A Nuclear Norm Minimization Algorithm with Application
نویسنده
چکیده
In this paper we present a new algorithm to reconstruct prestack (5D) seismic data. If one considers seismic data at a given frequency and, for instance, in the x midpoint, y midpoint, offset and azimuth domain, the data volume can be represented via a 4th order tensor. Seismic data reconstruction can be posed as a tensor completion problem where it is assumed that the fully sampled data can be represented by a low rank tensor. The alternating direction method of multipliers (ADMM) is utilized to estimate the fully sampled low rank tensor that honours the observations. A field example from a data set from a heavy oil field in Alberta is used to evaluate the proposed tensor completion method.
منابع مشابه
Some first order algorithms for `1/nuclear norm minimization
In the last decade, the problems related to l1/nuclear norm minimization attract a lot of attention in Signal Processing, Machine Learning and Optimization communities. In this paper, devoted to `1/nuclear norm minimization as “optimization beasts,” we give a detailed description of two attractive First Order optimization techniques for solving the problems of this type. The first one, aimed pr...
متن کاملInterior-Point Method for Nuclear Norm Approximation with Application to System Identification
The nuclear norm (sum of singular values) of a matrix is often used in convex heuristics for rank minimization problems in control, signal processing, and statistics. Such heuristics can be viewed as extensions of l1-norm minimization techniques for cardinality minimization and sparse signal estimation. In this paper we consider the problem of minimizing the nuclear norm of an affine matrix val...
متن کاملGuaranteed Minimum Rank Approximation from Linear Observations by Nuclear Norm Minimization with an Ellipsoidal Constraint
The rank minimization problem is to find the lowest-rank matrix in a given set. Nuclear norm minimization has been proposed as an convex relaxation of rank minimization. Recht, Fazel, and Parrilo have shown that nuclear norm minimization subject to an affine constraint is equivalent to rank minimization under a certain condition given in terms of the rank-restricted isometry property. However, ...
متن کاملIterative Reweighted Algorithms for Matrix Rank Minimization Iterative Reweighted Algorithms for Matrix Rank Minimization
The problem of minimizing the rank of a matrix subject to affine constraints has many applications in machine learning, and is known to be NP-hard. One of the tractable relaxations proposed for this problem is nuclear norm (or trace norm) minimization of the matrix, which is guaranteed to find the minimum rank matrix under suitable assumptions. In this paper, we propose a family of Iterative Re...
متن کاملScalable Algorithms for Tractable Schatten Quasi-Norm Minimization
The Schatten-p quasi-norm (0<p<1) is usually used to replace the standard nuclear norm in order to approximate the rank function more accurately. However, existing Schattenp quasi-norm minimization algorithms involve singular value decomposition (SVD) or eigenvalue decomposition (EVD) in each iteration, and thus may become very slow and impractical for large-scale problems. In this paper, we fi...
متن کاملIn-network Sparsity-regularized Rank Minimization: Algorithms and Applications
Given a limited number of entries from the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, recovery of the low-rank and sparse components is a fundamental task subsuming compressed sensing, matrix completion, and principal components pursuit. This paper develops algorithms for distributed sparsity-regularized rank minimization over ne...
متن کامل