Improved Algorithms for Matrix Recovery from Rank-One Projections

2017/05/21 by Mohammadreza Soltani, Chinmay Hegde, Soltani, Mohammadreza +1
Computer Science · Engineering · #Advanced Image Processing Techniques #Blind Source Separation Techniques #FOS: Computer and information sciences #Machine Learning (stat.ML) #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.1705.07469

openalex publication_date 2017/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the problem of estimation of a low-rank matrix from a limited number of noisy rank-one projections. In particular, we propose two fast, non-convex proper algorithms for matrix recovery and support them with rigorous theoretical analysis. We show that the proposed algorithms enjoy linear convergence and that their sample complexity is independent of the condition number of the unknown true low-rank matrix. By leveraging recent advances in low-rank matrix approximation techniques, we show that our algorithms achieve computational speed-ups over existing methods. Finally, we complement our theory with some numerical experiments.

Citations

• PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming
• Large-Scale Convex Minimization with a Low-Rank Constraint
• Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
• An Introduction To Compressive Sampling [A sensing/sampling paradigm that goes against the common knowledge in data acquisition]
• Approximation Algorithms for Model-Based Compressive Sensing

Related

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• Low-Rank Matrix Estimation From Rank-One Projections by Unlifted Convex\n Optimization
• Lecture notes on non-convex algorithms for low-rank matrix recovery
• Matrix Recovery from Rank-One Projection Measurements via Nonconvex Minimization