Fast methods for denoising matrix completion formulations, with applications to robust seismic data interpolation

2013-02-20 · Aleksandr Y. Aravkin, Rajiv Kumar, Hassan Mansour, Ben Recht, Felix J. Herrmann

Recent SVD-free matrix factorization formulations have enabled rank minimization for systems with millions of rows and columns, paving the way for matrix completion in extremely large-scale applications, such as seismic data interpolation. In this paper, we consider matrix completion formulations designed to hit a target data-fitting error level provided by the user, and propose an algorithm called LR-BPDN that is able to exploit factorized formulations to solve the corresponding optimization problem. Since practitioners typically have strong prior knowledge about target error level, this innovation makes it easy to apply the algorithm in practice, leaving only the factor rank to be determined. Within the established framework, we propose two extensions that are highly relevant to solving practical challenges of data interpolation. First, we propose a weighted extension that allows known subspace information to improve the results of matrix completion formulations. We show how this weighting can be used in the context of frequency continuation, an essential aspect to seismic data interpolation. Second, we propose matrix completion formulations that are robust to large measurement errors in the available data. We illustrate the advantages of LR-BPDN on the collaborative filtering problem using the MovieLens 1M, 10M, and Netflix 100M datasets. Then, we use the new method, along with its robust and subspace re-weighted extensions, to obtain high-quality reconstructions for large scale seismic interpolation problems with real data, even in the presence of data contamination.

📄 PDF Abstract BibTeX arXiv:1302.4886

Code (0)

등록된 구현이 없습니다.

Tasks

Collaborative Filtering DenoisingMatrix Completion

Basis Pursuit Denoise with Nonsmooth Constraints

2018-11-28 · Robert Baraldi, Rajiv Kumar, Aleksandr Aravkin

Level-set optimization formulations with data-driven constraints minimize a regularization functional subject to matching observations to a given error level. These formulations are widely used, particularly for matrix c…

Denoising Matrix Completion

Collaborative Filtering with Graph Information: Consistency and Scalable Methods

2015-12-01 · NeurIPS 2015 12 · Nikhil Rao, Hsiang-Fu Yu, Pradeep K. Ravikumar, Inderjit S. Dhillon

Low rank matrix completion plays a fundamental role in collaborative filtering applications, the key idea being that the variables lie in a smaller subspace than the ambient space. Often, additional information about the…

Collaborative Filtering Low-Rank Matrix Completion Matrix Completion Recommendation Systems

Optimum Codesign for Image Denoising Between Type-2 Fuzzy Identifier and Matrix Completion Denoiser

2020-10-13 · IEEE Transactions on Fuzzy Systems 2020 10 · Qi Liu, Xiaopeng Li, Jicheng Yang

With the wide deployment of digital image capturing equipment, the need of denoising to produce a crystal clear image from noisy capture environment has become indispensable. In this article, a novel type-2 fuzzy-based f…

Denoising Image Denoising Low-Rank Matrix Completion Matrix Completion+1

Error-Minimizing Estimates and Universal Entry-Wise Error Bounds for Low-Rank Matrix Completion

2013-12-01 · NeurIPS 2013 12 · Franz Kiraly, Louis Theran

We propose a general framework for reconstructing and denoising single entries of incomplete and noisy entries. We describe: effective algorithms for deciding if and entry can be reconstructed and, if so, for reconstruct…

Denoising Low-Rank Matrix Completion Matrix Completion

Obtaining error-minimizing estimates and universal entry-wise error bounds for low-rank matrix completion

2013-02-21 · Franz J. Király, Louis Theran