Recovery of Low-Rank Matrices Under Affine Constraints via a Smoothed Rank Function
نویسندگان
چکیده
منابع مشابه
Compressive Sensing via Nonlocal Smoothed Rank Function
Compressive sensing (CS) theory asserts that we can reconstruct signals and images with only a small number of samples or measurements. Recent works exploiting the nonlocal similarity have led to better results in various CS studies. To better exploit the nonlocal similarity, in this paper, we propose a non-convex smoothed rank function based model for CS image reconstruction. We also propose a...
متن کاملLow-rank matrix recovery via rank one tight frame measurements
The task of reconstructing a low rank matrix from incomplete linear measurements arises in areas such as machine learning, quantum state tomography and in the phase retrieval problem. In this note, we study the particular setup that the measurements are taken with respect to rank one matrices constructed from the elements of a random tight frame. We consider a convex optimization approach and s...
متن کاملLow-Rank Matrix Recovery from Row-and-Column Affine Measurements
We propose and study a row-and-column affine measurement scheme for low-rank matrix recovery. Each measurement is a linear combination of elements in one row or one column of a matrix X . This setting arises naturally in applications from different domains. However, current algorithms developed for standard matrix recovery problems do not perform well in our case, hence the need for developing ...
متن کاملValue function approximation via low-rank models
We propose a novel value function approximation technique for Markov decision processes. We consider the problem of compactly representing the state-action value function using a low-rank and sparse matrix model. The problem is to decompose a matrix that encodes the true value function into low-rank and sparse components, and we achieve this using Robust Principal Component Analysis (PCA). Unde...
متن کاملThe minimal measurement number for low-rank matrices recovery
The paper presents several results that address a fundamental question in low-rank matrices recovery: how many measurements are needed to recover low rank matrices? We begin by investigating the complex matrices case and show that 4nr−4r generic measurements are both necessary and sufficient for the recovery of rank-r matrices in C by algebraic tools developed in [10]. Thus, we confirm a conjec...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: IEEE Transactions on Signal Processing
سال: 2014
ISSN: 1053-587X,1941-0476
DOI: 10.1109/tsp.2013.2295557