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Space-Time Regularization for Video Decompression

Schaeffer, Hayden and Yang, Yi and Osher, Stanley (2015) Space-Time Regularization for Video Decompression. SIAM Journal on Imaging Sciences, 8 (1). pp. 373-402. ISSN 1936-4954.

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We consider the problem of reconstructing frames from a video which has been compressed using the video compressive sensing (VCS) method. In VCS data, each frame comes from first subsampling the original video data in space and then averaging the subsampled sequence in time. This results in a large linear system of equations whose inversion is ill-posed. We introduce a convex regularizer to invert the system, where the spatial component is regularized by the total variation seminorm, and the temporal component is regularized by enforcing sparsity on the difference between the spatial gradients of each frame. Since the regularizers are $L^1$-like norms, the model can be written in the form of an easy-to-solve saddle point problem. The saddle point problem is solved by the primal-dual algorithm, whose implementation calls for nearly pointwise operations (i.e., no direct linear inversion) and has a simple parallel version. Results show that our model decompresses videos more accurately than other popular models, with PSNR gains of several dB.

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Additional Information:© 2015 SIAM. Received by the editors July 14, 2014; accepted for publication (in revised form) October 17, 2014; published electronically February 12, 2015. The research of this author was supported by NSF grant 1303892. The research of this author was supported by NSF DMS 0835863, NSF DMS 0914561, and ONR N00014-11-0749. The authors would like to thank Wotao Yin and Tom Goldstein for their useful discussions. The authors would also like to thank Lawrence Carin, Guillermo Sapiro, Giang Tran, Jianbo Yang, Xin Yuan, and the anonymous reviewers for their helpful discussions and comments.
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-11-0749
Subject Keywords:video decompression; compressive sensing; total variation; temporal regularization
Issue or Number:1
Classification Code:AMS subject classifications: 49M30, 49M29, 94A08, 90C46
Record Number:CaltechAUTHORS:20150501-102829348
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Official Citation:Space-Time Regularization for Video Decompression Hayden Schaeffer, Yi Yang, and Stanley Osher SIAM Journal on Imaging Sciences 2015 8:1, 373-402
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:57143
Deposited By: Tony Diaz
Deposited On:01 May 2015 17:36
Last Modified:03 Oct 2019 08:21

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