
In this paper, we study the problem of robust phase recovery. We investigate a novel approach based on extremely quantized (one-bit) phase-less measurements and a corresponding recovery scheme. The proposed approach has surprising…
Matrix completion, i.e., the exact and provable recovery of a low-rank matrix from a small subset of its elements, is currently only known to be possible if the matrix satisfies a restrictive structural constraint---known as {\em…
Recovery of low-rank matrices has recently seen significant activity in many areas of science and engineering, motivated by recent theoretical results for exact reconstruction guarantees and interesting practical applications. A number of…
When considering post-training quantization, prior work has typically focused on developing a mixed precision scheme or learning the best way to partition a network for quantization. In our work, CPT-V, we look at a general way to improve…
In this paper, we propose a new algorithm for recovery of low-rank matrices from compressed linear measurements. The underlying idea of this algorithm is to closely approximate the rank function with a smooth function of singular values,…
This paper addresses the problem of low-rank distance matrix completion. This problem amounts to recover the missing entries of a distance matrix when the dimension of the data embedding space is possibly unknown but small compared to the…
The classical problem of phase retrieval has found a wide array of applications in optics, imaging and signal processing. In this paper, we consider the phase retrieval problem in a one-bit setting, where the signals are sampled using…
The large pre-trained vision transformers (ViTs) have demonstrated remarkable performance on various visual tasks, but suffer from expensive computational and memory cost problems when deployed on resource-constrained devices. Among the…
Given only a few observed entries from a low-rank matrix $X$, matrix completion is the problem of imputing the missing entries, and it formalizes a wide range of real-world settings that involve estimating missing data. However, when there…
Low-rank matrix completion consists of computing a matrix of minimal complexity that recovers a given set of observations as accurately as possible. Unfortunately, existing methods for matrix completion are heuristics that, while highly…
This research aims to optimize intricate learning models by implementing quantization and bit-depth optimization techniques. The objective is to significantly cut time complexity while preserving model efficiency, thus addressing the…
This paper considers the problem of reconstructing sparse or compressible signals from one-bit quantized measurements. We study a new method that uses a log-sum penalty function, also referred to as the Gaussian entropy, for sparse signal…
Understanding the singular value spectrum of a matrix $A \in \mathbb{R}^{n \times n}$ is a fundamental task in countless applications. In matrix multiplication time, it is possible to perform a full SVD and directly compute the singular…
Matrix completion is a class of machine learning methods that concerns the prediction of missing entries in a partially observed matrix. This paper studies matrix completion for mixed data, i.e., data involving mixed types of variables…