Off-the-grid low-rank matrix recovery and seismic data reconstruction

TitleOff-the-grid low-rank matrix recovery and seismic data reconstruction
Publication TypeJournal Article
Year of Publication2016
AuthorsOscar Lopez, Rajiv Kumar, Ozgur Yilmaz, Felix J. Herrmann
JournalIEEE Journal of Selected Topics in Signal Processing
Keywordsdata regularization, matrix completion, matrix sensing, nonuniform discrete Fourier transform, nuclear-norm relaxation, seismic data, seismic trace interpolation

Matrix sensing problems capitalize on the knowledge that a data matrix of interest exhibits low rank properties. This low dimensional structure often arises because the data matrix is obtained by sampling a smooth function on a regular (or structured) grid. However, in many practical situations the measurements are taken on an irregular grid (that is accurately known). This results in an "unstructured data matrix" that is less fit for the low rank model in comparison to its regular counterpart and therefore subject to degraded reconstruction via rank penalization techniques. In this paper, we propose and analyze a modified low-rank matrix recovery work-flow that admits unstructured observations. By incorporating a regularization operator which accurately maps structured data to unstructured data, into the nuclear-norm minimization problem, we are able to compensate for data irregularity. Furthermore, by construction our formulation yields output that is supported on a structured grid. We establish recovery error bounds for our methodology and offer matrix sensing and matrix completion numerical experiments including applications to seismic trace interpolation to demonstrate the potential of the approach.


(IEEE Journal of Selected Topics in Signal Processing)


Citation Keylopez2015IEEEogl